Difference between revisions of "4x4x4 parity algorithms"

From Speedsolving.com Wiki
m (→‎4x4x4 supercube safe algorithms: Simplified my alg (should have done that after manually expanding it for AnimCubeJS).)
 
(87 intermediate revisions by 4 users not shown)
Line 1: Line 1:
=Introduction=
+
<div class="noprint">
This page attempts to list move optimal [[algorithm]]s for every common form of <u>parity</u> encountered in popular [[4x4x4]] (Rubik's Revenge) solving methods.
+
* Click on the speedsolving.com cube logo [[Image:SS_Cube_Logo_HD_Tiny.png]] to the left the algorithms to see them executed with Lucas Garron's online cube simulator.
 +
* The <b>Printable version</b> of this page is now <i>actually printable</i> (and in color, if desired).</div>
 +
<div class="plainlinks" style="print-color-adjust:exact; background-color:rgb(28,28,28);color:rgb(255,0,0);">
 +
<ul style=" background-color:rgb(28,28,28);font-family:Verdana;font-size:100%;color:rgb(255,186,140);">
 +
=<span style="font-family:Georgia;color:rgb(0,200,0);">Quick Navigation</span>=
 +
For those who are just looking for lists of commonly used speedsolving (speedcubing) 4x4x4 parity algorithms and cannot find what they are looking for just based on looking at the Table of Contents, <u>this section is for you</u>!  However, it's important to read the {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Introduction|c=rgb(229,148,0)|t=Introduction}} to hopefully make clear the format of this page. (Note: Some of these algorithm lists are <i>LONG</i>.  If you don't find the type of algorithms that you are looking for, <u>keep scrolling down and chances are you will find them</u>!)
 +
{{br|b=1}}
  
 +
<span style="font-family:Georgia;font-size:120%;"><b>Last two {{LinkColorI|p=dedge|c=rgb(229,148,0)|t=dedge}} pairing algorithms</b></span>:
 +
{{br|b=-1}}
 +
* There are <i>none</i> on this page, as those are actually not parity cases!  See the explanation {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Other_parity_cases|c=rgb(229,148,0)|t=here}} in the {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Introduction|c=rgb(229,148,0)|t=Introduction}} and perhaps {{LinkColorE|u=http://bigcubes.com/|c=rgb(229,148,0)|t=BIGcubes.com}}.
 +
{{br|b=1}}
  
Solutions listed under a case image which are not move optimal (in the move [[metric]] in which algorithms are sorted by):
+
<span style="font-family:Georgia;font-size:120%;"><b>PLL Parity</b></span>:
*are faster to execute,
+
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Two_dedges_.28oriented.29|c=rgb(229,148,0)|t=For dedges}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Two_corner_swaps|c=rgb(229,148,0)|t=2 corner swaps}}
 +
{{br|b=1}}
  
*demonstrate a notable alternative way to solve the case (including, but not limited to using different types of moves),
+
<span style="font-family:Georgia;font-size:120%;"><b>OLL Parity (Speedcubing Form)</b></span>:
 +
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Single_parity|c=rgb(229,148,0)|t=(Single) OLL Parity}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Double_parity|c=rgb(229,148,0)|t=(Double) OLL Parity}}
 +
{{br|b=1}}
  
*have a different effect on the 4x4x4 [[supercube]], or
+
<span style="font-family:Georgia;font-size:120%;"><b>Single Parity ("Pure" Form)</b></span>:
 +
{{br|b=-1}}
 +
* (See {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Reduction_parity|c=rgb(229,148,0)|t=this section}} of the {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Introduction|c=rgb(229,148,0)|t=Introduction}} to see why "pure" is an <i>informal</i> way of describing these type of algorithms.)
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#One_dedge_flip|c=rgb(229,148,0)|t=Single Dedge Flip}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#2-Gen_and_.22Semi_2-gen.22_algorithms|c=rgb(229,148,0)|t=2-Gen}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#4x4x4_supercube_safe_algorithms|c=rgb(229,148,0)|t=Supercube safe}}
 +
{{br|b=1}}
  
*are shorter than "the move optimal algorithms" in other [https://www.speedsolving.com/forum/threads/move-count-metrics-for-big-cubes-standards-and-preferences.23546/ big cube move metrics].
+
<span style="font-family:Georgia;font-size:120%;"><b>Double Parity ("Pure" Form)</b></span>:
 +
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Opposite_double_parity|c=rgb(229,148,0)|t=Opposite}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Adjacent_double_parity|c=rgb(229,148,0)|t=Adjacent}}
 +
{{br|b=1}}
  
 +
<span style="font-family:Georgia;font-size:120%;"><b>Algorithms for <i>other</i> 3x3x3 methods besides the {{LinkColorI|p=CFOP method|c=rgb(229,148,0)|t=CFOP method}}</b> (or any 3x3x3 method which solves the cube layer-by-layer, in general)</span>:
 +
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#In_the_M_layer_2|c=rgb(229,148,0)|t=Roux}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Petrus|c=rgb(229,148,0)|t=Petrus}}
 +
{{br|b=1}}
  
==Reduction parity==
+
<span style="font-family:Georgia;font-size:120%;"><b>{{LinkColorI|p=K4 Method|c=rgb(229,148,0)|t=K4 Method}}</b></span>
The term "parity" can be used to describe a number of situations that occur during a 4x4x4 solve which cannot manifest during a [[3x3x3]] (standard size Rubik's cube) solve.  In fact, there has been debate about what situations are considered to be a <i>parity case</i>, but there is one situation of which any cuber who uses the term "parity" for the 4x4x4 identifies as parity: the single [[dedge]] flip.
+
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Non_Dedge-Preserving_Last_Layer_2-Cycle_Cases|c=rgb(229,148,0)|t=2-cycles}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Non_Dedge-Preserving_Last_Layer_4-Cycle_Cases_in_Two_Dedges|c=rgb(229,148,0)|t=4-cycles}}
 +
{{br|b=1}}
  
<center>[[Image:One_Dedge_Flip.png|80px|]]</center>
+
<span style="font-family:Georgia;font-size:120%;"><b>{{LinkColorI|p=Cage Method|c=rgb(229,148,0)|t=Cage Method}}</b></span>:
 +
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Algorithms_which_do_not_preserve_the_centers|c=rgb(229,148,0)|t=Algorithms which keep the <u>cage</u> intact}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#2-cycles|c=rgb(229,148,0)|t=Algorithms which DO NOT keep the cage intact}} &ndash; variants of the {{LinkColorI|p=Cage Method|c=rgb(229,148,0)|t=Cage Method}}.
 +
{{br|b=1}}
  
 +
<span style="font-family:Georgia;font-size:120%;"><b>{{LinkColorI|p=4x4x4 Blindfolded|c=rgb(229,148,0)|t=4x4x4 Blindfolded}}</b></span>:
 +
{{br|b=-1}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Two_corner_swaps_.28only_2_supercube_center_piece_exchange.29|c=rgb(229,148,0)|t=Switching two corners}} <i>and</i> two {{LinkColorI|p=Center_piece|c=rgb(229,148,0)|t=Center pieces}}
 +
* {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#4x4x4_supercube_safe_algorithms|c=rgb(229,148,0)|t=Switching two superube wing edge pieces}} - Also look for " //Safe" in the {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_parity_algorithms#Non_Dedge-Preserving_Last_Layer_2-Cycle_Cases|c=rgb(229,148,0)|t=K4 2-cycles}} section for EVERY case.
 +
{{br|b=1}}
  
The most popular <u>2-cycle</u> (a swap of two pieces) besides the single dedge flip case is the following.  This 2-cycle of wings is as common during a [[K4]] Method solve as the single dedge flip is, but it should never arise during a solve using the [[Reduction Method]] because two dedges are not paired up.  However, many who solve the [[5x5x5]] Rubik's cube using some variant of the Reduction Method will come across this case; and thus several (but not all) of the algorithms listed on this page which solve this case directly can be used for completing the tredge-tripling stage of a 5x5x5 Reduction solve.
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">Introduction</span>=
 +
This page attempts to list move optimal {{LinkColorI|p=algorithm|c=rgb(229,148,0)|t=algorithms}} for every common form of <u>parity</u> encountered in popular {{LinkColorI|p=4x4x4|c=rgb(229,148,0)|t=4x4x4}} (Rubik's Revenge) solving methods.
  
<center>[[Image:Adj2swap.png|80px|]]</center>
+
Solutions listed under a case image which are not move optimal (in the move {{LinkColorI|p=metric|c=rgb(229,148,0)|t=metric}} in which algorithms are sorted by):
 +
{{br|b=-1}}
 +
*are faster to execute,
 +
*demonstrate a notable alternative way to solve the case (including, but not limited to using different types of moves),
 +
*have a different effect on the 4x4x4 {{LinkColorI|p=supercube|c=rgb(229,148,0)|t=supercube}}, or
 +
*are shorter than "the move optimal algorithms" in other {{LinkColorE|u=https://www.speedsolving.com/forum/threads/move-count-metrics-for-big-cubes-standards-and-preferences.23546/|c=rgb(229,148,0)|t=big cube move metrics}}.
 +
{{br|b=1}}
  
 +
==<span style="font-family:Georgia;color:rgb(0,200,0);">Reduction parity</span>==
 +
The term "parity" can be used to describe a number of situations that occur during a 4x4x4 solve which cannot manifest during a {{LinkColorI|p=3x3x3|c=rgb(229,148,0)|t=3x3x3}} (standard size Rubik's cube) solve.  In fact, there has been debate about what situations are considered to be a <i>parity case</i>, but there is one situation of which any cuber who uses the term "parity" for the 4x4x4 identifies as parity: the single {{LinkColorI|p=dedge|c=rgb(229,148,0)|t=dedge}} flip.
 +
<center>[[Image:One_Dedge_Flip.png|80px|]]</center>
 +
{{br|b=1}}
  
An equally well-known form of <u>reduction parity</u> (this term will be defined formally soon) besides the single dedge flip is switching two opposite dedges in the same face.
+
The most popular <u>2-cycle</u> (a swap of two pieces) besides the single dedge flip case is the following.  This 2-cycle of wings is as common during a {{LinkColorI|p=K4|c=rgb(229,148,0)|t=K4 Method}} solve as the single dedge flip is, but it should never arise during a solve using the {{LinkColorI|p=Reduction Method|c=rgb(229,148,0)|t=Reduction Method}} because two dedges are not paired up.  However, many who solve the {{LinkColorI|p=5x5x5|c=rgb(229,148,0)|t=5x5x5}} Rubik's cube using some variant of the Reduction Method will come across this case, and thus several (but not all) of the algorithms listed on this page which solve this case directly can be used for completing the tredge-tripling stage of a 5x5x5 Reduction solve.
 +
{{br|b=-1}}
 +
<center>[[Image:Adj2swap.png|80px|]]</center>
  
 +
An equally well-known form of <u>reduction parity</u> (this term will be defined formally soon) besides the single dedge flip is switching two opposite dedges in the same face.
 +
{{br|b=-1}}
 
<center>[[Image:Opppllparity.png|80px|]]</center>
 
<center>[[Image:Opppllparity.png|80px|]]</center>
  
 
+
This parity situation can be transformed into 21 other last layer forms of what is commonly called <u>PLL parity</u> by performing a 3x3x3 {{LinkColorI|p=PLL|c=rgb(229,148,0)|t=PLL}} and adjusting the upper face ({{LinkColorI|p=AUF|c=rgb(229,148,0)|t=AUF}}) as needed.  That is, there is a total of 22 PLL parity cases.  (See the {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms#PLL_Parity|c=rgb(229,148,0)|t=PLL Parity}} section for details.)  The remaining PLL parity cases which involve the fewest number of pieces (besides the most popular case above) are the following.
This parity situation can be transformed into <b>21</b> other last layer forms of what is commonly called <u>PLL parity</u> by performing a 3x3x3 [[PLL]] and adjusting the upper face ([[AUF]]) as needed.  That is, there is a total of 22 PLL parity cases.  (See the [https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms#PLL_Parity PLL Parity] section for details.)  The remaining PLL parity cases which involve the fewest number of pieces (besides the most popular case above) are the following.
+
{{br|b=-1}}
 
<center>[[Image:Oadjpllparity.png|80px|]]  [[Image:Circ4cy.png|80px|]]  [[Image:Circ4cyccw.png|80px|]]  [[Image:Zigzag4cycdedges.png|80px|]]  [[Image:Adj2crnrsp.png|80px|]]  [[Image:Diag2cornerswap.png|80px|]]</center>
 
<center>[[Image:Oadjpllparity.png|80px|]]  [[Image:Circ4cy.png|80px|]]  [[Image:Circ4cyccw.png|80px|]]  [[Image:Zigzag4cycdedges.png|80px|]]  [[Image:Adj2crnrsp.png|80px|]]  [[Image:Diag2cornerswap.png|80px|]]</center>
  
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
| bgcolor="fbfb8b" |
+
Despite that one can technically solve all 22 PLL parity cases by executing an algorithm meant to solve any one of them (to any face) and then finish solving the 4x4x4 as if it was a 3x3x3, special algorithms have been developed for every case.  This allows one to use fewer moves to solve any given case and gives one more options.</ul>
Despite that one can technically solve all 22 PLL parity cases by executing an algorithm meant to solve any one of them (to any face) and then finish solving the 4x4x4 as if it was a 3x3x3, special algorithms have been developed for every case.  This allows one to use fewer moves to solve any given case and gives one more options.
+
{{br|b=1}}
|}
 
  
 +
Combining some form of PLL parity and a single dedge flip creates one of the many cases of what's commonly called <u>double parity</u>.  For example, performing a swap of dedges to a fully solved 4x4x4 and then flipping the front dedge resulting from that swap gives us the following.
 +
{{br|b=-1}}
 +
<center>[[Image:DblParity.png|80px|]]</center>
  
Combining some form of PLL parity and a single dedge flip creates one of the many cases of what's commonly called <b><u>double parity</u></b>.  For example, performing a swap of dedges to a fully solved 4x4x4 and then flipping the front dedge resulting from that swap gives us the following.
 
  
<center>[[Image:DblParity.png|80px|]]</center>
+
Since the <i>double parity</i> case above and the single dedge flip case both have a single dedge flipped, and since {{LinkColorI|p=OLL|c=rgb(229,148,0)|t=OLL}} algorithms do not necessarily aim to {{LinkColorI|p=permute|c=rgb(229,148,0)|t=permute}} (move) the pieces that they correctly {{LinkColorI|p=orient|c=rgb(229,148,0)|t=orient}} in any particular fashion, any 4x4x4 algorithm which solves:
 +
{{br|b=-1}}
 +
*A case containing an odd number of flipped dedges (which will be called "<u>single parity</u>" on this page)
 +
<center>OR</center>
 +
*A case which additionally has an odd permutation of dedges and an even permutation of corners (or vice versa) (which will be called "<u>double parity</u>" on this page)
  
 +
is called an <u>OLL parity algorithm</u>.
  
Since the <b>double parity</b> case above and the single dedge flip case both have a single dedge flipped, and since [[OLL]] algorithms do not necessarily aim to [[permute]] (move) the pieces that they correctly [[orient]] in any particular fashion, any 4x4x4 algorithm which solves:
 
  
*a case containing an odd number of flipped dedges (which will be called "<u>single parity</u>" on this page)
+
It is common convention among the speedcubing community to use algorithms which contain <u>wide</u> (double layer) turns to solve OLL parity instead of single inner layer slices.  The notation used in {{LinkColorE|u=http://www.speedcubing.com/chris/4-solution.html|c=rgb(229,148,0)|t=Chris Hardwick's Rubik's Revenge Solution}} signifies a wide right turn as (Rr), for example.  In old WCA notation (the notation used on this page), (Rr) is expressed as Rw.  (The "w" is short for "wide".)  In fact, the most popular speedcubing <i>single parity</i> algorithms perform additional swaps besides flipping a single dedge due to the use of wide turns.
 +
{{br|b=-1}}
 +
<center>[[Image:Non-Pure_Single_Dedge_Flip.png|80px|]]</center>
  
or
 
  
*a case which additionally has an odd permutation of dedges and an even permutation of corners (or vice versa) (which will be called "<u>double parity</u>" on this page)
+
Such an algorithm is called a <u>non-pure</u> algorithm when compared to algorithms which just flip a single dedge, which are often called <u>pure flips</u>.  However, the term <i>pure</i> is more formally associated with an algorithm being <u>supercube safe</u> &ndash; algorithms which do not permute (move) any centers in the {{LinkColorI|p=supercube|c=rgb(229,148,0)|t=supercube}} version of a given {{LinkColorI|p=order|c=rgb(229,148,0)|t=order}}.
 +
{{br|b=-1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Most of the algorithms on this page affect some centers of the 4x4x4 supercube: not all algorithms affect the supercube centers in the same manner.  Algorithms followed by a " //Safe" are supercube safe.</ul>
 +
{{br|b=1}}
  
 +
There are many types of parity cases which can occur during a 4x4x4 solve (when considering the parity cases which can arise in <i>every</i> 4x4x4 method), but the most widely known cases are the cases which can manifest after reducing a fully scrambled 4x4x4 into a <u>pseudo 3x3x3</u> &ndash; an <i>n</i>x<i>n</i>x<i>n</i> cube in which all of its composite edges are complete and all of its centers are complete and are in the correct locations with respect to each other with regards to the cube's {{LinkColorI|p=Color Scheme|c=rgb(229,148,0)|t=Color Scheme}} &ndash; are called <u>reduction parity cases</u>.  (Because this is the objective of the {{LinkColorI|p=Reduction Method|c=rgb(229,148,0)|t=Reduction Method}} and its variants.)
  
is called an <b><u>OLL parity algorithm</u></b>.
+
In May 2013, {{LinkColorI|p=Michael Gottlieb|c=rgb(229,148,0)|t=Michael Gottlieb}} defined reduction parity in detail.
 +
{{br|b=-1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,235);background-color:rgb(80,80,140);">
 +
<ul>"Reduction parity occurs when you try to reduce the puzzle so it can be solved by a constrained set of moves, putting it into some subset of the positions. However, you can often reach a position which seems like it is in your subset, but which is actually not, and to solve the puzzle you have to briefly go outside your constrained set of moves to bring the puzzle back into the subset you want. Typically the number of positions you can encounter is some small multiple of the number of positions you expect. The obvious example is PLL parity in 4x4x4: all the centers and edges are properly paired, so you expect to be able to finish the puzzle with only outer layer turns, but this isn't quite possible. OLL parity falls under this definition too (so the reduced 4x4x4 has four times as many positions as you would expect)."{{LinkColorE|u=http://www.speedsolving.com/forum/threads/parity-errors.41972/#post-852756|c=rgb(229,148,0)|t=(Post)}}</ul></ul>
 +
{{br|b=1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
There is a 50/50 chance that PLL parity will be present (assuming that one is doing a solve using reduction).  Independently, there is a 50/50 chance to get a single dedge flip.  Therefore there is a (1/2)&times;(1/2) = (chance of <i>PLL parity</i>)&times;(chance of <i>single parity</i>) = a 1/4 chance of getting all possibilities, separately.
  
 +
That is, for the reduction method (and its variants),
  
It is common convention among the speedcubing community to use algorithms which contain <u>wide</u> (double layer) turns to solve OLL parity instead of single inner layer slices.  The notation used in [http://www.speedcubing.com/chris/4-solution.html Chris Hardwick's Rubik's Revenge Solution] signifies a wide right turn as (Rr), for example.  In old WCA notation (the notation used on this page), (Rr) is expressed as Rw.  (The "w" is short for "wide".)  In fact, the most popular speedcubing <b><i>single parity</i></b> algorithms perform additional swaps besides flipping a single dedge due to the use of wide turns.
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(255,255,0);background-color:rgb(90,90,180);">
 +
*PLL parity occurs by itself 25% of the time,
 +
*Single parity occurs 25% of the time,
 +
*Double parity occurs 25% of the time, and
 +
*No reduction parity 25% of the time.</ul></ul>
 +
{{br|b=1}}
  
<center>[[Image:Non-Pure_Single_Dedge_Flip.png|80px|]]</center>
+
This page will keep strong focus on reduction parity (OLL parity and PLL parity) cases, but it will also include a limited number of other parity situations which are also common in other solving methods, as well as cases which share some characteristics with reduction parity algorithms.
 +
{{br|b=2}}
 +
The key characteristics of 4x4x4 reduction parity algorithms are:
 +
{{br|b=-1}}
 +
*They preserve the colors of the centers.  (Note that most reduction parity algorithms do not technically preserve the centers themselves, because if they are applied to a fully solved 4x4x4 supercube, one can see that same color centers are swapped with each other.)
 +
*They do not break up (and therefore do not pair up) any dedges.  (They <u>preserve</u> the coupling of the dedges, but they may move entire dedges.)
 +
{{br|b=2}}
 +
Additionally (with no exceptions),
 +
{{br|b=-1}}
 +
*All OLL parity algorithms contain an <b><span style="color:red;">odd</span></b> number of inner slice quarter turns.  (They are called <u><b><span style="color:red;">odd</span></b> parity algorithms</u>.)
  
 +
*All PLL parity algorithms contain an <b><span style="color:rgb(0,128,128);">even</span></b> number of inner slice quarter turns.  (They are called <u><b><span style="color:rgb(0,128,128);">even</span></b> parity algorithms</u>.)
 +
{{br|b=1}}
 +
==<span style="font-family:Georgia;color:rgb(0,200,0);">Other parity cases</span>==
 +
It turns out that we are not limited to using well-known dedge-pairing (even parity) algorithms to pair dedges.
 +
{{br|b=-1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Websites such as {{LinkColorE|u=http://bigcubes.com/|c=rgb(229,148,0)|t=BIGcubes.com}} present algorithms with an <b><span style="color:rgb(0,128,128);">even</span></b> number of inner slice quarter turns for the dedge-pairing stage of the {{LinkColorI|p=Reduction Method|c=rgb(229,148,0)|t=Reduction Method}}.</ul>
 +
{{br|b=1}}
  
Such an algorithm is called a <u>non-pure</u> algorithm when compared to algorithms which just flip a single dedge, which are often called <u>pure flips</u>.  However, the term <b><i>pure</i></b> is more formally associated with an algorithm being <u>supercube safe</u>--algorithms which do not permute (move) any centers in the [[supercube]] version of a given [[order]].
+
Algorithms which solve/generate any case in which dedges are broken up (including <b><span style="color:red;">odd parity algorithms</span></b>) can be usedFor example, algorithms for {{LinkColorE|u=https://www.speedsolving.com/wiki/images/thumb/9/96/Adj2swap.png/80px-Adj2swap.png|c=rgb(229,148,0)|t=this parity case}} (mentioned previously) can be used.  This page contains quite a few algorithms which solve that case and other 2-cycle cases like
 +
{{br|b=-1}}
 +
<center>[[Image:Diag.opp.png|80px|]] [[Image:Adj.case1.png|80px|]]</center>
 +
{{br|b=2}}
 +
as well as <u>4-cycle</u> cases <i>which are contained within two dedges</i> (which also can be used to pair the last two dedges).
 +
{{br|b=-1}}
 +
<center>[[Image:Chkbrd.png|80px|]] [[Image:Adjchkbd.png|80px|]]</center>
 +
{{br|b=2}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
There is actually a total of {{LinkColorE|u=https://archive.garron.us/img/2010/K4LL_4cycles.png|c=rgb(229,148,0)|t=110}} last layer 4-cycles, but since 4-cycles in two dedges are the only ones encountered using the most popular 4x4x4 solving methods, they are the only ones shown on this page.  However, {{LinkColorE|u=https://goo.gl/dtLuYp|c=rgb(229,148,0)|t=this PDF}} includes all 110 cases and relatively short algorithms to solve each one directly.
  
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
(All of these cases often occur in the {{LinkColorE|u=http://snk.digibase.ca/k4/7.htm|c=rgb(229,148,0)|t=ELL}} stage of the {{LinkColorI|p=K4|c=rgb(229,148,0)|t=K4 Method}}.  Algorithms for the {{LinkColorI|p=Cage Method|c=rgb(229,148,0)|t=Cage Method}}, as well as algorithms for theoretical purposes and general 4x4x4 exploration are present as well.)</ul>
| bgcolor="fbfb8b" |
+
{{br|b=1}}
Most of the algorithms on this page affect some centers of the 4x4x4 supercube: not all algorithms affect the supercube centers in the same manner.
 
  
Algorithms followed by a "//Safe" are supercube safe.
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Some short/easy parity fixes</span>==
|}
+
Since all OLL parity algorithms contain an <b><span style="color:red;">odd</span></b> number of inner slice quarter turns, one can technically fix any 4x4x4 wing edge odd parity case by executing a single slice quarter turn and then resolve the cube using an <b><span style="color:rgb(0,128,128);">even</span></b> number of inner slice quarter turns.  {{LinkColorE|u=https://youtu.be/-6INPKC7sfo?t=133|c=rgb(229,148,0)|t=Here's one video tutorial}} that illustrates the typical process.
 +
{{br|b=-1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Similar to doing an inner slice quarter turn like r to technically fix the single dedge flip parity, an inner slice half turn such as r2 is technically all that is needed to fix PLL parity. In fact, only two inner slice quarter turns + 3x3x3 turns is all that is needed to create/solve PLL parity on the 4x4x4
  
 +
One can split up r2 as r r or as r' r' and insert 3x3x3 moves to obtain the pure form of PLL parity.
 +
<br><br>
 +
This is an example algorithm found by Christoper Mowla in {{LinkColorE|u=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-935545|c=rgb(229,148,0)|t=December of 2013}}.<br>
 +
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=(2R-_U-_D-_R2_U-_D-_s2_2R-)(F-_U-_D-_F2_R_F2_U2_R_e-_R_F2_L-_U2_R_D2_R_B2_R-_x2_y-)|c=rgb(229,148,0)|t=(r' U' D' R2 U' D' S2 r')(F' U' D' F2 R F2 U2 R E' R F2 L' U2 R D2 R B2 R' x2 y')}}
 +
{{br|b=1}}
 +
However, we can also just use the inner slice turns r and r' as well.
 +
{{br|b=-1}}
 +
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=(2R-_U_D_s2_U-_D-_s2_2R)(U2_B_D2_U2_F-_U2_F2_L-_R_D-_B2_L-_R_D2_F-)|c=rgb(229,148,0)|t=(r' U D S2 U' D' S2 r)(U2 B D2 U2 F' U2 F2 L' R D' B2 L' R D2 F')}}</ul>
  
There are many types of parity cases which can occur during a 4x4x4 solve, but the cases which result from attempting to reduce a fully scrambled 4x4x4 into a <u>pseudo 3x3x3</u> state (this means an even <i>n</i>x<i>n</i>x<i>n</i> cube in which all of its composite edges are complete and all of its centers are complete and are in the correct center orientation, in general).  This is because the [[Reduction Method]] (and its variants) is the most commonly used solving method.  Naturally, these type of parity cases are called <b>reduction parity</b>.
 
  
 +
Should one wish to <i>induce an <b><span style="color:red;">odd</span></b> permutation</i> in the wing edges of the 4x4x4 with a short algorithm without having to restore the cube as much as applying an inner slice quarter turn requires, below are fairly short (and simple) algorithms one can use.
 +
{{br|b=-1}}
 +
* The shortest <i>half turn</i> 4x4x4 cube odd parity fix which preserves the colors of the centers ({{LinkColorE|u=https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975763|c=rgb(229,148,0)|t=essentially}} found in 2014 by {{LinkColorE|u=https://www.speedsolving.com/forum/showthread.php?46925-Announcing-New-4x4x4-Brute-Force-Solver&p=975170&viewfull=1#post975170|c=rgb(229,148,0)|t=Tom Rokicki}} and {{LinkColorE|u=https://www.speedsolving.com/forum/showthread.php?46925-Announcing-New-4x4x4-Brute-Force-Solver&p=975561&viewfull=1#post975561|c=rgb(229,148,0)|t=Ed Trice}}) is {{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=2F2_2R_e2_2R_e2_2R_2F2|c=rgb(229,148,0)|t=f2 r E2 r E2 r f2 (11,7)}}.
 +
{{br|b=1}}
 +
* The shortest <i>quarter turn</i> 4x4x4 cube odd parity fix which preserves the colors of the centers was (found by {{LinkColorE|u=https://www.speedsolving.com/threads/a-collection-of-algorithms.708/page-124#post-1439284|c=rgb(229,148,0)|t=Tom Rokicki}} on April 27, 2021) is {{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=2U2_2R_2U_m_2U_m'_2U_2R'|c=rgb(229,148,0)|t=u2 r u M u M' u r' (9,8)}}.
 +
{{br|b=1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Although these algorithms are not listed under a case image on this page, they would appear in the following format (in an "algorithm bar") if they were.
  
In May 2013, [[Michael Gottlieb]] defined reduction parity in detail.
 
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="F8F8F8" |
 
<blockquote>
 
Reduction parity occurs when you try to reduce the puzzle so it can be solved by a constrained set of moves, putting it into some subset of the positions. However, you can often reach a position which seems like it is in your subset, but which is actually not, and to solve the puzzle you have to briefly go outside your constrained set of moves to bring the puzzle back into the subset you want. Typically the number of positions you can encounter is some small multiple of the number of positions you expect. The obvious example is PLL parity in 4x4x4: all the centers and edges are properly paired, so you expect to be able to finish the puzzle with only outer layer turns, but this isn't quite possible. OLL parity falls under this definition too (so the reduced 4x4x4 has four times as many positions as you would expect).[http://www.speedsolving.com/forum/threads/parity-errors.41972/#post-852756]
 
</blockquote>
 
|}
 
  
 +
{{Alg6|wca=f2 r E2 r E2 r f2
 +
|sign=2F2 2R e2 2R e2 2R 2F2
 +
|length=(11,7)|name=|wide=N|author=Tom Rokicki and Ed Trice
 +
|url=https://www.speedsolving.com/forum/showthread.php?46925-Announcing-New-4x4x4-Brute-Force-Solver&p=975170&viewfull=1#post975170
 +
}}
 +
{{Alg6|wca=u2 r u M u M' u r'
 +
|sign=2U2 2R 2U m 2U m' 2U 2R'
 +
|length=(9,8)|name=|wide=N|author=Tom Rokicki
 +
|url=https://www.speedsolving.com/threads/a-collection-of-algorithms.708/page-124#post-1439284
 +
}}
 +
{{br|b=-0.75}}
 +
There are links to either forum posts or video URLs in the right-most column of many "algorithm bars".  These links are intended to either show one of the (if not the) first place the algorithm (or a simple conjugation, transformation, and/or a directly related version of it) was first published, and/or show one of the (if not the) earliest date of publish.
  
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(255,255,0);background-color:rgb(90,90,180);">
| bgcolor="fbfb8b" |
+
{{br|b=-1}}
There is a 50/50 chance that PLL parity will be present (assuming that one is doing a solve using reduction).
+
Besides just showing parity cases and algorithms for those cases, this page attempts to attribute credit to the original founder of an algorithm as well.
 +
</ul>
 +
{{br|b=1}}
 +
(More will be explained about what other pieces of information in the algorithm bars above mean later in this introduction.)</ul>
 +
{{br|b=1}}
  
 +
Since the shortest 4x4x4 (half turn) odd parity fix contains <u><i>move repetition</i></u>, it can be written more compactly as f2 (r E2)2 r f2.  Clearly this algorithm does not preserve the pairing of dedges, but it does preserve the colors of the centers; <i>and</i> it contains 7 inner slice quarter turns, an <b><span style="color:red;">odd</span></b> number.
 +
{{br|b=-1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
We can break up this algorithm as (f f r E E r E E r f f) to count 4 f's and 3 r's.  At the same time, we can count a total of 11 <u>block quarter turn moves</u> (BQTM).  We can count that this algorithm has 7 <u>block half turn moves</u> (BHTM) without breaking it up.
  
Independently, there is a 50/50 chance to get a single dedge flip.  Therefore there is a 1/2&times;1/2 = (chance of PLL parity)&times;(chance of <b>single parity</b>) = a 1/4 chance of getting all possibilities, separately.
+
In addition to the fact that all parity cases on this page are each represented by a case image,
 +
*The number of moves an algorithm contains in these two big cube move {{LinkColorI|p=metric|c=rgb(229,148,0)|t=metrics}} is written next to them in the form of the ordered pair, (BQTM, BHTM). (We can clearly see this in the above algorithm bar.)
  
 +
*Algorithms with fewer BHTM are listed first in each category.
  
That is, for the reduction method (and its variants),
+
*Algorithms with fewer BQTM are listed before other algorithms which have the same number of BHTM as they.</ul>
*PLL parity occurs by itself 25% of the time,
+
{{br|b=1}}
  
*<b>single parity</b> occurs 25% of the time,  
+
The shortest (and well-known) <i>n</i>x<i>n</i>x<i>n</i> cube odd parity fix which preserves the colors of the centers is {{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=(2R_U2)4_2R|c=rgb(229,148,0)|t=(r U2)4 r (13,9)}}.
 +
{{br|b=-1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Although this algorithm affects the same number of pieces as the (11,7) move algorithm above on the 4x4x4, it also "works"/does the same for the <i>n</i>x<i>n</i>x<i>n</i> cube.  The (11,7) above discolors centers on, say, the 5x5x5 cube.
 +
*Many of the algorithms on this page need to be "adjusted" to work for the <i>n</i>x<i>n</i>x<i>n</i> Rubik's cube.
  
*<b>double parity</b> occurs 25% of the time, and
+
*Some algorithms may only be translatable to higher order even cubes (6x6x6, and larger).
 +
:All algorithms can be applied to the 6x6x6 if instead of turning the outer 2 layers, turn the outer 3 layers; instead of turning 1 inner layer slice, turn 2 inner layer slices.</ul>
 +
{{br|b=1}}
  
*there is no reduction parity 25% of the time.
+
Finally, one of the simplest OLL parity (more specifically, a <i>double parity</i>) algorithms (found in {{LinkColorE|u=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/|c=rgb(229,148,0)|t=December of 2017}} by Christopher Mowla) to remember also consists of a short repeated sequence:<br>
|}
+
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=r-_(F2_U-_l-_U)5_r|c=rgb(229,148,0)|t=Rw' (F2 U' Lw' U)5 Rw (27,22)}}
 +
{{br|b=1}}
 +
This was deduced from the same idea that Floyd Newberry came up with for using a short repeated sequence to directly solve a 2-cycle.  Below are two single dedge flip (2-cycle) algorithms illustrating the idea.
  
 +
{{Alg6|wca=(Rw B' z')(r' F U2 F')4 r' (z B Rw')
 +
|sign=(Rw B' z') (2R' F U2 F')4 2R' (z B Rw')
 +
|length=(25,21)|name=|wide=N|author=Floyd Newberry
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 +
}}
 +
{{Alg6|wca=(Rw B' z')(r F U2 F')4 r (z B Rw')
 +
|sign=(Rw B' z') (2R F U2 F')4 2R (z B Rw')
 +
|length=(25,21)|name=|wide=N|author=Floyd Newberry
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 +
}}
 +
{{br|b=1}}
  
This page will keep strong focus on reduction parity (OLL parity and PLL parity) cases, but it will also include a limited number of other parity situations which are also common in other solving methods, as well as cases which share some characteristics with reduction parity algorithms.
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Additional notes about the algorithms</span>==
 +
Besides the notes mentioned already about what types of algorithms are contained within this page, including some of the specific common characteristics they share, this section touches on how they "look" and "feel" when they are displayed in notation and executed on a cube, respectively.
 +
{{br|b=1}}
 +
===<span style="font-family:Georgia;color:rgb(0,200,0);">Notation and animations</span>===
 +
*All algorithms on this page are written in old WCA notation, where lowercase letters represent inner slice turns, uppercase letters and xyz have the same meaning as {{LinkColorE|u=https://www.reddit.com/r/Cubers/comments/63ufuu/awesome_cube_notation_gif_found_on_ello/|c=rgb(229,148,0)|t=standard 3x3x3 notation}}, and a move like Rw, for example, means to turn both the face and inner slice parallel and adjacent to it simultaneously in the same direction.  (Using the same example, Rw = (Rr).)
  
 +
*Click the cube logo (the cube image to the far left of the algorithm bars), to see the algorithm animated in {{LinkColorE|u=https://www.youtube.com/watch?v=j-svGANFGXc|c=rgb(229,148,0)|t=SiGN notation}} at alpha.twizzle.net.
 +
{{br|b=1}}
  
The key characteristics of 4x4x4 reduction parity algorithms are:
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Move sets</span>===
 +
Two algorithms of similar <u>length</u> (the number of moves an algorithm contains) can look (and feel, when executing) very different.  This is especially common if two algorithms are in a different <u>move set</u> (consist only of certain types of turns).
  
*They preserve the colors of the centers.  (Note that most reduction parity algorithms do not technically preserve the centers themselves, because if they are applied to a fully solved 4x4x4 supercube, one can see that same color centers are swapped with each other.)
+
For example, one of the most common <i>single parity</i> algorithms used by the speedcubing community is "Lucas Parity"Notice that it only contains the (and inverses of the) moves Rw, U2, x and Lw.
 +
{{br|b=1}}
 +
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&type=alg&alg=r_U2_x_r_U2_r_U2_r-_U2_l_U2_r-_U2_r_U2_r-_U2_r-|c=rgb(229,148,0)|t=Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw' (25,17)}}
 +
{{br|b=1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
<b>Interesting Fact</b>:
 +
{{br|b=1}}
 +
On {{LinkColorE|u=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-12#post-311475|c=rgb(229,148,0)|t=January 24, 2010}}, speedsolving.com forum member reThinking the Cube showed that Lucas Garron's "Lucas Parity" (published in {{LinkColorE|u=https://www.speedsolving.com/forum/threads/4x4-oll-parity.4237/#post-52481|c=rgb(229,148,0)|t=mid 2008}}) is equivalent to Stefan Pochmann's "New Dedge Flip" from {{LinkColorE|u=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity|c=rgb(229,148,0)|t=his webpage}} (published in or before early 2007).</ul>
 +
{{br|b=1}}
  
*They do not break up (and therefore do not pair up) any dedges.  (They <u>preserve</u> the coupling of the dedges, but they may move entire dedges.)
+
One alternate algorithm of the same move length in BHTM (but contains 5 fewer BQTM) is the following.  (Clearly this algorithm has much more of a variety of moves than "Lucas Parity".  It is also clearly not a speedsolving algorithm as "Lucas Parity" is.)<br>
 +
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&type=alg&alg=l_e_r2_u_2R-_u-_r2_d_R2_u_2R-_u-_r_R_d-_e-_l-|c=rgb(229,148,0)|t=Lw E Rw2 Uw r' Uw' Rw2 Dw R2 Uw r' Uw' Rw R Dw' E' Lw' (20,17)}}
 +
{{br|b=1}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(90,90,180);">
 +
This page not only contains commonly practiced speedsolving algorithms: it also contains algorithms which illustrate the veracity of the 4x4x4 cube parity algorithm domain.</ul>
 +
{{br|b=1}}
 +
===<span style="font-family:Georgia;color:rgb(0,200,0);">Single slices vs. wide turns</span>===
  
 +
Two of the most popular 15 BHTM move algorithms which flip a single dedge on the 4x4x4 are the following.<br>
 +
<ul>{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=2R-_U2_2L_F2_2L-_F2_2R2_U2_2R_U2_2R-_U2_F2_2R2_F2|c=rgb(229,148,0)|t=r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 (25,15)}}
 +
{{br|b=1}}
 +
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=2R2_B2_U2_2L_U2_2R-_U2_2R_U2_F2_2R_F2_2L-_B2_2R2|c=rgb(229,148,0)|t=r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 (25,15)}}</ul>
 +
{{br|b=1}}
 +
Their inner slice turns may all be replaced with wide turns and still preserve the first three layers (F3L) of the 4x4x4 and flip one dedge.
  
Additionally (with no exceptions),
+
<ul>{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=Rw-_U2_Lw_F2_Lw-_F2_Rw2_U2_Rw_U2_Rw-_U2_F2_Rw2_F2|c=rgb(229,148,0)|t=Rw' U2 Lw F2 Lw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2 (25,15)}}
 +
{{br|b=1}}
 +
{{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=Rw2_B2_U2_Lw_U2_Rw-_U2_Rw_U2_F2_Rw_F2_Lw-_B2_Rw2|c=rgb(229,148,0)|t=Rw2 B2 U2 Lw U2 Rw' U2 Rw U2 F2 Rw F2 Lw' B2 Rw2 (25,15)}}</ul>
 +
{{br|b=1}}
  
*All OLL parity algorithms contain an <b><span style="color: red;">odd</span></b> number of inner slice quarter turns(They are called <u><b><span style="color: red;">odd</span></b> parity algorithms</u>.)
+
The fourth column of algorithm bars (as can be seen in the bar below) is either labelled:
 +
*<b>Y</b> (short for "Yes"), if all of an algorithm's inner slice turns can be substituted with their corresponding wide turns to still preserve F3L (<i>or if an algorithm does not contain any inner layer slices</i>)
 +
<center>OR</center>
  
*All PLL parity algorithms contain an <b><span style="color: blue;">even</span></b> number of inner slice quarter turns.  (They are called <u><b><span style="color: blue;">even</span></b> parity algorithms</u>.)
+
*<b>N</b> (short for "No"), if their inner slices cannot be substituted with wide turns and still preserve F3L.
  
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Note that with many algorithms, it's not "all or nothing".  A few of the slice turns can be wide to still just flip a single dedge, for example.
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(255,255,0);background-color:rgb(90,90,180);">For convenience, an algorithm is written with the maximum number of wide turns, should that version of it still preserve as much as the version of it without any wide turns.</ul></ul>
  
==Other parity cases==
 
Besides containing case images and algorithms for reduction parity cases, this page also contains <b><span style="color: red;">odd parity cases</span></b> which can technically be used to pair dedges, since they [[permute]] wing edges in a manner which separates wing edges in the same dedge from each other.  Algorithms for [https://www.speedsolving.com/wiki/images/thumb/9/96/Adj2swap.png/80px-Adj2swap.png one such parity case already mentioned] are included on this page.
 
  
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
The second 15 BHTM algorithm mentioned above could be expressed later on this page with the following algorithm bar, since all of its inner slice turns can be made wide (hence the "Y" instead of an "N") <i>and</i>  its first and last moves can be wide and still solve the pure dedge flip case (hence why the algorithm begins and ends with Rw2 instead of r2).
| bgcolor="fbfb8b" |
 
Websites such as [http://bigcubes.com/ bigcubes.com] present algorithms with an even number of inner slice quarter turns for the dedge-pairing stage of the [[Reduction Method]].
 
|}
 
  
 
+
As an example of how algorithm bars are going to be labelled, let us temporarily name it "Old Standard Alg" and called the author "anonymous".  (Algorithm names will be explained next.)
  
Also included on this page are other last layer 2-cycle cases:
+
{{Alg6|wca=Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2
 +
|sign=r2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 r2
 +
|length=(25,15)|name=Old Standard Alg
 +
|wide=Y|author=anonymous
 +
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
 +
}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
Despite that all (25,15) single dedge flip solutions which begin and end with an l2 or r2 move can instead be Lw2 and Rw2, respectively, all slices will be expressed as single slice (lowercase) turns for simplicity for all (25,15) solutions.</ul>
 +
{{br|b=1}}
 +
===<span style="font-family:Georgia;color:rgb(0,200,0);">Names/labels</span>===
  
[[Image:Diag.opp.png|80px|]] [[Image:Adj.case1.png|80px|]]
+
Although the third column in the majority of the algorithm bars on this page is blank, when it is not blank, it is either an algorithm name (given by the algorithm author) or an algorithm label (for organizational or classification purposes).
 +
*Some algorithms like "Lucas Parity" have been named.
  
 +
*Some algorithms are labelled (named) "Alg1(v1)", "v3", etc., (short for "algorithm 1, version 1" and "version 3", respectively) to:
 +
:*represent consecutive ordered version algorithms which are different versions (transformations) of each other
 +
{{br|b=0}}
 +
<center>OR</center>
  
and <u>4-cycle</u> cases <b><i>which are contained within two dedges </i></b>.
+
:*prove things like "there are actually fewer distinct paths than it appears for an algorithm in this move set and of this length" and also to show that "one algorithm is just another in disguise".
  
[[Image:Chkbrd.png|80px|]] [[Image:Adjchkbd.png|80px|]]
+
*Algorithms that have been named "5x5x5 Alg" are significantly longer algorithms than their related 4x4x4 algorithm counterparts, but they are algorithms which follow a lot of constraints and manage to work on the 4x4x4 and the 5x5x5.
 +
{{br|b=1}}
  
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">PLL Parity</span>=
| bgcolor="fbfb8b" |
 
There is actually a total of [https://archive.garron.us/img/2010/K4LL_4cycles.png 110] last layer 4-cycles, but since 4-cycles in two dedges are the only ones encountered using the most popular 4x4x4 solving methods, they are the only ones shown on this page.  However, [https://goo.gl/dtLuYp this PDF] includes all 110 cases and relatively short algorithms to solve each one directly.
 
|}
 
  
 
+
*This section shows all 22 possible PLL parity cases. In addition, algorithms for the two cases when two dedges are unoriented (and corners are solved) and the three cases when all four last layer dedges are unoriented (and the corners are solved) are also included.
(All of these cases often occur in the [http://snk.digibase.ca/k4/7.htm ELL] stage of the [[K4]] Method.)
+
**{{LinkColorE|u=https://web.archive.org/web/20090808131640/http://www.math.leidenuniv.nl/~mfung/speedcubing/algs/4x4x4/|c=rgb(229,148,0)|t=Michael Fung's old page}}.
 
+
**{{LinkColorE|u=http://frederickbadie.free.fr/444PLLparity.html|c=rgb(229,148,0)|t=Frédérick Badie's formula sheet}} for PLL parity cases
 
+
*Of course, all PLL parity cases can be handled by using the first case shown, commonly called "opposite parity" (OP).
Algorithms for the [[Cage Method]], as well as algorithms for theoretical purposes and general 4x4x4 exploration are present as well.
+
*{{LinkColorE|u=https://www.reddit.com/r/Cubers/comments/59cvc0/i_made_a_pdf_of_all_22_4x4_pllparity_cases/|c=rgb(229,148,0)|t=This PDF}} shows how to handle all 22 cases using a combination of OP and 3x3x3 {{LinkColorI|p=PLL|c=rgb(229,148,0)|t=PLL}} algorithms.
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Dedges</span>==
==Some short/easy parity fixes==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Two dedges (oriented)</span>===
Since all OLL parity algorithms contain an <b><span style="color: red;">odd</span></b> number of inner slice quarter turns, one can technically fix any 4x4x4 wing edge odd parity case by executing a single slice quarter turn and then resolve the cube using an <b><span style="color: blue;">even</span></b> number of inner slice quarter turns.  [https://www.youtube.com/watch?v=-6INPKC7sfo Here's one video tutorial] that illustrates the typical process.
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">I permutation</span>====
 
+
[[Image:Opppllparity.png|110px|]]
 
+
{{Alg6|wca=r2 U2 r2 Uw2 r2 u2
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
|sign=2R2 U2 2R2 u2 2R2 2U2
| bgcolor="fbfb8b" |
+
|length=(12,6)|name=|wide=N|author=Chris Hardwick
Similar to doing an inner slice quarter turn like r to technically fix the single dedge flip parity, an inner slice half turn such as r2 is technically all that is needed to fix PLL parity. In fact, only two inner slice quarter turns + 3x3x3 turns is all that is needed to create/solve PLL parity on the 4x4x4. One can split up r2 as r r or as r' r' and insert 3x3x3 moves to obtain the pure form of PLL parity. Below is an example algorithm found in [https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-935545 December of 2013].
+
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
+
}}
(r' U' D' R2 U' D' S2 r')(F' U' D' F2 R F2 U2 R E' R F2 L' U2 R D2 R B2 R' x2 y') [https://alg.cubing.net/?puzzle=4x4x4&alg=(2R-_U-_D-_R2_U-_D-_s2_2R-)(F-_U-_D-_F2_R_F2_U2_R_e-_R_F2_L-_U2_R_D2_R_B2_R-_x2_y-) Animation]
+
{{Alg6|wca=r2 U2 r2 U2 d2 r2 d2
 
+
|sign=2R2 U2 2R2 U2 2D2 2R2 2D2
 
+
|length=(14,7)|name=|wide=N|author=|url=
However, we can also just use the inner slice turns r and r' as well.
 
(r' U D S2 U' D' S2 r)(U2 B D2 U2 F' U2 F2 L' R D' B2 L' R D2 F') [https://alg.cubing.net/?puzzle=4x4x4&alg=(2R-_U_D_s2_U-_D-_s2_2R)(U2_B_D2_U2_F-_U2_F2_L-_R_D-_B2_L-_R_D2_F-)  Animation]
 
|}
 
 
 
 
 
Should one wish to <i>induce an odd permutation</i> in the wing edges of the 4x4x4 with a short algorithm without having to restore the cube as much as applying an inner slice quarter turn requires, below are fairly short (and simple) algorithms one can use.
 
 
 
 
 
The shortest 4x4x4 cube odd parity fix which preserves the colors of the centers ([https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975763 essentially] independently found in 2014 by [https://www.speedsolving.com/forum/showthread.php?46925-Announcing-New-4x4x4-Brute-Force-Solver&p=975170&viewfull=1#post975170 Tom Rokicki] and [https://www.speedsolving.com/forum/showthread.php?46925-Announcing-New-4x4x4-Brute-Force-Solver&p=975561&viewfull=1#post975561 Ed Trice]) is f2 r E2 r E2 r f2 [https://alg.cubing.net/?puzzle=4x4x4&alg=2F2_2R_e2_2R_e2_2R_2F2 (11,7)].
 
 
 
 
 
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="fbfb8b" |
 
Although this algorithm is not listed under a case image on this page, it would appear in the following format (in an <b>"algorithm bar"</b>) if it was.
 
 
 
{{Alg5|wca=f2 r E2 r E2 r f2
 
|sign=2F2 2R e2 2R e2 2R 2F2
 
|length=(11,7)|name=|wide=N|author=Tom Rokicki and Ed Trice
 
|url=https://www.speedsolving.com/forum/showthread.php?46925-Announcing-New-4x4x4-Brute-Force-Solver&p=975170&viewfull=1#post975170
 
 
}}
 
}}
 
+
{{Alg6|wca=U2 r2 U2 r2 Uw2 r2 Uw2
There are links to either forum posts or video URLs in the right-most column of many "algorithm bars".  These links are intended to either show one of the (if not the) first place the algorithm (or a simple conjugation, transformation, and/or a directly related version of it) was first published, and/or show one of the (if not the) earliest date of publish.  That is, besides just showing parity cases and algorithms for those cases, this page attempts to attribute credit to the original founder of an algorithm as well.
+
|sign=U2 2R2 U2 2R2 u2 2R2 u2
 
+
|length=(14,7)|name=|wide=N|author=Chris Hardwick
(More will be explained about what other pieces of information in the <b>algorithm bar</b> above mean later.)
+
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
|}
+
}}
 
+
{{Alg6|wca=(Uw2 Rw2 U2) r2 (U2 Rw2 Uw2)
 
+
|sign=(u2 r2 U2) 2R2 (U2 r2 u2)
Since this algorithm contains <u><i>move repetition</i></u>, it can be written more compactly as f2 (r E2)2 r f2.
+
|length=(14,7)|name=SP01
 
+
|wide=N|author=Stefan Pochmann
 
+
|url=http://frederickbadie.free.fr/444PLLparity.html
Clearly this algorithm does not preserve the pairing of dedges, but it does preserve the colors of the centers; <b>and</b> it contains 7 inner slice quarter turns, an odd number.
+
}}
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
{{Alg6|wca=(Dw2 Rw2 U2) r2 (U2 Rw2 Dw2)
| bgcolor="fbfb8b" |
+
|sign=(d2 r2 U2) 2R2 (U2 r2 d2)
We can break up this algorithm as (f f r E E r E E r f f) to count 4 f's and 3 r's. At the same time, we can count a total of <b>11</b> <b><u>block quarter turn moves</u></b> (BQTM).  We can count that this algorithm has <b>7 <u>block half turn moves</u></b> (BHTM) without breaking it up.
+
|length=(14,7)|name=|wide=N|author=|url=
 
+
}}
In addition to the fact that all parity cases on this page are each represented by a case image,
+
{{Alg6|wca=(Rw2 F2 U2) r2 (U2 F2 Rw2)
 
+
|sign=(r2 F2 U2) 2R2 (U2 F2 r2)
*The number of moves an algorithm contains in these two big cube move [[metric]]s is written next to them in the form of the ordered pair, (BQTM, BHTM)(We can clearly see this in the above <b>algorithm bar</b>.)
+
|length=(14,7)|name=|wide=N|author=Stefan Pochmann
 
+
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
*Algorithms with fewer BHTM are listed first in each category.
 
 
 
*Algorithms with fewer BQTM are listed before other algorithms which have the same number of BHTM as they.
 
|}
 
 
 
 
 
The shortest (and well-known) <i>n</i>x<i>n</i>x<i>n</i> cube odd parity fix which preserves the colors of the centers is (r U2)4 r [https://alg.cubing.net/?puzzle=4x4x4&alg=(2R_U2)4_2R (13,9)].
 
 
 
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="fbfb8b" |
 
Although this algorithm affects the same number of pieces as the (11,7) move algorithm above on the 4x4x4, it also "works"/does the same for the <i>n</i>x<i>n</i>x<i>n</i> cube. The (11,7) above discolors centers on, say, the 5x5x5 cube.
 
 
 
*Many of the algorithms on this page need to be "adjusted" to work for the <i>n</i>x<i>n</i>x<i>n</i> Rubik's cube.
 
 
 
*Some algorithms may only be translatable to higher order even cubes (6x6x6, and larger).
 
:All algorithms can be applied to the 6x6x6 if instead of turning the outer 2 layers, turn the outer 3 layers; instead of turning 1 inner layer slice, turn 2 inner layer slices.
 
|}
 
 
 
 
 
Finally, one of the simplest OLL parity (more specifically, a <b>double parity</b>) algorithms (found in [https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/ December of 2017]) to remember also consists of a short repeated sequence:
 
 
 
Rw' (F2 U' Lw' U)5 Rw [https://alg.cubing.net/?puzzle=4x4x4&alg=r-_(F2_U-_l-_U)5_r (27,22)].
 
 
 
 
 
This was deduced from the same idea that Floyd Newberry came up with for using a short repeated sequence to directly solve a 2-cycle.  Below are two single dedge flip (2-cycle) algorithms illustrating the idea.
 
{{Alg5|wca=(Rw B' z')(r' F U2 F')4 r' (z B Rw')
 
|sign=(Rw B' z')(2R' F U2 F')4 2R' (z B Rw')
 
|length=(25,21)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
 
}}
 
}}
{{Alg5|wca=(Rw B' z')(r F U2 F')4 r (z B Rw')
+
{{Alg6|wca=(Rw2 B2 U2) r2 (U2 B2 Rw2)
|sign=(Rw B' z')(2R F U2 F')4 2R (z B Rw')
+
|sign=(r2 B2 U2) 2R2 (U2 B2 r2)
|length=(25,21)|name=|wide=N|author=Floyd Newberry
+
|length=(14,7)|name=|wide=N|author=Stefan Pochmann
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
+
|url=
 
}}
 
}}
 
+
{{Alg6|wca=Rw2 (U2 r U2 S2)2 Rw2 //Safe
==Additional notes about the algorithms==
+
|sign=r2 (U2 2R U2 s2)2 r2 //Safe
Besides the notes mentioned already about what types of algorithms are contained within this page, including some of the specific common characteristics they share, this section touches on how they "look" and "feel" when they are displayed in notation and executed on a cube, respectively.
+
|length=(18,10)|name=|wide=Y|author=Walter Randelshofer
 
+
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350303#p350303
 
+
}}
===Notation and animations===
+
{{Alg6|wca=r2 U2 r E2 r2 E2 r' D2 l2 E2 y2 //Safe
*All algorithms on this page are written in old WCA notation, where lowercase letters represent inner slice turns, uppercase letters and xyz have the same meaning as [https://www.reddit.com/r/Cubers/comments/63ufuu/awesome_cube_notation_gif_found_on_ello/ standard 3x3x3 notation], <b>and</b> a move like Rw, for example, means to turn both the face and inner slice parallel and adjacent to it simultaneously in the same direction.  (Using the same example, Rw = (Rr).)
+
|sign=2R2 U2 2R e2 2R2 e2 2R' D2 2L2 e2 y2 //Safe
 
+
|length=(18,10)|name=|wide=Y|author=|url=
*Click the move length ordered pairs of the form, (number of block quarter turns, number of block half turns) (which are to the right of the algorithm in the <b>algorithm bar</b>), to see the algorithm animated in [https://www.youtube.com/watch?v=j-svGANFGXc SiGN notation] at alg.cubing.net.
+
}}
 
+
{{Alg6|wca=r2 D2 l E2 l2 E2 l' U2 l2 E2 y2 //Safe
 
+
|sign=2R2 D2 2L e2 2L2 e2 2L' U2 2L2 e2 y2 //Safe
===Move sets===
+
|length=(18,10)|name=|wide=Y|author=|url=
Two algorithms of similar <u>length</u> (the number of moves an algorithm contains) can look (and feel, when executing) very different.  This is especially common if two algorithms are in a different <u>move set</u> (consist only of certain types of turns).
+
}}
 
+
{{Alg6|wca=r2 U2 r' E2 r2 E2 r D2 l2 E2 y2 //Safe
 
+
|sign=2R2 U2 2R' e2 2R2 e2 2R D2 2L2 e2 y2 //Safe
For example, one of the most common <b>single parity</b> algorithms used by the speedcubing community is "Lucas Parity".
+
|length=(18,10)|name=|wide=Y|author=|url=
 
+
}}
Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw' [https://alg.cubing.net/?puzzle=4x4x4&type=alg&alg=r_U2_x_r_U2_r_U2_r-_U2_l_U2_r-_U2_r_U2_r-_U2_r- (25,17)]
+
{{Alg6|wca=r2 D2 l' E2 l2 E2 l U2 l2 E2 y2 //Safe
 
+
|sign=2R2 D2 2L' e2 2L2 e2 2L U2 2L2 e2 y2 //Safe
 
+
|length=(18,10)|name=|wide=Y|author=|url=
<i>Notice that it only contains the (and inverses of the) moves Rw, U2, x and Lw.</i>
+
}}
 
+
{{Alg6|wca=r2 U2 l S2 r2 S2 l' D2 l2 E2 y2 //Safe
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
|sign=2R2 U2 2L s2 2R2 s2 2L' D2 2L2 e2 y2 //Safe
| bgcolor="fbfb8b" |
+
|length=(18,10)|name=|wide=Y|author=|url=
<b>Interesting Note:</b>
+
}}
 
+
{{Alg6|wca=r2 D2 r S2 l2 S2 r' U2 l2 E2 y2 //Safe
[https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-12#post-311475 On January 24, 2010], speedsolving.com forum member reThinking the Cube showed that Lucas Garron's "Lucas Parity" (published in [https://www.speedsolving.com/forum/threads/4x4-oll-parity.4237/#post-52481 mid 2008]) is equivalent to Stefan Pochmann's "New Dedge Flip" from [http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity his webpage] (published in or before early 2007).
+
|sign=2R2 D2 2R s2 2L2 s2 2R' U2 2L2 e2 y2 //Safe
|}
+
|length=(18,10)|name=|wide=Y|author=|url=
 
+
}}
 
+
{{Alg6|wca=r2 U2 l' S2 r2 S2 l D2 l2 E2 y2 //Safe
An alternate algorithm of the same move length in BHTM (but contains 5 fewer BQTM) is the following.
+
|sign=2R2 U2 2L' s2 2R2 s2 2L D2 2L2 e2 y2 //Safe
 
+
|length=(18,10)|name=|wide=Y|author=|url=
Lw E Rw2 Uw r' Uw' Rw2 Dw R2 Uw r' Uw' Rw R Dw' E' Lw' [https://alg.cubing.net/?puzzle=4x4x4&type=alg&alg=l_e_r2_u_2R-_u-_r2_d_R2_u_2R-_u-_r_R_d-_e-_l- (20,17)]
+
}}
 
+
{{Alg6|wca=r2 D2 r' S2 l2 S2 r U2 l2 E2 y2 //Safe
 
+
|sign=2R2 D2 2R' s2 2L2 s2 2R U2 2L2 e2 y2 //Safe
<i>Clearly this algorithm has much more of a variety of moves than "Lucas Parity".  It is also clearly not a speedsolving algorithm as "Lucas Parity" is.</i>
+
|length=(18,10)|name=|wide=Y|author=|url=
 
+
}}
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
{{Alg6|wca=r2 U2 B2 l r U2 M' U2 r2 B2 U2 //Safe
| bgcolor="fbfb8b" |
+
|sign=2R2 U2 B2 2L 2R U2 m' U2 2R2 B2 U2 //Safe
This page not only contains commonly practiced speedsolving algorithms: it also contains algorithms which illustrate the veracity of the 4x4x4 cube parity algorithm domain.
+
|length=(19,11)|name=|wide=N|author=Stefan Pochmann|url=
|}
 
 
 
 
 
===Single slices vs. wide turns===
 
Two of the most popular 15 BHTM move algorithms which flip a single dedge on the 4x4x4 are the following.
 
 
 
r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 [https://alg.cubing.net/?puzzle=4x4x4&alg=2R-_U2_2L_F2_2L-_F2_2R2_U2_2R_U2_2R-_U2_F2_2R2_F2 (25,15)]
 
 
 
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 [https://alg.cubing.net/?puzzle=4x4x4&alg=2R2_B2_U2_2L_U2_2R-_U2_2R_U2_F2_2R_F2_2L-_B2_2R2 (25,15)]
 
 
 
 
 
Their inner slice turns may all be replaced with wide turns and still preserve the first three layers (F3L) of the 4x4x4 and flip one dedge.
 
 
 
Rw' U2 Lw F2 Lw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2 [https://alg.cubing.net/?puzzle=4x4x4&alg=Rw-_U2_Lw_F2_Lw-_F2_Rw2_U2_Rw_U2_Rw-_U2_F2_Rw2_F2 (25,15)]
 
 
 
Rw2 B2 U2 Lw U2 Rw' U2 Rw U2 F2 Rw F2 Lw' B2 Rw2 [https://alg.cubing.net/?puzzle=4x4x4&alg=Rw2_B2_U2_Lw_U2_Rw-_U2_Rw_U2_F2_Rw_F2_Lw-_B2_Rw2_ (25,15)]
 
 
 
 
 
The fourth column of <b>algorithm bars</b> is either labelled:
 
 
 
*<b>Y</b> (short for "Yes"), if all of an algorithm's inner slice turns can be substituted with their corresponding wide turns to still preserve F3L (<b>or if an algorithm does not contain any inner layer slices</b>)
 
 
 
or
 
 
 
*<b>N</b> (short for "No"), if their inner slices cannot be substituted with wide turns and still preserve F3L.
 
 
 
 
 
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="fbfb8b" |
 
Note that with many algorithms, it's not "all or nothing".  A few of the slice turns can be wide to still just flip a single dedge, for example.  <b>For convenience, an algorithm is written with the maximum number of wide turns, should that version of it still preserve as much as the version of it without any wide turns.</b>
 
|}
 
 
 
 
 
For example, the second 15 BHTM algorithm mentioned above could be expressed later on this page with the following algorithm bar, since all of its inner slice turns can be made wide (hence the "Y" instead of an "N") <b>and</b>  its first and last moves can be wide and still solve the pure dedge flip case (hence why the algorithm begins and ends with Rw2 instead of r2).
 
 
 
 
 
For illustration of how algorithm bars are going to be labelled, let us temporarily name it "Old Standard Alg" and called the author "anonymous".  (Algorithm names will be explained next.)
 
{{Alg5|wca=Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2
 
|sign=r2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 r2
 
|length=(25,15)|name=Old Standard Alg
 
|wide=Y|author=anonymous
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
 
 
}}
 
}}
 
+
{{Alg6|wca=M U2 l2 B2 D2 r2 D2 B2 r l U2 //Safe
 
+
|sign=m U2 2L2 B2 D2 2R2 D2 B2 2R 2L U2 //Safe
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
|length=(19,11)|name=|wide=Y|author=|url=
| bgcolor="fbfb8b" |
 
However, despite that all (25,15) single dedge flip solutions which begin and end with an l2 or r2 move can instead be Lw2 and Rw2, respectively, all slices will be expressed as single slice (lowercase) turns for simplicity for all (25,15) solutions.
 
|}
 
 
 
 
 
===Names/labels===
 
Although the third column in the majority of the <b>algorithm bars</b> on this page is blank, when it is not blank, it is either an algorithm name (given by the algorithm author) or an algorithm label (for organizational or classification purposes).
 
 
 
*Some algorithms like "Lucas Parity" have been named.
 
 
 
*Some algorithms are labelled (named) "Alg1(v1)", "v3", etc., (short for "algorithm 1, version 1" and "version 3", respectively) to: 
 
:*represent consecutive ordered version algorithms which are different versions (transformations) of each other
 
 
 
OR
 
 
 
:*prove things like "there are actually fewer distinct paths than it appears for an algorithm in this move set and of this length" and also to show that "one algorithm is just another in disguise".
 
 
 
*Algorithms that have been named "5x5x5 Alg" are significantly longer algorithms than their related 4x4x4 algorithm counterparts, but they are algorithms which follow a lot of constraints and manage to work on the 4x4x4 and the 5x5x5.
 
 
 
 
 
 
 
 
 
=PLL Parity=
 
 
 
*This section shows all <b>22</b> possible PLL parity cases.  In addition, algorithms for the two cases when two dedges are unoriented (and corners are solved) and the three cases when all four last layer dedges are unoriented (and the corners are solved) are also included.
 
**[https://web.archive.org/web/20090808131640/http://www.math.leidenuniv.nl/~mfung/speedcubing/algs/4x4x4/ Michael Fung's old page].
 
**[http://frederickbadie.free.fr/444PLLparity.html Frédérick Badie's formula sheet for PLL parity cases]
 
**[http://hem.bredband.net/_zlv_/rubiks/4x4/444pllpar.html Stefan Lidström's website]
 
 
 
*Of course, all PLL parity cases can be handled by using the first case shown, commonly called "opposite parity" (OP).
 
 
 
*[https://www.reddit.com/r/Cubers/comments/59cvc0/i_made_a_pdf_of_all_22_4x4_pllparity_cases/ Here's a link to a PDF resource] that shows how to handle all 22 cases using a combination of OP and 3x3x3 [[PLL]] algorithms.
 
 
 
 
 
==Dedges==
 
===Two dedges (oriented)===
 
====Opposite====
 
[[Image:Opppllparity.png|110px|]]
 
{{Alg5|wca=r2 U2 r2 Uw2 r2 u2
 
|sign=2R2 U2 2R2 u2 2R2 2U2
 
|length=(12,6)|name=|wide=N|author=Chris Hardwick
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
 
}}
 
}}
{{Alg5|wca=r2 U2 r2 U2 d2 r2 d2
+
{{Alg6|wca=M' U2 r2 B2 U2 r2 U2 B2 r l U2 //Safe
|sign=2R2 U2 2R2 U2 2D2 2R2 2D2
+
|sign=m' U2 2R2 B2 U2 2R2 U2 B2 2R 2L U2 //Safe
|length=(14,7)|name=|wide=N|author=|url=
+
|length=(19,11)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r2 U2 r2 Uw2 r2 Uw2
+
{{Alg6|wca=M' U2 l' r' D2 B2 r2 B2 D2 l2 U2 //Safe
|sign=U2 2R2 U2 2R2 u2 2R2 u2
+
|sign=m' U2 2L' 2R' D2 B2 2R2 B2 D2 2L2 U2 //Safe
|length=(14,7)|name=|wide=N|author=Chris Hardwick
+
|length=(19,11)|name=|wide=Y|author=|url=
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
 
}}
 
}}
{{Alg5|wca=(Uw2 Rw2 U2) r2 (U2 Rw2 Uw2)
+
{{Alg6|wca=M U2 l' r' U2 B2 r2 B2 U2 r2 U2 //Safe
|sign=(u2 r2 U2) 2R2 (U2 r2 u2)
+
|sign=m U2 2L 2R D2 F2 2R2 F2 D2 2L2 U2 //Safe
|length=(14,7)|name=SP01
+
|length=(19,11)|name=|wide=Y|author=|url=
|wide=N|author=Stefan Pochmann
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
}}
 
{{Alg5|wca=(Dw2 Rw2 U2) r2 (U2 Rw2 Dw2)
 
|sign=(d2 r2 U2) 2R2 (U2 r2 d2)
 
|length=(14,7)|name=|wide=N|author=|url=
 
}}
 
{{Alg5|wca=(Rw2 F2 U2) r2 (U2 F2 Rw2)
 
|sign=(r2 F2 U2) 2R2 (U2 F2 r2)
 
|length=(14,7)|name=|wide=N|author=Stefan Pochmann
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
{{Alg5|wca=(Rw2 B2 U2) r2 (U2 B2 Rw2)
 
|sign=(r2 B2 U2) 2R2 (U2 B2 r2)
 
|length=(14,7)|name=|wide=N|author=Stefan Pochmann
 
|url=
 
 
}}
 
}}
{{Alg5|wca=Rw2 (U2 r U2 S2)2 Rw2//Safe
+
{{Alg6|wca=M U2 l r D2 F2 r2 F2 D2 l2 U2 //Safe
|sign=r2 (U2 2R U2 s2)2 r2//Safe
+
|sign=m U2 2L' 2R' U2 B2 2R2 B2 U2 2R2 U2 //Safe
|length=(18,10)|name=|wide=Y|author=Walter Randelshofer
+
|length=(19,11)|name=|wide=Y|author=|url=
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350303#p350303
 
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 l r U2 M' U2 r2 B2 U2//Safe
+
{{Alg6|wca=M' U2 l r U2 F2 r2 F2 U2 r2 U2 //Safe
|sign=2R2 U2 B2 2L 2R U2 m' U2 2R2 B2 U2//Safe
+
|sign=m' U2 2L 2R U2 F2 2R2 F2 U2 2R2 U2 //Safe
|length=(19,11)|name=|wide=N|author=Stefan Pochmann|url=
+
|length=(19,11)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=(y Rw2 U2) Rw U2 (Rw2 U2)2 Rw (U2 Rw2 y')
+
{{Alg6|wca=(y Rw2 U2) Rw U2 (Rw2 U2)2 Rw (U2 Rw2 y')
 
|sign=(y r2 U2) r U2 (r2 U2)2 r (U2 r2 y')
 
|sign=(y r2 U2) r U2 (r2 U2)2 r (U2 r2 y')
 
|length=(20,11)|name=v1
 
|length=(20,11)|name=v1
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=(y Rw2 U2) Rw' U2 (Rw2 U2)2 Rw' (U2 Rw2 y')
+
{{Alg6|wca=(y Rw2 U2) Rw' U2 (Rw2 U2)2 Rw' (U2 Rw2 y')
 
|sign=(y r2 U2) r' U2 (r2 U2)2 r' (U2 r2 y')
 
|sign=(y r2 U2) r' U2 (r2 U2)2 r' (U2 r2 y')
 
|length=(20,11)|name=v2
 
|length=(20,11)|name=v2
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 U2)(E r2 E' r)2 (U2 Rw2)//Safe
+
{{Alg6|wca=(Rw2 U2) (E r2 E' r)2 (U2 Rw2) //Safe
|sign=(r2 U2)(e 2R2 e' 2R)2 (U2 r2)//Safe
+
|sign=(r2 U2) (e 2R2 e' 2R)2 (U2 r2) //Safe
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 U2)(E' r2 E r)2 (U2 Rw2)//Safe
+
{{Alg6|wca=(Rw2 U2)(E' r2 E r)2 (U2 Rw2) //Safe
|sign=(r2 U2)(e' 2R2 e 2R)2 (U2 r2)//Safe
+
|sign=(r2 U2) (e' 2R2 e 2R)2 (U2 r2) //Safe
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 U2)(E r2 E' r')2 (U2 Rw2)//Safe
+
{{Alg6|wca=(Rw2 U2)(E r2 E' r')2 (U2 Rw2) //Safe
|sign=(r2 U2)(e 2R2 e' 2R')2 (U2 r2)//Safe
+
|sign=(r2 U2) (e 2R2 e' 2R')2 (U2 r2) //Safe
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 U2)(E' r2 E r')2 (U2 Rw2)//Safe
+
{{Alg6|wca=(Rw2 U2)(E' r2 E r')2 (U2 Rw2) //Safe
|sign=(r2 U2)(e' 2R2 e 2R')2 (U2 r2)//Safe
+
|sign=(r2 U2) (e' 2R2 e 2R')2 (U2 r2) //Safe
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
|length=(15,12)|name=|wide=Y|author=Werner Randelshofer, Walter Randelshofer, and André Boulouard|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2//Safe
+
{{Alg6|wca=r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2 //Safe
|sign=2R2 U2 2R U2 2R2 U2 2R2 U2 2R U2 2R2 U2//Safe
+
|sign=2R2 U2 2R U2 2R2 U2 2R2 U2 2R U2 2R2 U2 //Safe
 
|length=(22,12)|name=|wide=Y|author=|url=
 
|length=(22,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F U' R F' U l r U' F R' U F' l'//Safe
+
{{Alg6|wca=r' F U' R F' U l r U' F R' U F' l' //Safe
|sign=2R' F U' R F' U 2L 2R U' F R' U F' 2L'//Safe
+
|sign=2R' F U' R F' U 2L 2R U' F R' U F' 2L' //Safe
 
|length=(14,14)|name=|wide=N|author=|url=
 
|length=(14,14)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 U2)(r E2)6 (U2 Rw2)//Safe
+
{{Alg6|wca=(Rw2 U2)(r E2)6 (U2 Rw2) //Safe
|sign=(r2 U2)(2R e2)6 (U2 r2)//Safe
+
|sign=(r2 U2) (2R e2)6 (U2 r2) //Safe
 
|length=(24,15)|name=|wide=N|author=Christopher Mowla|url=
 
|length=(24,15)|name=|wide=N|author=Christopher Mowla|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 U2)(r' E2)6 (U2 Rw2)//Safe
+
{{Alg6|wca=(Rw2 U2)(r' E2)6 (U2 Rw2) //Safe
|sign=(r2 U2)(2R' e2)6 (U2 r2)//Safe
+
|sign=(r2 U2) (2R' e2)6 (U2 r2) //Safe
 
|length=(24,15)|name=|wide=N|author=Christopher Mowla|url=
 
|length=(24,15)|name=|wide=N|author=Christopher Mowla|url=
 
}}
 
}}
{{Alg5|wca=y' Rw2 3Uw2 Rw 3Uw Rw2 3Uw2 Rw2 3Uw' Rw2 3Uw Rw2 3Uw' Rw2 3Uw' Rw2 3Uw Rw2 3Uw Rw2 3Uw' Rw 3Uw2 Rw2 y
+
{{Alg6|wca=y' Rw2 3Uw2 Rw 3Uw Rw2 3Uw2 Rw2 3Uw' Rw2 3Uw Rw2 3Uw' Rw2 3Uw' Rw2 3Uw Rw2 3Uw Rw2 3Uw' Rw 3Uw2 Rw2 y
 
|sign=y' r2 3u2 r 3u r2 3u2 r2 3u' r2 3u r2 3u' r2 3u' r2 3u r2 3u r2 3u' r 3u2 r2 y
 
|sign=y' r2 3u2 r 3u r2 3u2 r2 3u' r2 3u r2 3u' r2 3u' r2 3u r2 3u r2 3u' r 3u2 r2 y
 
|length=(36,23)|name=|wide=Y|author=Ben Whitmore
 
|length=(36,23)|name=|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_3u/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_3u/index.html
 
}}
 
}}
{{Alg5|wca=M2 Uw M Uw M' Uw' M' Uw M Uw M Uw2 M' Uw2 M' Uw' M' Uw M Uw2 M Uw' M' Uw2 M' Uw' M Uw' M' Uw' M Uw M2
+
{{Alg6|wca=M2 Uw M Uw M' Uw' M' Uw M Uw M Uw2 M' Uw2 M' Uw' M' Uw M Uw2 M Uw' M' Uw2 M' Uw' M Uw' M' Uw' M Uw M2
 
|sign=m2 u m u m' u' m' u m u m u2 m' u2 m' u' m' u m u2 m u' m' u2 m' u' m u' m' u' m u m2
 
|sign=m2 u m u m' u' m' u m u m u2 m' u2 m' u' m' u m u2 m u' m' u2 m' u' m u' m' u' m u m2
 
|length=(38,33)|name=|wide=N|author=Ben Whitmore
 
|length=(38,33)|name=|wide=N|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_m_u/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_m_u/index.html
 
}}
 
}}
 +
{{br|b=1}}
 +
====<span style="font-family:Georgia;color:rgb(0,200,0);">Double slash (//) permutation</span>====
 +
[[Image:Oadjpllparity.png|110px|]]
  
====Adjacent====
+
{{Alg6|wca=(R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2)
[[Image:Oadjpllparity.png|110px|]]
 
{{Alg5|wca=(R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2)
 
 
|sign=(R2 D' x) 2R2 U2 2R2 u2 2R2 2U2 (x' D R2)
 
|sign=(R2 D' x) 2R2 U2 2R2 u2 2R2 2U2 (x' D R2)
 
|length=(18,10)|name=|wide=N|author=Chris Hardwick
 
|length=(18,10)|name=|wide=N|author=Chris Hardwick
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=(R2 D' x Uw2 Rw2 U2) r2 (U2 Rw2 Uw2 x' D R2)
+
{{Alg6|wca=(R2 D' x Uw2 Rw2 U2) r2 (U2 Rw2 Uw2 x' D R2)
 
|sign=(R2 D' x u2 r2 U2) 2R2 (U2 r2 u2 x' D R2)
 
|sign=(R2 D' x u2 r2 U2) 2R2 (U2 r2 u2 x' D R2)
 
|length=(20,11)|name=SP02
 
|length=(20,11)|name=SP02
Line 467: Line 519:
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
}}
 
}}
{{Alg5|wca=(R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2)
+
{{Alg6|wca=(R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2)
 
|sign=(R2 D' r2 U2 F2) 2R2 (F2 U2 r2 D R2)
 
|sign=(R2 D' r2 U2 F2) 2R2 (F2 U2 r2 D R2)
 
|length=(20,11)|name=FB02
 
|length=(20,11)|name=FB02
Line 473: Line 525:
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
}}
 
}}
{{Alg5|wca=(F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2)
+
{{Alg6|wca=(F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2)
 
|sign=(F2 U r2 U2 F2) 2R2 (F2 U2 r2 U' F2)
 
|sign=(F2 U r2 U2 F2) 2R2 (F2 U2 r2 U' F2)
 
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
 
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R2 D' x Rw2 F2 U2) r2 (U2 F2 Rw2 x' D R2)
+
{{Alg6|wca=(R2 D' x Rw2 F2 U2) r2 (U2 F2 Rw2 x' D R2)
 
|sign=(R2 D' x r2 F2 U2) 2R2 (U2 F2 r2 x' D R2)
 
|sign=(R2 D' x r2 F2 U2) 2R2 (U2 F2 r2 x' D R2)
 
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
 
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R2 D' x Rw2 B2 U2) r2 (U2 B2 Rw2 x' D R2)
+
{{Alg6|wca=(R2 D' x Rw2 B2 U2) r2 (U2 B2 Rw2 x' D R2)
 
|sign=(R2 D' x r2 B2 U2) 2R2 (U2 B2 r2 x' D R2)
 
|sign=(R2 D' x r2 B2 U2) 2R2 (U2 B2 r2 x' D R2)
 
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
 
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(F U' F') r2 U2 r2 Uw2 r2 u2 (F U F')
+
{{Alg6|wca=(F U' F') r2 U2 r2 Uw2 r2 u2 (F U F')
 
|sign=(F U' F') 2R2 U2 2R2 u2 2R2 2U2 (F U F')
 
|sign=(F U' F') 2R2 U2 2R2 u2 2R2 2U2 (F U F')
 
|length=(18,12)|name=|wide=N|author=Chris Hardwick
 
|length=(18,12)|name=|wide=N|author=Chris Hardwick
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(F U' F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U F')
+
{{Alg6|wca=(F U' F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U F')
 
|sign=(F U' F' r2 F2 U2) 2R2 (U2 F2 r2 F U F')
 
|sign=(F U' F' r2 F2 U2) 2R2 (U2 F2 r2 F U F')
 
|length=(20,13)|name=|wide=N|author=Stefan Pochmann
 
|length=(20,13)|name=|wide=N|author=Stefan Pochmann
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' R' F) l E F2 E' l' r' E F2 E' r (F' R y)//Safe
+
{{Alg6|wca=(y' R' F) l E F2 E' l' r' E F2 E' r (F' R y) //Safe
|sign=(y' R' F) 2L e F2 e' 2L' 2R' e F2 e' 2R (F' R y)//Safe
+
|sign=(y' R' F) 2L e F2 e' 2L' 2R' e F2 e' 2R (F' R y) //Safe
 
|length=(16,14)|name=Alg.1|wide=N|author=Christopher Mowla
 
|length=(16,14)|name=Alg.1|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/contructing-algorithms-not-a-how-to-sorry.26477/page-2#post-591759
 
|url=https://www.speedsolving.com/forum/threads/contructing-algorithms-not-a-how-to-sorry.26477/page-2#post-591759
 
}}
 
}}
{{Alg5|wca=(y' R' F) r' E F2 E' l r E F2 E' l' (F' R y)//Safe
+
{{Alg6|wca=(y' R' F) r' E F2 E' l r E F2 E' l' (F' R y) //Safe
|sign=(y' R' F) 2R' e F2 e' 2L 2R e F2 e' 2L' (F' R y)//Safe
+
|sign=(y' R' F) 2R' e F2 e' 2L 2R e F2 e' 2L' (F' R y) //Safe
 
|length=(16,14)|name=Inverse[Alg.1]|wide=N|author=Christopher Mowla
 
|length=(16,14)|name=Inverse[Alg.1]|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' R' F) l E' F2 E l' r' E' F2 E r (F' R y)//Safe
+
{{Alg6|wca=(y' R' F) l E' F2 E l' r' E' F2 E r (F' R y) //Safe
|sign=(y' R' F) 2L e' F2 e 2L' 2R' e' F2 e 2R (F' R y)//Safe
+
|sign=(y' R' F) 2L e' F2 e 2L' 2R' e' F2 e 2R (F' R y) //Safe
 
|length=(16,14)|name=Alg.2|wide=N|author=Christopher Mowla
 
|length=(16,14)|name=Alg.2|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' R' F) r' E' F2 E l r E' F2 E l' (F' R y)//Safe
+
{{Alg6|wca=(y' R' F) r' E' F2 E l r E' F2 E l' (F' R y) //Safe
|sign=(y' R' F) 2R' e' F2 e 2L 2R e' F2 e 2L' (F' R y)//Safe
+
|sign=(y' R' F) 2R' e' F2 e 2L 2R e' F2 e 2L' (F' R y) //Safe
 
|length=(16,14)|name=Inverse[Alg.2]|wide=N|author=Christopher Mowla
 
|length=(16,14)|name=Inverse[Alg.2]|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R B') l S U2 S' l' r' S U2 S' r (B R')//Safe
+
{{Alg6|wca=(R B') l S U2 S' l' r' S U2 S' r (B R') //Safe
 
|sign=(R B') 2L s U2 s' 2L' 2R' s U2 s' 2R (B R')
 
|sign=(R B') 2L s U2 s' 2L' 2R' s U2 s' 2R (B R')
 
|length=(16,14)|name=Alg.3|wide=N|author=Walter Randelshofer
 
|length=(16,14)|name=Alg.3|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R B') r' S U2 S' l r S U2 S' l' (B R')//Safe
+
{{Alg6|wca=(R B') r' S U2 S' l r S U2 S' l' (B R') //Safe
 
|sign=(R B') 2R' s U2 s' 2L 2R s U2 s' 2L' (B R')
 
|sign=(R B') 2R' s U2 s' 2L 2R s U2 s' 2L' (B R')
 
|length=(16,14)|name=Inverse[Alg.3]|wide=N|author=Walter Randelshofer
 
|length=(16,14)|name=Inverse[Alg.3]|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R B') l S' U2 S l' r' S' U2 S r (B R')//Safe
+
{{Alg6|wca=(R B') l S' U2 S l' r' S' U2 S r (B R') //Safe
 
|sign=(R B') 2L s' U2 s 2L' 2R' s' U2 s 2R (B R')
 
|sign=(R B') 2L s' U2 s 2L' 2R' s' U2 s 2R (B R')
 
|length=(16,14)|name=Alg.4|wide=N|author=Walter Randelshofer
 
|length=(16,14)|name=Alg.4|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R B') r' S' U2 S l r S' U2 S l' (B R')//Safe
+
{{Alg6|wca=(R B') r' S' U2 S l r S' U2 S l' (B R') //Safe
 
|sign=(R B') 2R' s' U2 s 2L 2R s' U2 s 2L' (B R')
 
|sign=(R B') 2R' s' U2 s 2L 2R s' U2 s 2L' (B R')
 
|length=(16,14)|name=Inverse[Alg.4]|wide=N|author=Walter Randelshofer
 
|length=(16,14)|name=Inverse[Alg.4]|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R')
+
{{Alg6|wca=(R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R')
 
|sign=(R U R' U') 2R2 U2 2R2 u2 2R2 u2 (U' R U' R')
 
|sign=(R U R' U') 2R2 U2 2R2 u2 2R2 u2 (U' R U' R')
 
|length=(19,14)|name=|wide=N|author=Chris Hardwick
 
|length=(19,14)|name=|wide=N|author=Chris Hardwick
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=(R U R') U r2 U2 r2 Uw2 r2 Uw2 U (R U' R')
+
{{Alg6|wca=(R U R') U r2 U2 r2 Uw2 r2 Uw2 U (R U' R')
 
|sign=(R U R') U 2R2 U2 2R2 u2 2R2 u2 U (R U' R')
 
|sign=(R U R') U 2R2 U2 2R2 u2 2R2 u2 U (R U' R')
 
|length=(19,14)|name=|wide=N|author=Chris Hardwick
 
|length=(19,14)|name=|wide=N|author=Chris Hardwick
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Uw' R U' R' Uw' Rw2 U2) r2 (U2 Rw2 Uw R U R' Uw)
+
{{Alg6|wca=(Uw' R U' R' Uw' Rw2 U2) r2 (U2 Rw2 Uw R U R' Uw)
 
|sign=(u' R U' R' u' r2 U2) 2R2 (U2 r2 u R U R' u)
 
|sign=(u' R U' R' u' r2 U2) 2R2 (U2 r2 u R U R' u)
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
}}
 
}}
{{Alg5|wca=(y Uw' R U R' Uw' Rw2 U2) r2 (U2 Rw2 Uw R U' R' Uw y')
+
{{Alg6|wca=(y Uw' R U R' Uw' Rw2 U2) r2 (U2 Rw2 Uw R U' R' Uw y')
 
|sign=(y u' R U R' u' r2 U2) 2R2 (U2 r2 u R U' R' u y')
 
|sign=(y u' R U R' u' r2 U2) 2R2 (U2 r2 u R U' R' u y')
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
}}
 
}}
{{Alg5|wca=(y2 Uw R U' R' Uw Rw2 U2) r2 (U2 Rw2 Uw' R U R' Uw' y2)
+
{{Alg6|wca=(y2 Uw R U' R' Uw Rw2 U2) r2 (U2 Rw2 Uw' R U R' Uw' y2)
 
|sign=(y2 u R U' R' u r2 U2) 2R2 (U2 r2 u' R U R' u' y2)
 
|sign=(y2 u R U' R' u r2 U2) 2R2 (U2 r2 u' R U R' u' y2)
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
}}
 
}}
{{Alg5|wca=(y' Uw R U R' Uw Rw2 U2) r2 (U2 Rw2 Uw' R U' R' Uw' y)
+
{{Alg6|wca=(y' Uw R U R' Uw Rw2 U2) r2 (U2 Rw2 Uw' R U' R' Uw' y)
 
|sign=(y' u R U R' u r2 U2) 2R2 (U2 r2 u' R U' R' u' y)
 
|sign=(y' u R U R' u r2 U2) 2R2 (U2 r2 u' R U' R' u' y)
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|length=(20,15)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1291072
 
}}
 
}}
{{Alg5|wca=(y2 Uw2 R U R' U' Rw2 U2) r2 (U2 Rw2 U R U' R' Uw2 y2)
+
{{Alg6|wca=(y2 Uw2 R U R' U' Rw2 U2) r2 (U2 Rw2 U R U' R' Uw2 y2)
 
|sign=(y2 u2 R U R' U' r2 U2) 2R2 (U2 r U R U' R' u2 y2)
 
|sign=(y2 u2 R U R' U' r2 U2) 2R2 (U2 r U R U' R' u2 y2)
 
|length=(22,15)|name=|wide=N|author=xyzzy
 
|length=(22,15)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-99#post-1249927
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-99#post-1249927
 
}}
 
}}
{{Alg5|wca=(R2 D' x) r2 U2 B2 l r U2 M' U2 r2 B2 U2 (x' D R2)//Safe
+
{{Alg6|wca=(R2 D' x) r2 U2 B2 l r U2 M' U2 r2 B2 U2 (x' D R2) //Safe
|sign=(R2 D' x) 2R2 U2 B2 2L 2R U2 m' U2 2R2 B2 U2 (x' D R2)//Safe
+
|sign=(R2 D' x) 2R2 U2 B2 2L 2R U2 m' U2 2R2 B2 U2 (x' D R2) //Safe
 
|length=(24,15)|name=|wide=N|author=|url=
 
|length=(24,15)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw)
+
{{Alg6|wca=(Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw)
 
|sign=(r' U R U l' U2 r' U2) 2R2 (U2 r U2 l U' R' U' r)
 
|sign=(r' U R U l' U2 r' U2) 2R2 (U2 r U2 l U' R' U' r)
 
|length=(22,17)|name=v1
 
|length=(22,17)|name=v1
Line 583: Line 635:
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-37#post-585105
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-37#post-585105
 
}}
 
}}
{{Alg5|wca=y' (Rw U' R' U' Rw B2) (Rw B2 r2 B2 Rw') (B2 Rw' U R U Rw') y
+
{{Alg6|wca=y' (Rw U' R' U' Rw B2) (Rw B2 r2 B2 Rw') (B2 Rw' U R U Rw') y
 
|sign=y' (r U' R' U' r B2) (r B2 2R2 B2 r') (B2 r' U R U r') y
 
|sign=y' (r U' R' U' r B2) (r B2 2R2 B2 r') (B2 r' U R U r') y
 
|length=(22,17)|name=v2
 
|length=(22,17)|name=v2
Line 589: Line 641:
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935303
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935303
 
}}
 
}}
{{Alg5|wca=y2 Rw U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U R' U' R' U y2
+
{{Alg6|wca=y2 Rw U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U R' U' R' U y2
 
|sign=y2 r U r' R U' r' U' r U r U' r' U' r' R U r U R' U' R' U y2
 
|sign=y2 r U r' R U' r' U' r U r U' r' U' r' R U r U R' U' R' U y2
 
|length=(20,20)|name=|wide=Y|author=António Gomes
 
|length=(20,20)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935268
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935268
 
}}
 
}}
{{Alg5|wca=y2 R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U y2
+
{{Alg6|wca=y2 R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U y2
 
|sign=y2 R' U' R' U r U R r' U' r' U' r U r U' r' U' R r' U r U y2
 
|sign=y2 R' U' R' U r U R r' U' r' U' r U r U' r' U' R r' U r U y2
 
|length=(20,20)|name=|wide=Y|author=António Gomes
 
|length=(20,20)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' y'
+
{{Alg6|wca=y R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' y'
 
|sign=y R' U r U R r' U' r' U' r U r U' r' U' R r' U r U R' U' y'
 
|sign=y R' U r U R r' U' r' U' r U r U' r' U' R r' U r U R' U' y'
 
|length=(20,20)|name=|wide=Y|author=António Gomes
 
|length=(20,20)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y2 Bw2 R2 Bw2) Rw U Rw' U' Lw' U' Lw U2 Rw U' Rw' U' Lw' U Lw (Bw2 R2 Bw2 y2)
+
{{Alg6|wca=(y2 Bw2 R2 Bw2) Rw U Rw' U' Lw' U' Lw U2 Rw U' Rw' U' Lw' U Lw (Bw2 R2 Bw2 y2)
 
|sign=(y2 b2 R2 b2) r U r' U' l' U' l U2 r U' r' U' l' U l (b2 R2 b2 y2)
 
|sign=(y2 b2 R2 b2) r U r' U' l' U' l U2 r U' r' U' l' U l (b2 R2 b2 y2)
 
|length=(28,21)|name=|wide=Y|author=Moritz Karl
 
|length=(28,21)|name=|wide=Y|author=Moritz Karl
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-62#post-899611
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-62#post-899611
 
}}
 
}}
{{Alg5|wca=y Rw' U2 Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw' U' Rw U Rw2 U Rw U' Rw U Rw' U Rw U y'
+
{{Alg6|wca=y Rw' U2 Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw' U' Rw U Rw2 U Rw U' Rw U Rw' U Rw U y'
 
|sign=y r' U2 r U2 r' U2 r' U' r U' r U r' U' r U r2 U r U' r U r' U r U y'
 
|sign=y r' U2 r U2 r' U2 r' U' r U' r U r' U' r U r2 U r U' r U r' U r U y'
 
|length=(30,26)|name=|wide=Y|author=Ben Whitmore
 
|length=(30,26)|name=|wide=Y|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Two dedges (unoriented)===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Two dedges (unoriented)</span>===
====Opposite====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">I permutation</span>====
 
[[Image:Uopppllparity.png|110px|]]
 
[[Image:Uopppllparity.png|110px|]]
{{Alg5|wca=F2 l E F2 E' l' r' E F2 E' r F2//Safe
+
{{Alg6|wca=F2 l E F2 E' l' r' E F2 E' r F2 //Safe
|sign=F2 2L e F2 e' 2L' 2R' e F2 e' 2R F2//Safe
+
|sign=F2 2L e F2 e' 2L' 2R' e F2 e' 2R F2 //Safe
 
|length=(16,12)|name=Alg.1|wide=N|author=Christopher Mowla
 
|length=(16,12)|name=Alg.1|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/contructing-algorithms-not-a-how-to-sorry.26477/page-2#post-591759
 
|url=https://www.speedsolving.com/forum/threads/contructing-algorithms-not-a-how-to-sorry.26477/page-2#post-591759
 
}}
 
}}
{{Alg5|wca=F2 r' E' F2 E l r E' F2 E l' F2//Safe
+
{{Alg6|wca=F2 r' E' F2 E l r E' F2 E l' F2 //Safe
|sign=F2 2R' e' F2 e 2L 2R e' F2 e 2L' F2//Safe
+
|sign=F2 2R' e' F2 e 2L 2R e' F2 e 2L' F2 //Safe
 
|length=(16,12)|name=Mirror[Alg.1]|wide=N|author=Christopher Mowla
 
|length=(16,12)|name=Mirror[Alg.1]|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r' E F2 E' l r E F2 E' l' F2//Safe
+
{{Alg6|wca=F2 r' E F2 E' l r E F2 E' l' F2 //Safe
|sign=F2 2R' e F2 e' 2L 2R e F2 e' 2L' F2//Safe
+
|sign=F2 2R' e F2 e' 2L 2R e F2 e' 2L' F2 //Safe
 
|length=(16,12)|name=Inverse[Alg.1]|wide=N|author=Christopher Mowla
 
|length=(16,12)|name=Inverse[Alg.1]|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l E' F2 E l' r' E' F2 E r F2//Safe
+
{{Alg6|wca=F2 l E' F2 E l' r' E' F2 E r F2 //Safe
|sign=F2 2L e' F2 e 2L' 2R' e' F2 e 2R F2//Safe
+
|sign=F2 2L e' F2 e 2L' 2R' e' F2 e 2R F2 //Safe
 
|length=(16,12)|name=Mirror[Inverse[Alg.1]|wide=N|author=Christopher Mowla
 
|length=(16,12)|name=Mirror[Inverse[Alg.1]|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l' S U2 S' l r S U2 S' r' F2//Safe
+
{{Alg6|wca=F2 l' S U2 S' l r S U2 S' r' F2 //Safe
|sign=F2 2L' s U2 s' 2L 2R s U2 s' 2R' F2//Safe
+
|sign=F2 2L' s U2 s' 2L 2R s U2 s' 2R' F2 //Safe
 
|length=(16,12)|name=Alg.2|wide=N|author=Walter Randelshofer
 
|length=(16,12)|name=Alg.2|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r S' U2 S l' r' S' U2 S l F2//Safe
+
{{Alg6|wca=F2 r S' U2 S l' r' S' U2 S l F2 //Safe
|sign=F2 2R s' U2 s 2L' 2R' s' U2 s 2L F2//Safe
+
|sign=F2 2R s' U2 s 2L' 2R' s' U2 s 2L F2 //Safe
 
|length=(16,12)|name=Mirror[Alg.2]|wide=N|author=Walter Randelshofer
 
|length=(16,12)|name=Mirror[Alg.2]|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r S U2 S' l' r' S U2 S' l F2//Safe
+
{{Alg6|wca=F2 r S U2 S' l' r' S U2 S' l F2 //Safe
|sign=F2 2R s U2 s' 2L' 2R' s U2 s' 2L F2//Safe
+
|sign=F2 2R s U2 s' 2L' 2R' s U2 s' 2L F2 //Safe
 
|length=(16,12)|name=Inverse[Alg.2]|wide=N|author=Walter Randelshofer
 
|length=(16,12)|name=Inverse[Alg.2]|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l' S' U2 S l r S' U2 S r' F2//Safe
+
{{Alg6|wca=F2 l' S' U2 S l r S' U2 S r' F2 //Safe
|sign=F2 2L' s' U2 s 2L 2R s' U2 s 2R' F2//Safe
+
|sign=F2 2L' s' U2 s 2L 2R s' U2 s 2R' F2 //Safe
 
|length=(16,12)|name=Mirror[Inverse[Alg.2]|wide=N|author=Walter Randelshofer
 
|length=(16,12)|name=Mirror[Inverse[Alg.2]|wide=N|author=Walter Randelshofer
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=376019#p376019
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=376019#p376019
 
}}
 
}}
{{Alg5|wca=(y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y')
+
{{Alg6|wca=(y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y')
 
|sign=(y R' U F') 2R2 U2 2R2 u2 2R2 2U2 (F U' R y')
 
|sign=(y R' U F') 2R2 U2 2R2 u2 2R2 2U2 (F U' R y')
 
|length=(18,12)|name=|wide=N|author=Chris Hardwick
 
|length=(18,12)|name=|wide=N|author=Chris Hardwick
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=r U2 l D2 l' U2 M U2 r D2 r' U2 l'//Safe
+
{{Alg6|wca=r U2 l D2 l' U2 M U2 r D2 r' U2 l' //Safe
|sign=2R U2 2L D2 2L' U2 m U2 2R D2 2R' U2 2L'//Safe
+
|sign=2R U2 2L D2 2L' U2 m U2 2R D2 2R' U2 2L' //Safe
 
|length=(19,13)|name=|wide=N|author=Kenneth Gustavsson
 
|length=(19,13)|name=|wide=N|author=Kenneth Gustavsson
 
|url=http://web.archive.org/web/20090224225202/http://rachmaninovian.webs.com:80/step4b.htm
 
|url=http://web.archive.org/web/20090224225202/http://rachmaninovian.webs.com:80/step4b.htm
 
}}
 
}}
{{Alg5|wca=(y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y)
+
{{Alg6|wca=(y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y)
 
|sign=(y' R' F U' r2 U2 F2) 2R2 (F2 U2 r2 U F' R y)
 
|sign=(y' R' F U' r2 U2 F2) 2R2 (F2 U2 r2 U F' R y)
 
|length=(20,13)|name=|wide=N|author=Stefan Pochmann
 
|length=(20,13)|name=|wide=N|author=Stefan Pochmann
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=(y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y')
+
{{Alg6|wca=(y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y')
 
|sign=(y R' U F' r2 F2 U2) 2R2 (U2 F2 r2 F U' R y')
 
|sign=(y R' U F' r2 F2 U2) 2R2 (U2 F2 r2 F U' R y')
 
|length=(20,13)|name=|wide=N|author=|url=
 
|length=(20,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l U2 M l U2 M' l' U2 M' U2 Rw M' U2 M r' U2 Rw'//Safe
+
{{Alg6|wca=(F E' F Rw2 F2 U2) r2 (U2 F2 Rw2 F' E F')
|sign=2L U2 m 2L U2 m' 2L' U2 m' U2 r m' U2 m 2R' U2 r'//Safe
+
|sign=(F e' F r2 F2 U2) 2R2 (U2 F2 r2 F' e F')
 +
|length=(20,13)|name=|wide=N|author=Per Kristen Fredlund
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407669&sid=db01443fe90166a0c00c230c97385e70#p407669
 +
}}
 +
{{Alg6|wca=F' U R d2 R' U' F U2 F' U R d2 R' U' F U2 //Safe
 +
|sign=F' U R 2D2 R' U' F U2 F' U R 2D2 R' U' F U2 //Safe
 +
|length=(20,16)|name=|wide=N|author=Per Kristen Fredlund
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407669&sid=db01443fe90166a0c00c230c97385e70#p407669
 +
}}
 +
{{Alg6|wca=l U2 M l U2 M' l' U2 M' U2 Rw M' U2 M r' U2 Rw' //Safe
 +
|sign=2L U2 m 2L U2 m' 2L' U2 m' U2 r m' U2 m 2R' U2 r' //Safe
 
|length=(23,17)|name=|wide=N|author=Kenneth Gustavsson
 
|length=(23,17)|name=|wide=N|author=Kenneth Gustavsson
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(F r U' R U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R' U r' F')
+
{{Alg6|wca=(F r U' R U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R' U r' F')
 
|sign=(F 2R U' R U' l U2 r U2) 2R2 (U2 r' U2 l' U R' U 2R' F')
 
|sign=(F 2R U' R U' l U2 r U2) 2R2 (U2 r' U2 l' U R' U 2R' F')
 
|length=(24,19)|name=|wide=N|author=Christopher Mowla
 
|length=(24,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw U2 Rw' U l' U' Lw' U2 Rw' U' l2 U') r2 (U l2 U Rw U2 Lw U l U' Rw U2 Rw')
+
{{Alg6|wca=(Rw U2 Rw' U l' U' Lw' U2 Rw' U' l2 U') r2 (U l2 U Rw U2 Lw U l U' Rw U2 Rw')
 
|sign=(r U2 r' U 2L' U' l' U2 r' U' 2L2 U') 2R2 (U 2L2 U r U2 l U 2L U' r U2 r')
 
|sign=(r U2 r' U 2L' U' l' U2 r' U' 2L2 U') 2R2 (U 2L2 U r U2 l U 2L U' r U2 r')
 
|length=(32,25)|name=|wide=N|author=Christopher Mowla
 
|length=(32,25)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
====Adjacent====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Double slash (//) permutation</span>====
 
[[Image:Uoadjpllparity.png|110px|]]
 
[[Image:Uoadjpllparity.png|110px|]]
{{Alg5|wca=(R B) r2 U2 r2 Uw2 r2 u2 (B' R')
+
{{Alg6|wca=(R B) r2 U2 r2 Uw2 r2 u2 (B' R')
 
|sign=(R B) 2R2 U2 2R2 u2 2R2 2U2 (B' R')
 
|sign=(R B) 2R2 U2 2R2 u2 2R2 2U2 (B' R')
 
|length=(16,10)|name=|wide=N|author=Chris Hardwick
 
|length=(16,10)|name=|wide=N|author=Chris Hardwick
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=(R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R')
+
{{Alg6|wca=(R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R')
 
|sign=(R B r2 F2 U2) 2R2 (U2 F2 r2 B' R')
 
|sign=(R B r2 F2 U2) 2R2 (U2 F2 r2 B' R')
 
|length=(18,11)|name=|wide=N|author=Stefan Pochmann
 
|length=(18,11)|name=|wide=N|author=Stefan Pochmann
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=(3Lw U Rw2 U2 F2) r2 (F2 U2 Rw2 U' 3Lw')
+
{{Alg6|wca=(3Lw U Rw2 U2 F2) r2 (F2 U2 Rw2 U' 3Lw')
 
|sign=(3l U r2 U2 F2) 2R2 (F2 U2 r2 U' 3l')
 
|sign=(3l U r2 U2 F2) 2R2 (F2 U2 r2 U' 3l')
 
|length=(18,11)|name=|wide=N|author=Stefan Pochmann
 
|length=(18,11)|name=|wide=N|author=Stefan Pochmann
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
 
}}
 
}}
{{Alg5|wca=(R2 D) l' E F2 E' l r E F2 E' r' (D' R2)//Safe
+
{{Alg6|wca=(R2 D) l' E F2 E' l r E F2 E' r' (D' R2) //Safe
 
|sign=(R2 D) 2L' e F2 e' 2L 2R e F2 e' 2R' (D' R2)
 
|sign=(R2 D) 2L' e F2 e' 2L 2R e F2 e' 2R' (D' R2)
 
|length=(16,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(16,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=375857#p375857
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=375857#p375857
 
}}
 
}}
{{Alg5|wca=F' R d2 R' F U F' U2 R d2 R' U2 F U'//Safe
+
{{Alg6|wca=F' R d2 R' F U F' U2 R d2 R' U2 F U' //Safe
 
|sign=F' R 2D2 R' F U F' U2 R 2D2 R' U2 F U'
 
|sign=F' R 2D2 R' F U F' U2 R 2D2 R' U2 F U'
 
|length=(16,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(16,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=375757#p375757
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=375757#p375757
 
}}
 
}}
{{Alg5|wca=R' U2 B u2 B' U2 R U' R' B u2 B' R U//Safe
+
{{Alg6|wca=R' U2 B u2 B' U2 R U' R' B u2 B' R U //Safe
 
|sign=R' U2 B 2U2 B' U2 R U' R' B 2U2 B' R U
 
|sign=R' U2 B 2U2 B' U2 R U' R' B 2U2 B' R U
 
|length=(16,14)|name=|wide=N|author=Walter Randelshofer
 
|length=(16,14)|name=|wide=N|author=Walter Randelshofer
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=376015#p376015
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=376015#p376015
 
}}
 
}}
{{Alg5|wca=R B U2 r2 U2 B2 l r U2 M' U2 r2 B R'//Safe
+
{{Alg6|wca=R B U2 r2 U2 B2 l r U2 M' U2 r2 B R' //Safe
|sign=R B U2 2R2 U2 B2 2L 2R U2 m' U2 2R2 B R'//Safe
+
|sign=R B U2 2R2 U2 B2 2L 2R U2 m' U2 2R2 B R' //Safe
 
|length=(21,14)|name=|wide=N|author=Stefan Pochmann|url=
 
|length=(21,14)|name=|wide=N|author=Stefan Pochmann|url=
 
}}
 
}}
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
The four cases above clearly switch two {{LinkColorI|p=dedge|c=rgb(229,148,0)|t=dedges}}, but they can also be interpreted as doing two <i>separate</i> swaps of {{LinkColorI|p=wing|c=rgb(229,148,0)|t=wing edges}}.  Recalling that the term "2-cycle" is interchangeable with the common term "swap", these cases perform 2 2-cycles of wing edges.  (They are called "2 2-cycles" for short.)
  
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
There are actually 58 of these cases in the last layer, in general.  However, the other 54 will only be encountered during a {{LinkColorI|p=K4|c=rgb(229,148,0)|t=K4 Method}} solve.  {{LinkColorE|u=https://drive.google.com/file/d/0Bx0h7-zg0f4NdjQ3ZFg3N0RWems/view|c=rgb(229,148,0)|t=This PDF}} includes all 58 cases and short algorithms to solve each one directly.</ul>
| bgcolor="fbfb8b" |
+
{{br|b=1}}
The four cases above clearly switch two [[dedge]]s, but they can also be interpreted as doing two <b>separate</b> swaps of [[wing]] edges.  Recalling that the term "2-cycle" is interchangeable with the common term "swap", these cases perform 2 2-cycles of wing edges.  (They are called "2 2-cycles" for short.)
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Four dedges (oriented)</span>===
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">O permutation</span>====
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Oa</span>=====
There are actually <b>58</b> of these cases in the last layer, in general.  However, the other 54 will only be encountered during a [[K4]] Method solve.  [https://drive.google.com/file/d/0Bx0h7-zg0f4NdjQ3ZFg3N0RWems/view This PDF] includes all 58 cases and short algorithms to solve each one.
+
[[Image:Circ4cyccw.png|110px|]][[Image:Oa_Perm_Diagram.png|110px|]]
|}
+
{{Alg6|wca=r2 Uw2 b2 U' b2 r2 U b2 r2 Uw2 r2
 
 
 
 
 
 
===Four dedges (oriented)===
 
====O permutation====
 
 
 
=====Oa=====
 
[[Image:Circ4cyccw.png|110px|]][[Image:Oa_Perm_Diagram.png|110px|]]
 
{{Alg5|wca=r2 Uw2 b2 U' b2 r2 U b2 r2 Uw2 r2
 
 
|sign=2R2 u2 2B2 U' 2B2 2R2 U 2B2 2R2 u2 2R2
 
|sign=2R2 u2 2B2 U' 2B2 2R2 U 2B2 2R2 u2 2R2
 
|length=(20,11)|name=CG03
 
|length=(20,11)|name=CG03
 
|wide=N|author=Clément Gallet
 
|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=f2 Uw2 r2 U' r2 f2 U r2 f2 Uw2 f2
+
{{Alg6|wca=f2 Uw2 r2 U' r2 f2 U r2 f2 Uw2 f2
 
|sign=2F2 u2 2R2 U' 2R2 2F2 U 2R2 2F2 u2 2F2
 
|sign=2F2 u2 2R2 U' 2R2 2F2 U 2R2 2F2 u2 2F2
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 M2 U' M2 u Uw f2 M2 Dw2 b2 U2 b2
+
{{Alg6|wca=y2 M2 U' M2 u Uw f2 M2 Dw2 b2 U2 b2
 
|sign=y2 m2 U' m2 2U u 2F2 m2 d2 2B2 U2 2B2
 
|sign=y2 m2 U' m2 2U u 2F2 m2 d2 2B2 U2 2B2
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M' U2 Uw2 r2 Uw2 r2 U2 l2 U2 M' U M2 U M2
+
{{Alg6|wca=M' U2 Uw2 r2 Uw2 r2 U2 l2 U2 M' U M2 U M2
 
|sign=m' U2 u2 2R2 u2 2R2 U2 2L2 U2 m' U m2 U m2
 
|sign=m' U2 u2 2R2 u2 2R2 U2 2L2 U2 m' U m2 U m2
 
|length=(22,13)|name=|wide=N|author=|url=
 
|length=(22,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=M U2 Uw2 l2 Uw2 l2 U2 r2 U2 M U M2 U M2
+
{{Alg6|wca=M U2 Uw2 l2 Uw2 l2 U2 r2 U2 M U M2 U M2
 
|sign=m U2 u2 2L2 u2 2L2 U2 2R2 U2 m U m2 U m2
 
|sign=m U2 u2 2L2 u2 2L2 U2 2R2 U2 m U m2 U m2
 
|length=(22,13)|name=|wide=N|author=|url=
 
|length=(22,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=y2 D2 M E2 M U M2 U' l2 U2 r2 Uw2 r2 Uw2
+
{{Alg6|wca=y2 D2 M E2 M U M2 U' l2 U2 r2 Uw2 r2 Uw2
 
|sign=y2 D2 m e2 m U m2 U' 2L2 U2 2R2 u2 2R2 u2
 
|sign=y2 D2 m e2 m U m2 U' 2L2 U2 2R2 u2 2R2 u2
 
|length=(22,13)|name=PKF03
 
|length=(22,13)|name=PKF03
Line 775: Line 830:
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
}}
 
}}
{{Alg5|wca=(E2 M)2 U M2 U' l2 U2 r2 Uw2 r2 u2
+
{{Alg6|wca=(E2 M)2 U M2 U' l2 U2 r2 Uw2 r2 u2
 
|sign=(e2 m)2 U m2 U' 2L2 U2 2R2 u2 2R2 2U2
 
|sign=(e2 m)2 U m2 U' 2L2 U2 2R2 u2 2R2 2U2
 
|length=(22,13)|name=PKF03
 
|length=(22,13)|name=PKF03
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31044
+
|url=https://web.archive.org/web/20191022171501/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31044?guccounter=1
 
}}
 
}}
{{Alg5|wca=l2 U2 f2 U' l2 f2 U u2 f2 u2 l2 U2 l2
+
{{Alg6|wca=l2 U2 f2 U' l2 f2 U u2 f2 u2 l2 U2 l2
 
|sign=2L2 U2 2F2 U' 2L2 2F2 U 2U2 2F2 2U2 2L2 U2 2L2
 
|sign=2L2 U2 2F2 U' 2L2 2F2 U 2U2 2F2 2U2 2L2 U2 2L2
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 f2 U' l2 f2 U u2 f2 l2 U2 l2 u2
+
{{Alg6|wca=l2 U2 f2 U' l2 f2 U u2 f2 l2 U2 l2 u2
 
|sign=2L2 U2 2F2 U' 2L2 2F2 U 2U2 2F2 2L2 U2 2L2 2U2
 
|sign=2L2 U2 2F2 U' 2L2 2F2 U 2U2 2F2 2L2 U2 2L2 2U2
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 Uw2 b2 U' b2 r2 U b2 R2 Uw2 Rw2 Uw2 R2
+
{{Alg6|wca=r2 Uw2 b2 U' b2 r2 U b2 R2 Uw2 Rw2 Uw2 R2
 
|sign=2R2 u2 2B2 U' 2B2 2R2 U 2B2 R2 u2 r2 u2 R2
 
|sign=2R2 u2 2B2 U' 2B2 2R2 U 2B2 R2 u2 r2 u2 R2
 
|length=(24,13)|name=|wide=N|author=Clément Gallet
 
|length=(24,13)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=M2 U M U2 r' l' U2 F2 r2 F2 U2 r2 U M2
+
{{Alg6|wca=M2 U M U2 r' l' U2 F2 r2 F2 U2 r2 U M2
 
|sign=m2 U m U2 2R' 2L' U2 F2 2R2 F2 U2 2R2 U m2
 
|sign=m2 U m U2 2R' 2L' U2 F2 2R2 F2 U2 2R2 U m2
 
|length=(23,14)|name=|wide=N|author=|url=
 
|length=(23,14)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l' r' 3Dw L' R' u L R 3Dw' M2 3Dw' L R u L' R' 3Dw l' r'//Safe
+
{{Alg6|wca=M2 U S2 l2 S2 U2 r S2 l2 S2 r' U2 r2 U' M2 //Safe
|sign=2L' 2R' 3d L' R' 2U L R 3d' m2 3d' L R 2U L' R' 3d 2L' 2R'//Safe
+
|sign=m2 U s2 2L2 s2 U2 2R s2 2L2 s2 2R' U2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407863#p407863
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 S2 U2 r' S2 l2 S2 r U2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 s2 U2 2R' s2 2L2 s2 2R U2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 S2 U2 l E2 l2 E2 l' U2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 s2 U2 2L e2 2L2 e2 2L' U2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 S2 U2 l' E2 l2 E2 l U2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 s2 U2 2L' e2 2L2 e2 2L U2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 S2 D2 r S2 l2 S2 r' D2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 s2 D2 2R s2 2L2 s2 2R' D2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 S2 D2 r' S2 l2 S2 r D2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 s2 D2 2R' s2 2L2 s2 2R D2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 S2 D2 l E2 l2 E2 l' D2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 s2 D2 2L e2 2L2 e2 2L' D2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 S2 D2 l' E2 l2 E2 l D2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 s2 D2 2L' e2 2L2 e2 2L D2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 D2 l S2 r2 S2 l' D2 S2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 D2 2L s2 2R2 s2 2L' D2 s2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 D2 l' S2 r2 S2 l D2 S2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 D2 2L' s2 2R2 s2 2L D2 s2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 D2 r E2 r2 E2 r' D2 S2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 D2 2R e2 2R2 e2 2R' D2 s2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 l2 D2 r' E2 r2 E2 r D2 S2 r2 U' M2 //Safe
 +
|sign=m2 U s2 2L2 D2 2R' e2 2R2 e2 2R D2 s2 2R2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 U2 l S2 r2 S2 l' U2 S2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 U2 2L s2 2R2 s2 2L' U2 s2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 U2 l' S2 r2 S2 l U2 S2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 U2 2L' s2 2R2 s2 2L U2 s2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 U2 r E2 r2 E2 r' U2 S2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 U2 2R e2 2R2 e2 2R' U2 s2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U S2 r2 U2 r' E2 r2 E2 r U2 S2 l2 U' M2 //Safe
 +
|sign=m2 U s2 2R2 U2 2R' e2 2R2 e2 2R U2 s2 2L2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U' F2 M' F2 M U2 r2 D2 F2 r2 F2 D2 r2 U' M2 //Safe
 +
|sign=m2 U' F2 m' F2 m U2 2R2 D2 F2 2R2 F2 D2 2R2 U' m2 //Safe
 +
|length=(28,16)|name=|wide=N|author=Christopher Mowla
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407858#p407858
 +
}}
 +
{{Alg6|wca=F' L B D2 (R d L R' E2 M' f' M E2 L') D2 B' L' F //Safe
 +
|sign=F' L B D2 (R 2D L R' e2 m' 2F' m e2 L') D2 B' L' F //Safe
 +
|length=(21,17)|name=|wide=N|author=Walter Randelshofer
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407832#p407832
 +
}}
 +
{{Alg6|wca=l' r' 3Dw L' R' u L R 3Dw' M2 3Dw' L R u L' R' 3Dw l' r' //Safe
 +
|sign=2L' 2R' 3d L' R' 2U L R 3d' m2 3d' L R 2U L' R' 3d 2L' 2R' //Safe
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r 3Dw L R u' L' R' 3Dw' M2 3Dw' L' R' u' L R 3Dw l r//Safe
+
{{Alg6|wca=l r 3Dw L R u' L' R' 3Dw' M2 3Dw' L' R' u' L R 3Dw l r //Safe
|sign=2L 2R 3d L R 2U' L' R' 3d' m2 3d' L' R' 2U' L R 3d 2L 2R//Safe
+
|sign=2L 2R 3d L R 2U' L' R' 3d' m2 3d' L' R' 2U' L R 3d 2L 2R //Safe
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' 3Dw' L' R' u' L R 3Dw M2 3Dw L R u' L' R' 3Dw' l' r' //Safe
+
{{Alg6|wca=l' r' 3Dw' L' R' u' L R 3Dw M2 3Dw L R u' L' R' 3Dw' l' r' //Safe
|sign=2L' 2R' 3d' L' R' 2U' L R 3d m2 3d L R 2U' L' R' 3d' 2L' 2R'//Safe
+
|sign=2L' 2R' 3d' L' R' 2U' L R 3d m2 3d L R 2U' L' R' 3d' 2L' 2R' //Safe
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r y' U' L R u L' R' 3Dw M2 3Dw L' R' u L R y' U' l r//Safe
+
{{Alg6|wca=l r y' U' L R u L' R' 3Dw M2 3Dw L' R' u L R y' U' l r //Safe
|sign=2L 2R y' U' L R 2U L' R' 3d m2 3d L' R' 2U L R y' U' 2L 2R//Safe
+
|sign=2L 2R y' U' L R 2U L' R' 3d m2 3d L' R' 2U L R y' U' 2L 2R //Safe
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 (R' U' R' F R F' U R) (Uw2 r2 Uw2 r2 U2 r2) (F U R U' R' F')
+
{{Alg6|wca=U2 (R' U' R' F R F' U R) (Uw2 r2 Uw2 r2 U2 r2) (F U R U' R' F')
 
|sign=U2 (R' U' R' F R F' U R) (u2 2R2 u2 2R2 U2 2R2) (F U R U' R' F')
 
|sign=U2 (R' U' R' F R F' U R) (u2 2R2 u2 2R2 U2 2R2) (F U R U' R' F')
 
|length=(28,21)|name=|wide=N|author=Antoine Cantin
 
|length=(28,21)|name=|wide=N|author=Antoine Cantin
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-65#post-949468
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-65#post-949468
 
}}
 
}}
{{Alg5|wca=(F2 U2 M U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M' U2 F2)
+
{{Alg6|wca=(F2 U2 M U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M' U2 F2)
 
|sign=(F2 U2 m U f2 2R2 2U s' r2 2U2) m (2U2 r2 s 2U' 2R2 f2 U' m' U2 F2)
 
|sign=(F2 U2 m U f2 2R2 2U s' r2 2U2) m (2U2 r2 s 2U' 2R2 f2 U' m' U2 F2)
 
|length=(33,21)|name=|wide=N|author=Christopher Mowla
 
|length=(33,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U R2 U R U' R' U R Rw' U2 Rw2 U2 Rw2 U2 Rw' U' R U R' U2 Rw2 U'
+
{{Alg6|wca=Rw2 U R2 U R U' R' U R Rw' U2 Rw2 U2 Rw2 U2 Rw' U' R U R' U2 Rw2 U'
 
|sign=r2 U R2 U R U' R' U R r' U2 r2 U2 r2 U2 r' U' R U R' U2 r2 U'
 
|sign=r2 U R2 U R U' R' U R r' U2 r2 U2 r2 U2 r' U' R U R' U2 r2 U'
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-936495
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-936495
 
}}
 
}}
{{Alg5|wca=Rw2 U2 R' U R U' Rw' U2 Rw2 U2 Rw2 U2 R Rw' U R' U' R U R2 U Rw2 U'
+
{{Alg6|wca=Rw2 U2 R' U R U' Rw' U2 Rw2 U2 Rw2 U2 R Rw' U R' U' R U R2 U Rw2 U'
 
|sign=r2 U2 R' U R U' r' U2 r2 U2 r2 U2 R r' U R' U' R U R2 U r2 U'
 
|sign=r2 U2 R' U R U' r' U2 r2 U2 r2 U2 R r' U R' U' R U R2 U r2 U'
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw R U' Rw' R' U' Rw' R U Rw U' R2 U R U R U' Rw U Rw' R U' Rw' U' Rw
+
{{Alg6|wca=Rw R U' Rw' R' U' Rw' R U Rw U' R2 U R U R U' Rw U Rw' R U' Rw' U' Rw
 
|sign=r R U' r' R' U' r' R U r U' R2 U R U R U' r U r' R U' r' U' r
 
|sign=r R U' r' R' U' r' R U r U' R2 U R U R U' r U r' R U' r' U' r
 
|length=(24,23)|name=|wide=Y|author=António Gomes
 
|length=(24,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U R2 U R U' R U Rw U R' Rw2 U2 R Rw2 U2 R' Rw2 U Rw' U2 Rw2 U'
+
{{Alg6|wca=Rw2 U R2 U R U' R U Rw U R' Rw2 U2 R Rw2 U2 R' Rw2 U Rw' U2 Rw2 U'
 
|sign=r2 U R2 U R U' R U r U R' r2 U2 R r2 U2 R' r2 U r' U2 r2 U'
 
|sign=r2 U R2 U R U' R U r U R' r2 U2 R r2 U2 R' r2 U r' U2 r2 U'
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw' U R' Rw2 U2 R Rw2 U2 R' Rw2 U Rw U R U' R U R2 U Rw2 U'
+
{{Alg6|wca=Rw2 U2 Rw' U R' Rw2 U2 R Rw2 U2 R' Rw2 U Rw U R U' R U R2 U Rw2 U'
 
|sign=r2 U2 r' U R' r2 U2 R r2 U2 R' r2 U r U R U' R U R2 U r2 U'
 
|sign=r2 U2 r' U R' r2 U2 R r2 U2 R' r2 U r U R U' R U R2 U r2 U'
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U' R' U' R U R U' Rw U2 Rw2 U2 Rw2 U2 Rw U2 R U' R U R2 Rw2 U'
+
{{Alg6|wca=Rw2 U' R' U' R U R U' Rw U2 Rw2 U2 Rw2 U2 Rw U2 R U' R U R2 Rw2 U'
 
|sign=r2 U' R' U' R U R U' r U2 r2 U2 r2 U2 r U2 R U' R U R2 r2 U'
 
|sign=r2 U' R' U' R U R U' r U2 r2 U2 r2 U2 r U2 R U' R U R2 r2 U'
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U' R' U' R U R U' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R U' R U R2 Rw2 U'
+
{{Alg6|wca=Rw2 U' R' U' R U R U' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R U' R U R2 Rw2 U'
 
|sign=r2 U' R' U' R U R U' r' U2 r2 U2 r2 U2 r' U2 R U' R U R2 r2 U'
 
|sign=r2 U' R' U' R U R U' r' U2 r2 U2 r2 U2 r' U2 R U' R U R2 r2 U'
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R2 U R U' R U2 Rw U2 Rw2 U2 Rw2 U2 Rw U' R U R U' R' U' Rw2 U'
+
{{Alg6|wca=Rw2 R2 U R U' R U2 Rw U2 Rw2 U2 Rw2 U2 Rw U' R U R U' R' U' Rw2 U'
 
|sign=r2 R2 U R U' R U2 r U2 r2 U2 r2 U2 r U' R U R U' R' U' r2 U'
 
|sign=r2 R2 U R U' R U2 r U2 r2 U2 r2 U2 r U' R U R U' R' U' r2 U'
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R2 U R U' R U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U' R U R U' R' U' Rw2 U'
+
{{Alg6|wca=Rw2 R2 U R U' R U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U' R U R U' R' U' Rw2 U'
 
|sign=r2 R2 U R U' R U2 r' U2 r2 U2 r2 U2 r' U' R U R U' R' U' r2 U'
 
|sign=r2 R2 U R U' R U2 r' U2 r2 U2 r2 U2 r' U' R U R U' R' U' r2 U'
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R2 U R2 Rw2 U R2 U' Rw2 U' Rw2 U' Rw U' Rw2 U' R2 U Rw2 U Rw' U' R2
+
{{Alg6|wca=Rw2 R2 U R2 Rw2 U R2 U' Rw2 U' Rw2 U' Rw U' Rw2 U' R2 U Rw2 U Rw' U' R2
 
|sign=r2 R2 U R2 r2 U R2 U' r2 U' r2 U' r U' r2 U' R2 U r2 U r' U' R2
 
|sign=r2 R2 U R2 r2 U R2 U' r2 U' r2 U' r U' r2 U' R2 U r2 U r' U' R2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R2 U R2 Rw2 U R2 U' Rw2 U' Rw2 U' Rw' U' Rw2 U' R2 U Rw2 U Rw U' R2
+
{{Alg6|wca=Rw2 R2 U R2 Rw2 U R2 U' Rw2 U' Rw2 U' Rw' U' Rw2 U' R2 U Rw2 U Rw U' R2
 
|sign=r2 R2 U R2 r2 U R2 U' r2 U' r2 U' r' U' r2 U' R2 U r2 U r U' R2
 
|sign=r2 R2 U R2 r2 U R2 U' r2 U' r2 U' r' U' r2 U' R2 U r2 U r U' R2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R U' R' Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R2 Rw2 U R U R U' R' U' R2
+
{{Alg6|wca=R U' R' Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R2 Rw2 U R U R U' R' U' R2
 
|sign=R U' R' r2 U2 r U2 r2 U2 r2 U2 r U2 R2 r2 U R U R U' R' U' R2
 
|sign=R U' R' r2 U2 r U2 r2 U2 r2 U2 r U2 R2 r2 U R U R U' R' U' R2
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R U' R' Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R2 Rw2 U R U R U' R' U' R2
+
{{Alg6|wca=R U' R' Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R2 Rw2 U R U R U' R' U' R2
 
|sign=R U' R' r2 U2 r' U2 r2 U2 r2 U2 r' U2 R2 r2 U R U R U' R' U' R2
 
|sign=R U' R' r2 U2 r' U2 r2 U2 r2 U2 r' U2 R2 r2 U R U R U' R' U' R2
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U R2 U R U' R' U R Rw U2 Rw2 U2 Rw2 U2 Rw U' R U R' U2 Rw2 U'
+
{{Alg6|wca=Rw2 U R2 U R U' R' U R Rw U2 Rw2 U2 Rw2 U2 Rw U' R U R' U2 Rw2 U'
 
|sign=r2 U R2 U R U' R' U R r U2 r2 U2 r2 U2 r U' R U R' U2 r2 U'
 
|sign=r2 U R2 U R U' R' U R r U2 r2 U2 r2 U2 r U' R U R' U2 r2 U'
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 R' U R U' Rw U2 Rw2 U2 Rw2 U2 R Rw U R' U' R U R2 U Rw2 U'
+
{{Alg6|wca=Rw2 U2 R' U R U' Rw U2 Rw2 U2 Rw2 U2 R Rw U R' U' R U R2 U Rw2 U'
 
|sign=r2 U2 R' U R U' r U2 r2 U2 r2 U2 R r U R' U' R U R2 U r2 U'
 
|sign=r2 U2 R' U R U' r U2 r2 U2 r2 U2 R r U R' U' R U R2 U r2 U'
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R U2 R U R' Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R2 Rw2 U R2 U' R' U' R2//Safe
+
{{Alg6|wca=R U2 R U R' Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R2 Rw2 U R2 U' R' U' R2 //Safe
|sign=R U2 R U R' r2 U2 r U2 r2 U2 r2 U2 r U2 R2 r2 U R2 U' R' U' R2//Safe
+
|sign=R U2 R U R' r2 U2 r U2 r2 U2 r2 U2 r U2 R2 r2 U R2 U' R' U' R2 //Safe
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R U2 R U R' Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R2 Rw2 U R2 U' R' U' R2//Safe
+
{{Alg6|wca=R U2 R U R' Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R2 Rw2 U R2 U' R' U' R2 //Safe
|sign=R U2 R U R' r2 U2 r' U2 r2 U2 r2 U2 r' U2 R2 r2 U R2 U' R' U' R2//Safe
+
|sign=R U2 R U R' r2 U2 r' U2 r2 U2 r2 U2 r' U2 R2 r2 U R2 U' R' U' R2 //Safe
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Ob</span>=====
=====Ob=====
 
 
[[Image:Circ4cy.png|110px|]][[Image:Ob_Perm_Diagram.png|110px|]]
 
[[Image:Circ4cy.png|110px|]][[Image:Ob_Perm_Diagram.png|110px|]]
{{Alg5|wca=r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2
+
{{Alg6|wca=r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2
 
|sign=2R2 u2 2R2 2B2 U' 2R2 2B2 U 2B2 u2 2R2
 
|sign=2R2 u2 2R2 2B2 U' 2R2 2B2 U 2B2 u2 2R2
 
|length=(20,11)|name=CG03
 
|length=(20,11)|name=CG03
 
|wide=N|author=Clément Gallet
 
|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=f2 Uw2 f2 r2 U' f2 r2 U r2 Uw2 f2
+
{{Alg6|wca=f2 Uw2 f2 r2 U' f2 r2 U r2 Uw2 f2
 
|sign=2F2 u2 2F2 2R2 U' 2F2 2R2 U 2R2 u2 2F2
 
|sign=2F2 u2 2F2 2R2 U' 2F2 2R2 U 2R2 u2 2F2
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=b2 U2 b2 Dw2 M2 f2 Uw' u' M2 U M2 y2
+
{{Alg6|wca=b2 U2 b2 Dw2 M2 f2 Uw' u' M2 U M2 y2
 
|sign=2B2 U2 2B2 d2 m2 2F2 u' 2U' m2 U m2 y2
 
|sign=2B2 U2 2B2 d2 m2 2F2 u' 2U' m2 U m2 y2
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|length=(20,11)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 U' M2 U' M U2 l2 U2 r2 Uw2 r2 Uw2 U2 M
+
{{Alg6|wca=M2 U' M2 U' M U2 l2 U2 r2 Uw2 r2 Uw2 U2 M
 
|sign=m2 U' m2 U' m U2 2L2 U2 2R2 u2 2R2 u2 U2 m
 
|sign=m2 U' m2 U' m U2 2L2 U2 2R2 u2 2R2 u2 U2 m
 
|length=(22,13)|name=|wide=N|author=|url=
 
|length=(22,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=M2 U' M2 U' M' U2 r2 U2 l2 Uw2 l2 Uw2 U2 M'
+
{{Alg6|wca=M2 U' M2 U' M' U2 r2 U2 l2 Uw2 l2 Uw2 U2 M'
 
|sign=m2 U' m2 U' m' U2 2R2 U2 2L2 u2 2L2 u2 U2 m'
 
|sign=m2 U' m2 U' m' U2 2R2 U2 2L2 u2 2L2 u2 U2 m'
 
|length=(22,13)|name=|wide=N|author=|url=
 
|length=(22,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2
+
{{Alg6|wca=Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2
 
|sign=u2 2R2 u2 2R2 U2 2L2 U m2 U' m' e2 m' D2 y2
 
|sign=u2 2R2 u2 2R2 U2 2L2 U m2 U' m' e2 m' D2 y2
 
|length=(22,13)|name=PKF03
 
|length=(22,13)|name=PKF03
Line 949: Line 1,093:
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
}}
 
}}
{{Alg5|wca=u2 r2 Uw2 r2 U2 l2 U M2 U' (M' E2)2
+
{{Alg6|wca=u2 r2 Uw2 r2 U2 l2 U M2 U' (M' E2)2
 
|sign=2U2 2R2 u2 2R2 U2 2L2 U m2 U' (m' e2)2
 
|sign=2U2 2R2 u2 2R2 U2 2L2 U m2 U' (m' e2)2
 
|length=(22,13)|name=PKF03
 
|length=(22,13)|name=PKF03
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31044
+
|url=https://web.archive.org/web/20191022171501/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31044?guccounter=1
 
}}
 
}}
{{Alg5|wca=l2 U2 l2 u2 f2 u2 U' f2 l2 U f2 U2 l2
+
{{Alg6|wca=l2 U2 l2 u2 f2 u2 U' f2 l2 U f2 U2 l2
 
|sign=2L2 U2 2L2 2U2 2F2 2U2 U' 2F2 2L2 U 2F2 U2 2L2
 
|sign=2L2 U2 2L2 2U2 2F2 2U2 U' 2F2 2L2 U 2F2 U2 2L2
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=u2 l2 U2 l2 f2 u2 U' f2 l2 U f2 U2 l2
+
{{Alg6|wca=u2 l2 U2 l2 f2 u2 U' f2 l2 U f2 U2 l2
 
|sign=2U2 2L2 U2 2L2 2F2 2U2 U' 2F2 2L2 U 2F2 U2 2L2
 
|sign=2U2 2L2 U2 2L2 2F2 2U2 U' 2F2 2L2 U 2F2 U2 2L2
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|length=(23,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 Uw2 Rw2 Uw2 R2 b2 U' r2 b2 U b2 Uw2 r2
+
{{Alg6|wca=R2 Uw2 Rw2 Uw2 R2 b2 U' r2 b2 U b2 Uw2 r2
 
|sign=R2 u2 r2 u2 R2 2B2 U' 2R2 2B2 U 2B2 u2 2R2
 
|sign=R2 u2 r2 u2 R2 2B2 U' 2R2 2B2 U 2B2 u2 2R2
 
|length=(24,13)|name=|wide=N|author=Clément Gallet
 
|length=(24,13)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2
+
{{Alg6|wca=M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2
 
|sign=m2 U' 2R2 U2 F2 2R2 F2 U2 2L 2R U2 m' U' m2
 
|sign=m2 U' 2R2 U2 F2 2R2 F2 U2 2L 2R U2 m' U' m2
 
|length=(23,14)|name=|wide=N|author=|url=
 
|length=(23,14)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l r 3Dw' L R u' L' R' 3Dw M2 3Dw L' R' u' L R 3Dw' l r//Safe
+
{{Alg6|wca=M2 U r2 U2 r S2 l2 S2 r' U2 S2 l2 S2 U' M2 //Safe
|sign=2L 2R 3d' L R 2U' L' R' 3d m2 3d L' R' 2U' L R 3d' 2L 2R//Safe
+
|sign=m2 U 2R2 U2 2R s2 2L2 s2 2R' U2 s2 2L2 s2 U' m2 //Safe
|length=(20,19)|name=|wide=N|author=Christopher Mowla
+
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407863#p407863
 +
}}
 +
{{Alg6|wca=M2 U r2 U2 r' S2 l2 S2 r U2 S2 l2 S2 U' M2 //Safe
 +
|sign=m2 U 2R2 U2 2R' s2 2L2 s2 2R U2 s2 2L2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' 3Dw' L' R' u L R 3Dw M2 3Dw L R u L' R' 3Dw' l' r'//Safe
+
{{Alg6|wca=M2 U r2 U2 l E2 l2 E2 l' U2 S2 l2 S2 U' M2 //Safe
|sign=2L' 2R' 3d' L' R' 2U L R 3d m2 3d L R 2U L' R' 3d' 2L' 2R'//Safe
+
|sign=m2 U 2R2 U2 2L e2 2L2 e2 2L' U2 s2 2L2 s2 U' m2 //Safe
|length=(20,19)|name=|wide=N|author=Christopher Mowla
+
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r 3Dw L R u L' R' 3Dw' M2 3Dw' L' R' u L R 3Dw l r//Safe
+
{{Alg6|wca=M2 U r2 U2 l' E2 l2 E2 l U2 S2 l2 S2 U' M2 //Safe
|sign=2L 2R 3d L R 2U L' R' 3d' m2 3d' L' R' 2U L R 3d 2L 2R//Safe
+
|sign=m2 U 2R2 U2 2L' e2 2L2 e2 2L U2 s2 2L2 s2 U' m2 //Safe
|length=(20,19)|name=|wide=N|author=Christopher Mowla
+
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' U y L' R' u' L R 3Dw' M2 3Dw' L R u' L' R' U y l' r'//Safe
+
{{Alg6|wca=M2 U l2 D2 r S2 l2 S2 r' D2 S2 r2 S2 U' M2 //Safe
|sign=2L' 2R' U y L' R' 2U' L R 3d' m2 3d' L R 2U' L' R' U y 2L' 2R'//Safe
+
|sign=m2 U 2L2 D2 2R s2 2L2 s2 2R' D2 s2 2R2 s2 U' m2 //Safe
|length=(20,19)|name=|wide=N|author=Christopher Mowla
+
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(F R U R' U' F') (r2 U2 r2 Uw2 r2 Uw2) (R' U' F R' F' R U R) U2
+
{{Alg6|wca=M2 U l2 D2 r' S2 l2 S2 r D2 S2 r2 S2 U' M2 //Safe
|sign=(F R U R' U' F') (2R2 U2 2R2 u2 2R2 u2) (R' U' F R' F' R U R) U2
+
|sign=m2 U 2L2 D2 2R' s2 2L2 s2 2R D2 s2 2R2 s2 U' m2 //Safe
|length=(28,21)|name=|wide=N|author=Antoine Cantin
+
|length=(26,15)|name=|wide=N|author=Christopher Mowla
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-65#post-949468
+
|url=
 
}}
 
}}
{{Alg5|wca=(F2 U2 M U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M' U2 F2)
+
{{Alg6|wca=M2 U l2 D2 l E2 l2 E2 l' D2 S2 r2 S2 U' M2 //Safe
|sign=(F2 U2 m U f2 2R2 2U s' r2 2U2) m' (2U2 r2 s 2U' 2R2 f2 U' m' U2 F2)
+
|sign=m2 U 2L2 D2 2L e2 2L2 e2 2L' D2 s2 2R2 s2 U' m2 //Safe
|length=(33,21)|name=|wide=N|author=Christopher Mowla
+
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U2 R U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw R' U' R U R' U' R2 U' Rw2
+
{{Alg6|wca=M2 U l2 D2 l' E2 l2 E2 l D2 S2 r2 S2 U' M2 //Safe
 +
|sign=m2 U 2L2 D2 2L' e2 2L2 e2 2L D2 s2 2R2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U r2 S2 D2 l S2 r2 S2 l' D2 l2 S2 U' M2 //Safe
 +
|sign=m2 U 2R2 s2 D2 2L s2 2R2 s2 2L' D2 2L2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U r2 S2 D2 l' S2 r2 S2 l D2 l2 S2 U' M2 //Safe
 +
|sign=m2 U 2R2 s2 D2 2L' s2 2R2 s2 2L D2 2L2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U r2 S2 D2 r E2 r2 E2 r' D2 l2 S2 U' M2 //Safe
 +
|sign=m2 U 2R2 s2 D2 2R e2 2R2 e2 2R' D2 2L2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U r2 S2 D2 r' E2 r2 E2 r D2 l2 S2 U' M2 //Safe
 +
|sign=m2 U 2R2 s2 D2 2R' e2 2R2 e2 2R D2 2L2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U l2 S2 U2 l S2 r2 S2 l' U2 r2 S2 U' M2 //Safe
 +
|sign=m2 U 2L2 s2 U2 2L s2 2R2 s2 2L' U2 2R2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U l2 S2 U2 l' S2 r2 S2 l U2 r2 S2 U' M2 //Safe
 +
|sign=m2 U 2L2 s2 U2 2L' s2 2R2 s2 2L U2 2R2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U l2 S2 U2 r E2 r2 E2 r' U2 r2 S2 U' M2 //Safe
 +
|sign=m2 U 2L2 s2 U2 2R e2 2R2 e2 2R' U2 2R2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U l2 S2 U2 r' E2 r2 E2 r U2 r2 S2 U' M2 //Safe
 +
|sign=m2 U 2L2 s2 U2 2R' e2 2R2 e2 2R U2 2R2 s2 U' m2 //Safe
 +
|length=(26,15)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=M2 U r2 D2 F2 r2 F2 D2 r2 U2 M' F2 M F2 U M2 //Safe
 +
|sign=m2 U 2R2 D2 F2 2R2 F2 D2 2R2 U2 m' F2 m F2 U m2 //Safe
 +
|length=(28,16)|name=|wide=N|author=Christopher Mowla
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407858#p407858
 +
}}
 +
{{Alg6|wca=F' L B D2 (L E2 M' f M E2 L' R d' R') D2 B' L' F //Safe
 +
|sign=F' L B D2 (L e2 m' 2F m e2 L' R 2D' R') D2 B' L' F //Safe
 +
|length=(21,17)|name=|wide=N|author=Walter Randelshofer
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407832#p407832
 +
}}
 +
{{Alg6|wca=l r 3Dw' L R u' L' R' 3Dw M2 3Dw L' R' u' L R 3Dw' l r //Safe
 +
|sign=2L 2R 3d' L R 2U' L' R' 3d m2 3d L' R' 2U' L R 3d' 2L 2R //Safe
 +
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=l' r' 3Dw' L' R' u L R 3Dw M2 3Dw L R u L' R' 3Dw' l' r' //Safe
 +
|sign=2L' 2R' 3d' L' R' 2U L R 3d m2 3d L R 2U L' R' 3d' 2L' 2R' //Safe
 +
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=l r 3Dw L R u L' R' 3Dw' M2 3Dw' L' R' u L R 3Dw l r //Safe
 +
|sign=2L 2R 3d L R 2U L' R' 3d' m2 3d' L' R' 2U L R 3d 2L 2R //Safe
 +
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=l' r' U y L' R' u' L R 3Dw' M2 3Dw' L R u' L' R' U y l' r' //Safe
 +
|sign=2L' 2R' U y L' R' 2U' L R 3d' m2 3d' L R 2U' L' R' U y 2L' 2R' //Safe
 +
|length=(20,19)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=(F R U R' U' F') (r2 U2 r2 Uw2 r2 Uw2) (R' U' F R' F' R U R) U2
 +
|sign=(F R U R' U' F') (2R2 U2 2R2 u2 2R2 u2) (R' U' F R' F' R U R) U2
 +
|length=(28,21)|name=|wide=N|author=Antoine Cantin
 +
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-65#post-949468
 +
}}
 +
{{Alg6|wca=(F2 U2 M U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M' U2 F2)
 +
|sign=(F2 U2 m U f2 2R2 2U s' r2 2U2) m' (2U2 r2 s 2U' 2R2 f2 U' m' U2 F2)
 +
|length=(33,21)|name=|wide=N|author=Christopher Mowla
 +
|url=
 +
}}
 +
{{Alg6|wca=U Rw2 U2 R U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw R' U' R U R' U' R2 U' Rw2
 
|sign=U r2 U2 R U' R' U r U2 r2 U2 r2 U2 r R' U' R U R' U' R2 U' r2
 
|sign=U r2 U2 R U' R' U r U2 r2 U2 r2 U2 r R' U' R U R' U' R2 U' r2
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-936495
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-936495
 
}}
 
}}
{{Alg5|wca=U Rw2 U' R2 U' R' U R U' Rw R' U2 Rw2 U2 Rw2 U2 Rw U R' U' R U2 Rw2
+
{{Alg6|wca=U Rw2 U' R2 U' R' U R U' Rw R' U2 Rw2 U2 Rw2 U2 Rw U R' U' R U2 Rw2
 
|sign=U r2 U' R2 U' R' U R U' r R' U2 r2 U2 r2 U2 r U R' U' R U2 r2
 
|sign=U r2 U' R2 U' R' U R U' r R' U2 r2 U2 r2 U2 r U R' U' R U2 r2
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|length=(31,22)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw U R' Rw U' Rw' U R' U' R' U' R2 U Rw' U' R' Rw U R Rw U R' Rw'
+
{{Alg6|wca=Rw' U Rw U R' Rw U' Rw' U R' U' R' U' R2 U Rw' U' R' Rw U R Rw U R' Rw'
 
|sign=r' U r U R' r U' r' U R' U' R' U' R2 U r' U' R' r U R r U R' r'
 
|sign=r' U r U R' r U' r' U R' U' R' U' R2 U r' U' R' r U R r U R' r'
 
|length=(24,23)|name=|wide=Y|author=António Gomes
 
|length=(24,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U2 Rw U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw' U' R' U R' U' R2 U' Rw2
+
{{Alg6|wca=U Rw2 U2 Rw U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw' U' R' U R' U' R2 U' Rw2
 
|sign=U r2 U2 r U' r2 R U2 r2 R' U2 r2 R U' r' U' R' U R' U' R2 U' r2
 
|sign=U r2 U2 r U' r2 R U2 r2 R' U2 r2 R U' r' U' R' U R' U' R2 U' r2
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U' R2 U' R' U R' U' Rw' U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw U2 Rw2
+
{{Alg6|wca=U Rw2 U' R2 U' R' U R' U' Rw' U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw U2 Rw2
 
|sign=U r2 U' R2 U' R' U R' U' r' U' r2 R U2 r2 R' U2 r2 R U' r U2 r2
 
|sign=U r2 U' R2 U' R' U R' U' r' U' r2 R U2 r2 R' U2 r2 R U' r U2 r2
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|length=(29,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 R2 U' R' U R' U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R' U R U Rw2
+
{{Alg6|wca=U Rw2 R2 U' R' U R' U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R' U R U Rw2
 
|sign=U r2 R2 U' R' U R' U2 r' U2 r2 U2 r2 U2 r' U R' U' R' U R U r2
 
|sign=U r2 R2 U' R' U R' U2 r' U2 r2 U2 r2 U2 r' U R' U' R' U R U r2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 R2 U' R' U R' U2 Rw U2 Rw2 U2 Rw2 U2 Rw U R' U' R' U R U Rw2
+
{{Alg6|wca=U Rw2 R2 U' R' U R' U2 Rw U2 Rw2 U2 Rw2 U2 Rw U R' U' R' U R U Rw2
 
|sign=U r2 R2 U' R' U R' U2 r U2 r2 U2 r2 U2 r U R' U' R' U R U r2
 
|sign=U r2 R2 U' R' U R' U2 r U2 r2 U2 r2 U2 r U R' U' R' U R U r2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U R U R' U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R' U R' U' Rw2 R2
+
{{Alg6|wca=U Rw2 U R U R' U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R' U R' U' Rw2 R2
 
|sign=U r2 U R U R' U' R' U r' U2 r2 U2 r2 U2 r' U2 R' U R' U' r2 R2
 
|sign=U r2 U R U R' U' R' U r' U2 r2 U2 r2 U2 r' U2 R' U R' U' r2 R2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U R U R' U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw U2 R' U R' U' Rw2 R2
+
{{Alg6|wca=U Rw2 U R U R' U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw U2 R' U R' U' Rw2 R2
 
|sign=U r2 U R U R' U' R' U r U2 r2 U2 r2 U2 r U2 R' U R' U' r2 R2
 
|sign=U r2 U R U R' U' R' U r U2 r2 U2 r2 U2 r U2 R' U R' U' r2 R2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U Rw U' Rw2 U' R2 U Rw2 U Rw' U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2
+
{{Alg6|wca=R2 U Rw U' Rw2 U' R2 U Rw2 U Rw' U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2
 
|sign=R2 U r U' r2 U' R2 U r2 U r' U r2 U r2 U R2 U' r2 R2 U' r2 R2
 
|sign=R2 U r U' r2 U' R2 U r2 U r' U r2 U r2 U R2 U' r2 R2 U' r2 R2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U Rw' U' Rw2 U' R2 U Rw2 U Rw U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2
+
{{Alg6|wca=R2 U Rw' U' Rw2 U' R2 U Rw2 U Rw U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2
 
|sign=R2 U r' U' r2 U' R2 U r2 U r U r2 U r2 U R2 U' r2 R2 U' r2 R2
 
|sign=R2 U r' U' r2 U' R2 U r2 U r U r2 U r2 U R2 U' r2 R2 U' r2 R2
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|length=(30,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U R U R' U' R' U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U R'
+
{{Alg6|wca=R2 U R U R' U' R' U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U R'
 
|sign=R2 U R U R' U' R' U' r2 R2 U2 r' U2 r2 U2 r2 U2 r' U2 r2 R U R'
 
|sign=R2 U R U R' U' R' U' r2 R2 U2 r' U2 r2 U2 r2 U2 r' U2 r2 R U R'
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U R U R' U' R' U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U R'
+
{{Alg6|wca=R2 U R U R' U' R' U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U R'
 
|sign=R2 U R U R' U' R' U' r2 R2 U2 r U2 r2 U2 r2 U2 r U2 r2 R U R'
 
|sign=R2 U R U R' U' R' U' r2 R2 U2 r U2 r2 U2 r2 U2 r U2 r2 R U R'
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|length=(31,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U2 R U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' R' U' R U R' U' R2 U' Rw2
+
{{Alg6|wca=U Rw2 U2 R U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' R' U' R U R' U' R2 U' Rw2
 
|sign=U r2 U2 R U' R' U r' U2 r2 U2 r2 U2 r' R' U' R U R' U' R2 U' r2
 
|sign=U r2 U2 R U' R' U r' U2 r2 U2 r2 U2 r' R' U' R U R' U' R2 U' r2
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Rw2 U' R2 U' R' U R U' Rw' R' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R U2 Rw2
+
{{Alg6|wca=U Rw2 U' R2 U' R' U R U' Rw' R' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R U2 Rw2
 
|sign=U r2 U' R2 U' R' U R U' r' R' U2 r2 U2 r2 U2 r' U R' U' R U2 r2
 
|sign=U r2 U' R2 U' R' U R U' r' R' U2 r2 U2 r2 U2 r' U R' U' R U2 r2
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|length=(32,33)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U R U R2 U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U' R' U2 R'//Safe
+
{{Alg6|wca=R2 U R U R2 U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U' R' U2 R' //Safe
|sign=R2 U R U R2 U' r2 R2 U2 r' U2 r2 U2 r2 U2 r' U2 r2 R U' R' U2 R'//Safe
+
|sign=R2 U R U R2 U' r2 R2 U2 r' U2 r2 U2 r2 U2 r' U2 r2 R U' R' U2 R' //Safe
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U R U R2 U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U' R' U2 R'//Safe
+
{{Alg6|wca=R2 U R U R2 U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U' R' U2 R' //Safe
|sign=R2 U R U R2 U' r2 R2 U2 r U2 r2 U2 r2 U2 r U2 r2 R U' R' U2 R'//Safe
+
|sign=R2 U R U R2 U' r2 R2 U2 r U2 r2 U2 r2 U2 r U2 r2 R U' R' U2 R' //Safe
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|length=(33,23)|name=|wide=Y|author=António Gomes
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">B permutation</span>====
====8 permutation====
+
[[Image:Zigzag4cycdedges.png|110px|]][[Image:B_Perm_oriented.png|110px|]]
[[Image:Zigzag4cycdedges.png|110px|]][[Image:8_Perm_Diagram.png|110px|]]
 
  
 
*Note:  This is commonly called the "W" permutation.
 
*Note:  This is commonly called the "W" permutation.
 
+
*A list of algorithms for the inverse case are unnecessary.  Just do U2 (alg) U2 <i>or</i> y2 (alg) y2.
{{Alg5|wca=M2 U M' U2 M U l2 U2 r2 Uw2 r2 Uw2 U2
+
{{br|b=1}}
 +
{{Alg6|wca=M2 U M' U2 M U l2 U2 r2 Uw2 r2 Uw2 U2
 
|sign=m2 U m' U2 m U 2L2 U2 2R2 u2 2R2 u2 U2
 
|sign=m2 U m' U2 m U 2L2 U2 2R2 u2 2R2 u2 U2
 
|length=(20,12)|name=|wide=N|author=|url=
 
|length=(20,12)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=u2 S2 Uw' u' b2 R2 b2 Rw2 f2 r2 U S2
+
{{Alg6|wca=u2 S2 Uw' u' b2 R2 b2 Rw2 f2 r2 U S2
 
|sign=2U2 s2 u' 2U' 2B2 R2 2B2 r2 2F2 2R2 U s2
 
|sign=2U2 s2 u' 2U' 2B2 R2 2B2 r2 2F2 2R2 U s2
 
|length=(21,12)|name=|wide=N|author=Clément Gallet
 
|length=(21,12)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 D' f2 d2 b2 D' B2 Dw2 3Uw' M2 3Uw F2 Uw2
+
{{Alg6|wca=F2 D' f2 d2 b2 D' B2 Dw2 3Uw' M2 3Uw F2 Uw2
 
|sign=F2 D' 2F2 2D2 2B2 D' B2 d2 3u' m2 3u F2 u2
 
|sign=F2 D' 2F2 2D2 2B2 D' B2 d2 3u' m2 3u F2 u2
 
|length=(21,13)|name=|wide=N|author=Clément Gallet
 
|length=(21,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)
+
{{Alg6|wca=(r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)
 
|sign=(2R2 U2 2R2 u2 2R2 2U2) (F2 U m' U2 m U F2)
 
|sign=(2R2 U2 2R2 u2 2R2 2U2) (F2 U m' U2 m U F2)
 
|length=(22,13)|name=PKF04
 
|length=(22,13)|name=PKF04
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31049
+
|url=https://web.archive.org/save/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31049
 
}}
 
}}
{{Alg5|wca=R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2
+
{{Alg6|wca=R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2
 
|sign=R2 u2 B2 R2 u2 B2 R2 U R2 B2 R2 U B2 u2
 
|sign=R2 u2 B2 R2 u2 B2 R2 U R2 B2 R2 U B2 u2
 
|length=(26,14)|name=CG04
 
|length=(26,14)|name=CG04
Line 1,122: Line 1,356:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 Uw' u' M2 U' F2 D S2 Dw d Bw2 u2 b2 U2 y2
+
{{Alg6|wca=F2 Uw' u' M2 U' F2 D S2 Dw d Bw2 u2 b2 U2 y2
 
|sign=F2 u' 2U' m2 U' F2 D s2 d 2D b2 2U2 2B2 U2 y2
 
|sign=F2 u' 2U' m2 U' F2 D s2 d 2D b2 2U2 2B2 U2 y2
 
|length=(22,14)|name=|wide=N|author=Clément Gallet
 
|length=(22,14)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 B2 Rw2 B2 D2 l2 F2 U' F2 L2 F2 U' L2
+
{{Alg6|wca=(Rw2 F2 U2 r2 U2 F2 Rw2) (F2 U M' U2 M U F2) //Safe
 +
|sign=(r2 F2 U2 2R2 U2 F2 r2) (F2 U m' U2 m U F2) //Safe
 +
|length=(24,14)|name=|wide=N|author=Christopher Mowla
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407857#p407857
 +
}}
 +
{{Alg6|wca=l2 D2 B2 Rw2 B2 D2 l2 F2 U' F2 L2 F2 U' L2
 
|sign=2L2 D2 B2 r2 B2 D2 2L2 F2 U' F2 L2 F2 U' L2
 
|sign=2L2 D2 B2 r2 B2 D2 2L2 F2 U' F2 L2 F2 U' L2
 
|length=(26,14)|name=|wide=N|author=Clément Gallet
 
|length=(26,14)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' M2 U' r2 b2 Rw2 Bw2 R2 Bw2 L2 U2 M2 U2 F2 D M2 x2 y
+
{{Alg6|wca=y' M2 U' r2 b2 Rw2 Bw2 R2 Bw2 L2 U2 M2 U2 F2 D M2 x2 y
 
|sign=y' m2 U' 2R2 2B2 r2 b2 R2 b2 L2 U2 m2 U2 F2 D m2 x2 y
 
|sign=y' m2 U' 2R2 2B2 r2 b2 R2 b2 L2 U2 m2 U2 F2 D m2 x2 y
 
|length=(28,15)|name=|wide=N|author=Doug
 
|length=(28,15)|name=|wide=N|author=Doug
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30921
+
|url=https://web.archive.org/web/20191022173123/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30921?guccounter=1
 
}}
 
}}
{{Alg5|wca=R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2
+
{{Alg6|wca=R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2
 
|sign=R' U R' U' R' U' R' U R U' u2 2R2 u2 2R2 U2 r2
 
|sign=R' U R' U' R' U' R' U R U' u2 2R2 u2 2R2 U2 r2
 
|length=(21,16)|name=SP04
 
|length=(21,16)|name=SP04
Line 1,143: Line 1,382:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U R' U' R2 U R U Rw2 U2 R' Rw U2 R' Rw2 U2 Rw2 U2 Rw U2 Rw2//Safe
+
{{Alg6|wca=R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2
|sign=R2 U R' U' R2 U R U r2 U2 R' r U2 R' r2 U2 r2 U2 r U2 r2//Safe
+
|sign=R' U R' U' R' U' R' U R U' u2 2R2 u2 2R2 U2 r2
 +
|length=(21,16)|name=SP04
 +
|wide=N|author=Stefan Pochmann
 +
|url=
 +
}}
 +
{{Alg6|wca=r2 (U2 r U2 S2)2 Rw2 S2 D' F2 D S2 D' F2 D R2 //Safe
 +
|sign=2R2 (U2 2R U2 s2)2 r2 s2 D' F2 D s2 D' F2 D R2 //Safe
 +
|length=(32,19)|name=|wide=N|author=Walter Randelshofer
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407876#p407876
 +
}}
 +
{{Alg6|wca=R2 U R' U' R2 U R U Rw2 U2 R' Rw U2 R' Rw2 U2 Rw2 U2 Rw U2 Rw2 //Safe
 +
|sign=R2 U R' U' R2 U R U r2 U2 R' r U2 R' r2 U2 r2 U2 r U2 r2 //Safe
 
|length=(30,20)|name=|wide=Y|author=António Gomes
 
|length=(30,20)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
}}
 
}}
{{Alg5|wca=R2 U R' U' R2 U R U R' Rw2 U2 R' Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2//Safe
+
{{Alg6|wca=R2 U R' U' R2 U R U R' Rw2 U2 R' Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 //Safe
|sign=R2 U R' U' R2 U R U R' r2 U2 R' r U2 r2 U2 r2 U2 r U2 r2//Safe
+
|sign=R2 U R' U' R2 U R U R' r2 U2 R' r U2 r2 U2 r2 U2 r U2 r2 //Safe
 
|length=(30,20)|name=|wide=Y|author=António Gomes
 
|length=(30,20)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
}}
 
}}
{{Alg5|wca=R2 U R' U' R2 U R U R' Rw2 U2 R' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2//Safe
+
{{Alg6|wca=R2 U R' U' R2 U R U R' Rw2 U2 R' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 //Safe
|sign=R2 U R' U' R2 U R U R' r2 U2 R' r' U2 r2 U2 r2 U2 r' U2 r2//Safe
+
|sign=R2 U R' U' R2 U R U R' r2 U2 R' r' U2 r2 U2 r2 U2 r' U2 r2 //Safe
 
|length=(31,21)|name=|wide=Y|author=António Gomes
 
|length=(31,21)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
}}
 
}}
{{Alg5|wca=y R2 U' R' U' R U2 Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U R Rw y'
+
{{Alg6|wca=y R2 U' R' U' R U2 Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U R Rw y'
 
|sign=y R2 U' R' U' R U2 r U R r' U' r' U' r U r U' r' U' R r' U R r y'
 
|sign=y R2 U' R' U' R U2 r U R r' U' r' U' r U r U' r' U' R r' U R r y'
 
|length=(24,22)|name=|wide=Y|author=António Gomes
 
|length=(24,22)|name=|wide=Y|author=António Gomes
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/#post-935374
 
}}
 
}}
{{Alg5|wca=y' U' Rw2 U2 Rw' U Rw2 U' Rw2 U Rw' U Rw U Rw' U' Rw' U Rw U Rw' U Rw2 U' Rw2 U Rw U2 Rw2 y
+
{{Alg6|wca=y' U' Rw2 U2 Rw' U Rw2 U' Rw2 U Rw' U Rw U Rw' U' Rw' U Rw U Rw' U Rw2 U' Rw2 U Rw U2 Rw2 y
 
|sign=y' U' r2 U2 r' U r2 U' r2 U r' U r U r' U' r' U r U r' U r2 U' r2 U r U2 r2 y
 
|sign=y' U' r2 U2 r' U r2 U' r2 U r' U r U r' U' r' U r U r' U r2 U' r2 U r U2 r2 y
 
|length=(36,28)|name=|wide=Y|author=Ben Whitmore
 
|length=(36,28)|name=|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 u r2 Uw2 S' U' B R B' R2 U) M' (U' R2 B R' B' U S Uw2 r2 u' r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 u r2 Uw2 S' U' B R B' R2 U) M' (U' R2 B R' B' U S Uw2 r2 u' r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2U 2R2 u2 s' U' B R B' R2 U) m' (U' R2 B R' B' U s u2 2R2 2U' 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2U 2R2 u2 s' U' B R B' R2 U) m' (U' R2 B R' B' U s u2 2R2 2U' 2R2 f2 U' m2)
 
|length=(41,29)|name=|wide=N|author=Christopher Mowla
 
|length=(41,29)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
 
}}
 
}}
 
+
{{br|b=1}}
===Four Dedges (unoriented)===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Four Dedges (unoriented)</span>===
====O permutation====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">O permutation</span>====
=====Oa=====
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Oa</span>=====
 
[[Image:Oa4unoriented.png|110px|]][[Image:Oa_Perm_Diagram_(4_unoriented).png|110px|]]
 
[[Image:Oa4unoriented.png|110px|]][[Image:Oa_Perm_Diagram_(4_unoriented).png|110px|]]
{{Alg5|wca=F2 M F2 U' l2 U2 r2 Uw2 r2 U' Uw2 B2 M B2
+
{{Alg6|wca=F2 M F2 U' l2 U2 r2 Uw2 r2 U' Uw2 B2 M B2
 
|sign=F2 m F2 U' 2L2 U2 2R2 u2 2R2 U' u2 B2 m B2
 
|sign=F2 m F2 U' 2L2 U2 2R2 u2 2R2 U' u2 B2 m B2
 
|length=(23,14)|name=|wide=N|author=Christopher Mowla
 
|length=(23,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' U2 Rw2 U2 r2 Uw2 r2 y Uw2 M U' M2 U' F2 U2 M
+
{{Alg6|wca=y' U2 Rw2 U2 r2 Uw2 r2 y Uw2 M U' M2 U' F2 U2 M
 
|sign=y' U2 r2 U2 2R2 u2 2R2 y u2 m U' m2 U' F2 U2 m
 
|sign=y' U2 r2 U2 2R2 u2 2R2 y u2 m U' m2 U' F2 U2 m
 
|length=(24,14)|name=|wide=N|author=Christopher Mowla
 
|length=(24,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 S' (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S' L2
+
{{Alg6|wca=R2 S' (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S' L2
 
|sign=R2 s' (2U2 2R2 u2 2R2 U2) r2 U' s2 U L2 s' L2
 
|sign=R2 s' (2U2 2R2 u2 2R2 U2) r2 U' s2 U L2 s' L2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350903#p350903
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350903#p350903
 
}}
 
}}
{{Alg5|wca=R2 S (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S L2
+
{{Alg6|wca=R2 S (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S L2
 
|sign=R2 s (2U2 2R2 u2 2R2 U2) r2 U s2 U' L2 s L2
 
|sign=R2 s (2U2 2R2 u2 2R2 U2) r2 U s2 U' L2 s L2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=L2 S L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S R2
+
{{Alg6|wca=L2 S L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S R2
 
|sign=L2 s L2 U s2 U' r2 (U2 2R2 u2 2R2 2U2) s R2
 
|sign=L2 s L2 U s2 U' r2 (U2 2R2 u2 2R2 2U2) s R2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=L2 S' L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S' R2
+
{{Alg6|wca=L2 S' L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S' R2
 
|sign=L2 s' L2 U' s2 U r2 (U2 2R2 u2 2R2 2U2) s' R2
 
|sign=L2 s' L2 U' s2 U r2 (U2 2R2 u2 2R2 2U2) s' R2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D R' L' u' R L D2 R L y M2 u' M2 y' R' L' D M2 //Safe
+
{{Alg6|wca=M2 D R' L' u' R L D2 R L y M2 u' M2 y' R' L' D M2 //Safe
 
|sign=m2 D R' L' 2U' R L D2 R L y m2 2U' m2 y' R' L' D m2 //Safe
 
|sign=m2 D R' L' 2U' R L D2 R L y m2 2U' m2 y' R' L' D m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D R L u R' L' D2 R' L' y M2 u M2 y' R L D M2 //Safe
+
{{Alg6|wca=M2 D R L u R' L' D2 R' L' y M2 u M2 y' R L D M2 //Safe
 
|sign=m2 D R L 2U R' L' D2 R' L' y m2 2U m2 y' R L D m2 //Safe
 
|sign=m2 D R L 2U R' L' D2 R' L' y m2 2U m2 y' R L D m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D' R' L' y M2 d' M2 y' R L D2 R L d' R' L' D' M2 //Safe
+
{{Alg6|wca=M2 D' R' L' y M2 d' M2 y' R L D2 R L d' R' L' D' M2 //Safe
 
|sign=m2 D' R' L' y m2 2D' m2 y' R L D2 R L 2D' R' L' D' m2 //Safe
 
|sign=m2 D' R' L' y m2 2D' m2 y' R L D2 R L 2D' R' L' D' m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D' R L y M2 d M2 y' R' L' D2 R' L' d R L D' M2 //Safe
+
{{Alg6|wca=M2 D' R L y M2 d M2 y' R' L' D2 R' L' d R L D' M2 //Safe
 
|sign=m2 D' R L y m2 2D m2 y' R' L' D2 R' L' 2D R L D' m2 //Safe
 
|sign=m2 D' R L y m2 2D m2 y' R' L' D2 R' L' 2D R L D' m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 U F2 D2 r F2 r2 F2 D2 l2 F2 D2 r2 D2 l U' M2
+
{{Alg6|wca=M2 U F2 D2 r F2 r2 F2 D2 l2 F2 D2 r2 D2 l U' M2
 
|sign=m2 U F2 D2 2R F2 2R2 F2 D2 2L2 F2 D2 2R2 D2 2L U' m2
 
|sign=m2 U F2 D2 2R F2 2R2 F2 D2 2L2 F2 D2 2R2 D2 2L U' m2
 
|length=(30,17)|name=|wide=N|author=Christopher Mowla
 
|length=(30,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2U s' r2 2U2) m' (2U2 r2 s 2U' 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2U s' r2 2U2) m' (2U2 r2 s 2U' 2R2 f2 U' m2)
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 u' S' Rw2 u2) M' (u2 Rw2 S u r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 u' S' Rw2 u2) M' (u2 Rw2 S u r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2U' s' r2 2U2) m' (2U2 r2 s 2U 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2U' s' r2 2U2) m' (2U2 r2 s 2U 2R2 f2 U' m2)
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' Rw2 U' r2 U' Rw' U R' U2 R' U Rw' U' r2 U' Rw2 U' Rw U2
+
{{Alg6|wca=Rw U' Rw2 U' r2 U' Rw' U R' U2 R' U Rw' U' r2 U' Rw2 U' Rw U2
 
|sign=r U' r2 U' 2R2 U' r' U R' U2 R' U r' U' 2R2 U' r2 U' r U2
 
|sign=r U' r2 U' 2R2 U' r' U R' U2 R' U r' U' 2R2 U' r2 U' r U2
 
|length=(26,20)|name=|wide=N|author=xyzzy
 
|length=(26,20)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
}}
 
}}
 
+
{{br|b=1}}
=====Ob=====
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Ob</span>=====
 
[[Image:O_Permutation_(unoriented).png|110px|]][[Image:Ob_Perm_Diagram_(4_unoriented).png|110px|]]
 
[[Image:O_Permutation_(unoriented).png|110px|]][[Image:Ob_Perm_Diagram_(4_unoriented).png|110px|]]
{{Alg5|wca=B2 M' B2 Uw2 U r2 Uw2 r2 U2 l2 U F2 M' F2
+
{{Alg6|wca=B2 M' B2 Uw2 U r2 Uw2 r2 U2 l2 U F2 M' F2
 
|sign=B2 m' B2 u2 U 2R2 u2 2R2 U2 2L2 U F2 m' F2
 
|sign=B2 m' B2 u2 U 2R2 u2 2R2 U2 2L2 U F2 m' F2
 
|length=(23,14)|name=|wide=N|author=Christopher Mowla
 
|length=(23,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M' U2 F2 U M2 U M' Uw2 y' r2 Uw2 r2 U2 Rw2 U2 y
+
{{Alg6|wca=M' U2 F2 U M2 U M' Uw2 y' r2 Uw2 r2 U2 Rw2 U2 y
 
|sign=m' U2 F2 U m2 U m' u2 y' 2R2 u2 2R2 U2 r2 U2 y
 
|sign=m' U2 F2 U m2 U m' u2 y' 2R2 u2 2R2 U2 r2 U2 y
 
|length=(24,14)|name=|wide=N|author=Christopher Mowla
 
|length=(24,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=L2 S L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S R2
+
{{Alg6|wca=L2 S L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S R2
 
|sign=L2 s L2 U' s2 U r2 (U2 2R2 u2 2R2 2U2) s R2
 
|sign=L2 s L2 U' s2 U r2 (U2 2R2 u2 2R2 2U2) s R2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350903#p350903
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350903#p350903
 
}}
 
}}
{{Alg5|wca=L2 S' L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S' R2
+
{{Alg6|wca=L2 S' L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S' R2
 
|sign=L2 s' L2 U s2 U' r2 (U2 2R2 u2 2R2 2U2) s' R2
 
|sign=L2 s' L2 U s2 U' r2 (U2 2R2 u2 2R2 2U2) s' R2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 S' (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S' L2
+
{{Alg6|wca=R2 S' (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S' L2
 
|sign=R2 s' (2U2 2R2 u2 2R2 U2) r2 U s2 U' L2 s' L2
 
|sign=R2 s' (2U2 2R2 u2 2R2 U2) r2 U s2 U' L2 s' L2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 S (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S L2
+
{{Alg6|wca=R2 S (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S L2
 
|sign=R2 s (2U2 2R2 u2 2R2 U2) r2 U' s2 U L2 s L2
 
|sign=R2 s (2U2 2R2 u2 2R2 U2) r2 U' s2 U L2 s L2
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D' L R y M2 u M2 y' L' R' D2 L' R' u L R D' M2//Safe
+
{{Alg6|wca=M2 D' L R y M2 u M2 y' L' R' D2 L' R' u L R D' M2 //Safe
|sign=m2 D' L R y m2 2U m2 y' L' R' D2 L' R' 2U L R D' m2//Safe
+
|sign=m2 D' L R y m2 2U m2 y' L' R' D2 L' R' 2U L R D' m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D' L' R' y M2 u' M2 y' L R D2 L R u' L' R' D' M2//Safe
+
{{Alg6|wca=M2 D' L' R' y M2 u' M2 y' L R D2 L R u' L' R' D' M2 //Safe
|sign=m2 D' L' R' y m2 2U' m2 y' L R D2 L R 2U' L' R' D' m2//Safe
+
|sign=m2 D' L' R' y m2 2U' m2 y' L R D2 L R 2U' L' R' D' m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D L R d L' R' D2 L' R' y M2 d M2 y' L R D M2//Safe
+
{{Alg6|wca=M2 D L R d L' R' D2 L' R' y M2 d M2 y' L R D M2 //Safe
|sign=m2 D L R 2D L' R' D2 L' R' y m2 2D m2 y' L R D m2//Safe
+
|sign=m2 D L R 2D L' R' D2 L' R' y m2 2D m2 y' L R D m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D L' R' d' L R D2 L R y M2 d' M2 y' L' R' D M2//Safe
+
{{Alg6|wca=M2 D L' R' d' L R D2 L R y M2 d' M2 y' L' R' D M2 //Safe
|sign=m2 D L' R' 2D' L R D2 L R y m2 2D' m2 y' L' R' D m2//Safe
+
|sign=m2 D L' R' 2D' L R D2 L R y m2 2D' m2 y' L' R' D m2 //Safe
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 U l' D2 r2 D2 F2 l2 D2 F2 r2 F2 r' D2 F2 U' M2
+
{{Alg6|wca=M2 U l' D2 r2 D2 F2 l2 D2 F2 r2 F2 r' D2 F2 U' M2
 
|sign=m2 U 2L' D2 2R2 D2 F2 2L2 D2 F2 2R2 F2 2R' D2 F2 U' m2
 
|sign=m2 U 2L' D2 2R2 D2 F2 2L2 D2 F2 2R2 F2 2R' D2 F2 U' m2
 
|length=(30,17)|name=|wide=N|author=Christopher Mowla
 
|length=(30,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2U s' r2 2U2) m (2U2 r2 s 2U' 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2U s' r2 2U2) m (2U2 r2 s 2U' 2R2 f2 U' m2)
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 u' S' Rw2 u2) M (u2 Rw2 S u r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 u' S' Rw2 u2) M (u2 Rw2 S u r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2U' s' r2 2U2) m (2U2 r2 s 2U 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2U' s' r2 2U2) m (2U2 r2 s 2U 2R2 f2 U' m2)
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw2 U r2 U Rw U' R U2 R U' Rw U r2 U Rw2 U Rw' U2
+
{{Alg6|wca=Rw' U Rw2 U r2 U Rw U' R U2 R U' Rw U r2 U Rw2 U Rw' U2
 
|sign=r' U r2 U 2R2 U r U' R U2 R U' r U 2R2 U r2 U r' U2
 
|sign=r' U r2 U 2R2 U r U' R U2 R U' r U 2R2 U r2 U r' U2
 
|length=(26,20)|name=|wide=N|author=xyzzy
 
|length=(26,20)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
}}
 
}}
 
+
{{br|b=1}}
====8 permutation====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">B permutation</span>====
[[Image:W_Permutation_(unoriented).png|110px|]][[Image:8_Perm_Diagram_(4_unoriented).png|110px|]]
+
[[Image:W_Permutation_(unoriented).png|110px|]][[Image:B_Perm_unoriented.png|110px|]]
 
+
{{br|b=1}}
 
*Note:  This is commonly called the "W" permutation.
 
*Note:  This is commonly called the "W" permutation.
 
+
*A list of algorithms for the inverse case are unnecessary.  Just do U2 (alg) U2 <i>or</i> y2 (alg) y2.
{{Alg5|wca=y' M2 U' D2 r2 S2 l S2 r2 E2 r' U' M2 y'//Safe
+
{{br|b=1}}
|sign=y' m2 U' D2 2R2 s2 2L s2 2R2 e2 2R' U' m2 y'//Safe
+
{{Alg6|wca=y' M2 U' D2 r2 S2 l S2 r2 E2 r' U' M2 y' //Safe
 +
|sign=y' m2 U' D2 2R2 s2 2L s2 2R2 e2 2R' U' m2 y' //Safe
 
|length=(19,12)|name=|wide=N|author=Christopher Mowla
 
|length=(19,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 U' r U D L2 U D S2 r S2 D' U' L2 D' M2//Safe
+
{{Alg6|wca=M2 U' r U D L2 U D S2 r S2 D' U' L2 D' M2 //Safe
|sign=m2 U' 2R U D L2 U D s2 2R s2 D' U' L2 D' m2//Safe
+
|sign=m2 U' 2R U D L2 U D s2 2R s2 D' U' L2 D' m2 //Safe
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M2 U r' U' D' L2 U' D' S2 r' S2 D U L2 D M2 y'//Safe
+
{{Alg6|wca=y M2 U r' U' D' L2 U' D' S2 r' S2 D U L2 D M2 y' //Safe
|sign=y m2 U 2R' U' D' L2 U' D' s2 2R' s2 D U L2 D m2 y'//Safe
+
|sign=y m2 U 2R' U' D' L2 U' D' s2 2R' s2 D U L2 D m2 y' //Safe
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2 D R2 D U r U' D' R2 U' D' S2 r S2 U M2//Safe
+
{{Alg6|wca=M2 D R2 D U r U' D' R2 U' D' S2 r S2 U M2 //Safe
|sign=m2 D R2 D U 2R U' D' R2 U' D' s2 2R s2 U m2//Safe
+
|sign=m2 D R2 D U 2R U' D' R2 U' D' s2 2R s2 U m2 //Safe
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M2 D' R2 D' U' r' U D R2 U D S2 r' S2 U' M2 y'//Safe
+
{{Alg6|wca=y M2 D' R2 D' U' r' U D R2 U D S2 r' S2 U' M2 y' //Safe
|sign=y m2 D' R2 D' U' 2R' U D R2 U D s2 2R' s2 U' m2 y'//Safe
+
|sign=y m2 D' R2 D' U' 2R' U D R2 U D s2 2R' s2 U' m2 y' //Safe
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U')(r' E2 l E2)3 (U M2)//Safe
+
{{Alg6|wca=(M2 U')(r' E2 l E2)3 (U M2) //Safe
|sign=(m2 U')(2R' e2 2L e2)3 (U m2)//Safe
+
|sign=(m2 U') (2R' e2 2L e2)3 (U m2) //Safe
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U')(E2 r' E2 l)3 (U M2)//Safe
+
{{Alg6|wca=(M2 U')(E2 r' E2 l)3 (U M2) //Safe
|sign=(m2 U')(e2 2R' e2 2L)3 (U m2)//Safe
+
|sign=(m2 U') (e2 2R' e2 2L)3 (U m2) //Safe
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y x' M2 Fw f r2 u r2 S' u2) M (u2 S r2 u' r2 f' Fw' M2 x y')  
+
{{Alg6|wca=(y x' M2 Fw f r2 u r2 S' u2) M (u2 S r2 u' r2 f' Fw' M2 x y')
|sign=(y x' m2 f 2F 2R2 2U 2R2 s' 2U2) m (2U2 s 2R2 2U' 2R2 2F' f' m2 x y')  
+
|sign=(y x' m2 f 2F 2R2 2U 2R2 s' 2U2) m (2U2 s 2R2 2U' 2R2 2F' f' m2 x y')
 
|length=(25,17)|name=|wide=N|author=Christopher Mowla
 
|length=(25,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
 
}}
 
}}
{{Alg5|wca=(y x' M2 Fw f r2 u' r2 S' u2) M (u2 S r2 u r2 f' Fw' M2 x y')  
+
{{Alg6|wca=(y x' M2 Fw f r2 u' r2 S' u2) M (u2 S r2 u r2 f' Fw' M2 x y')
|sign=(y x' m2 f 2F 2R2 2U' 2R2 s' 2U2) m (2U2 s 2R2 2U 2R2 2F' f' m2 x y')  
+
|sign=(y x' m2 f 2F 2R2 2U' 2R2 s' 2U2) m (2U2 s 2R2 2U 2R2 2F' f' m2 x y')
 
|length=(25,17)|name=|wide=N|author=Christopher Mowla
 
|length=(25,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 d r2 Uw2 S') M (S Uw2 r2 d' r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 d r2 Uw2 S') M (S Uw2 r2 d' r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2D 2R2 u2 s') m (s u2 2R2 2D' 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2D 2R2 u2 s') m (s u2 2R2 2D' 2R2 f2 U' m2)
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(M2 U Fw2 r2 d' r2 Uw2 S') M (S Uw2 r2 d r2 Fw2 U' M2)
+
{{Alg6|wca=(M2 U Fw2 r2 d' r2 Uw2 S') M (S Uw2 r2 d r2 Fw2 U' M2)
 
|sign=(m2 U f2 2R2 2D' 2R2 u2 s') m (s u2 2R2 2D 2R2 f2 U' m2)
 
|sign=(m2 U f2 2R2 2D' 2R2 u2 s') m (s u2 2R2 2D 2R2 f2 U' m2)
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
==Two corner swaps==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Two corner swaps</span>==
===Adjacent===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Underscore ( _ ) permutation</span>===
 
[[Image:Adj2crnrsp.png|110px|]]
 
[[Image:Adj2crnrsp.png|110px|]]
{{Alg5|wca=F2 R2 B' D' B R2 F' U Fw2 F L2 f2 Lw2 f2 l2 U'
+
{{Alg6|wca=F2 R2 B' D' B R2 F' U Fw2 F L2 f2 Lw2 f2 l2 U'
 
|sign=F2 R2 B' D' B R2 F' U f2 F L2 2F2 l2 2F2 2L2 U'
 
|sign=F2 R2 B' D' B R2 F' U f2 F L2 2F2 l2 2F2 2L2 U'
 
|length=(24,16)|name=|wide=N|author=Clément Gallet
 
|length=(24,16)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=L' U Lw2 L B2 l2 Bw2 l2 b2 U' L2 F2 R' D' R F2
+
{{Alg6|wca=L' U Lw2 L B2 l2 Bw2 l2 b2 U' L2 F2 R' D' R F2
 
|sign=L' U l2 L B2 2L2 b2 2L2 2B2 U' L2 F2 R' D' R F2
 
|sign=L' U l2 L B2 2L2 b2 2L2 2B2 U' L2 F2 R' D' R F2
 
|length=(24,16)|name=|wide=N|author=Clément Gallet
 
|length=(24,16)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 y
+
{{Alg6|wca=y' B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 y
 
|sign=y' B2 L U L' B2 R D' 2R2 F2 2R2 f2 2R2 2F2 R D R2 y
 
|sign=y' B2 L U L' B2 R D' 2R2 F2 2R2 f2 2R2 2F2 R D R2 y
 
|length=(25,16)|name=PKF10
 
|length=(25,16)|name=PKF10
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050
+
|url=https://web.archive.org/web/20191022173219/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050?guccounter=1
 
}}
 
}}
{{Alg5|wca=R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2
+
{{Alg6|wca=R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2
 
|sign=R U' R B2 L' D L B2 R2 U 2R2 F2 2R2 f2 2R2 2F2
 
|sign=R U' R B2 L' D L B2 R2 U 2R2 F2 2R2 f2 2R2 2F2
 
|length=(25,16)|name=|wide=N|author=|url=
 
|length=(25,16)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 L2 B D B' L2 F U' F f2 U2 L2 b2 L2 U2 f2 U
+
{{Alg6|wca=F2 L2 B D B' L2 F U' F f2 U2 L2 b2 L2 U2 f2 U
 
|sign=F2 L2 B D B' L2 F U' F 2F2 U2 L2 2B2 L2 U2 2F2 U
 
|sign=F2 L2 B D B' L2 F U' F 2F2 U2 L2 2B2 L2 U2 2F2 U
 
|length=(26,17)|name=|wide=N|author=Clément Gallet
 
|length=(26,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R U' 3Lw U2' L' B L U2' 3Lw2' B Lw2 F2 U2' l2' U2' F2 Lw2' x'
+
{{Alg6|wca=R U' 3Lw U2' L' B L U2' 3Lw2' B Lw2 F2 U2' l2' U2' F2 Lw2' x'
 
|sign=R U' 3l U2' L' B L U2' 3l2' B l2 F2 U2' 2L2' U2' F2 l2' x'
 
|sign=R U' 3l U2' L' B L U2' 3l2' B l2 F2 U2' 2L2' U2' F2 l2' x'
 
|length=(27,17)|name=|wide=N|author=Clément Gallet &Christopher Mowla
 
|length=(27,17)|name=|wide=N|author=Clément Gallet &Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(F2 D R2 U' R2 F2 U' F2 U F2 D')(r2 U2 r2 Uw2 r2 u2)
+
{{Alg6|wca=(F2 D R2 U' R2 F2 U' F2 U F2 D')(r2 U2 r2 Uw2 r2 u2)
 
|sign=(F2 D R2 U' R2 F2 U' F2 U F2 D')(2R2 U2 2R2 u2 2R2 2U2)
 
|sign=(F2 D R2 U' R2 F2 U' F2 U F2 D')(2R2 U2 2R2 u2 2R2 2U2)
 
|length=(29,17)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(29,17)|name=|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31048
+
|url=https://web.archive.org/web/20191022173432/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31048?guccounter=1
 
}}
 
}}
{{Alg5|wca=z r2 U2 R' U2 R' U2 R x U2 Rw2 U2 B2' L U2 L' U2 Rw2 U2' z' y'
+
{{Alg6|wca=z r2 U2 R' U2 R' U2 R x U2 Rw2 U2 B2' L U2 L' U2 Rw2 U2' z' y'
 
|sign=z 2R2 U2 R' U2 R' U2 R x U2 r2 U2 B2' L U2 L' U2 r2 U2' z' y'
 
|sign=z 2R2 U2 R' U2 R' U2 R x U2 r2 U2 B2' L U2 L' U2 r2 U2' z' y'
 
|length=(29,17)|name=|wide=N|author=Christopher Mowla
 
|length=(29,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-420187
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-420187
 
}}
 
}}
{{Alg5|wca=z' Rw2 x U2 R' U2 x' U2 R' U2 R U2 L' x U2 Rw2 U2 Rw2 U2 Rw2 x' U2 Rw2 z U
+
{{Alg6|wca=y' R Uw Rw' U' Rw' F r R' Fw' U f r U Rw' Uw' R Uw r Uw' y
 +
|sign=y' R u r' U' r' F 2R R' f' U 2F 2R U r' u' R u 2R u' y
 +
|length=(19,19)|name=|wide=N|author=Ben Whitmore
 +
|url=
 +
}}
 +
{{Alg6|wca=z' Rw2 x U2 R' U2 x' U2 R' U2 R U2 L' x U2 Rw2 U2 Rw2 U2 Rw2 x' U2 Rw2 z U
 
|sign=z' r2 x U2 R' U2 x' U2 R' U2 R U2 L' x U2 r2 U2 r2 U2 r2 x' U2 r2 z U
 
|sign=z' r2 x U2 R' U2 x' U2 R' U2 R U2 L' x U2 r2 U2 r2 U2 r2 x' U2 r2 z U
 
|length=(33,19)|name=|wide=Y|author=Christopher Mowla
 
|length=(33,19)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/#post-406962
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/#post-406962
 
}}
 
}}
{{Alg5|wca=r2 U2 r2 Uw2 r2 u2 y' R U R' U' R' F R2 U' R' U' R U R' F' y
+
{{Alg6|wca=r2 U2 r2 Uw2 r2 u2 y' R U R' U' R' F R2 U' R' U' R U R' F' y
 
|sign=2R2 U2 2R2 u2 2R2 2U2 y' R U R' U' R' F R2 U' R' U' R U R' F' y
 
|sign=2R2 U2 2R2 u2 2R2 2U2 y' R U R' U' R' F R2 U' R' U' R U R' F' y
 
|length=(27,20)|name=|wide=N|author=|url=
 
|length=(27,20)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=y' (R U R' F') U' r2 U2 r2 Uw2 r2 Uw2 U' (R U R' U') R' F R2 U' R' U' y
+
{{Alg6|wca=y' (R U R' F') U' r2 U2 r2 Uw2 r2 Uw2 U' (R U R' U') R' F R2 U' R' U' y
 
|sign=y' (R U R' F') U' 2R2 U2 2R2 u2 2R2 u2 U' (R U R' U') R' F R2 U' R' U' y
 
|sign=y' (R U R' F') U' 2R2 U2 2R2 u2 2R2 u2 U' (R U R' U') R' F R2 U' R' U' y
 
|length=(28,22)|name=|wide=N|author=Stefan Lidström
 
|length=(28,22)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' x Rw2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z
+
{{Alg6|wca=z' x Rw2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z
 
|sign=z' x r2 R' U2 r' U2 r2 U2 r2 U2 L r' U2 R' U2 R U2 L' R U2 R U2 r2 x' z
 
|sign=z' x r2 R' U2 r' U2 r2 U2 r2 U2 L r' U2 R' U2 R U2 L' R U2 R U2 r2 x' z
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-413961
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-413961
 
}}
 
}}
{{Alg5|wca=z' x Rw2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z
+
{{Alg6|wca=z' x Rw2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z
 
|sign=z' x r2 R' U2 r U2 r2 U2 r2 U2 L r U2 R' U2 R U2 L' R U2 R U2 r2 x' z
 
|sign=z' x r2 R' U2 r U2 r2 U2 r2 U2 L r U2 R' U2 R U2 L' R U2 R U2 r2 x' z
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' (Rw U L U' Rw' U L' U' F)9 z
+
{{Alg6|wca=z' (Rw U L U' Rw' U L' U' F)9 z
 
|sign=z' (r U L U' r' U L' U' F)9 z
 
|sign=z' (r U L U' r' U L' U' F)9 z
 
|length=(81,81)|name=|wide=Y|author=Christopher Mowla
 
|length=(81,81)|name=|wide=Y|author=Christopher Mowla
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374983#p374983
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374983#p374983
 
}}
 
}}
 
+
{{br|b=1}}
===Opposite/diagonal===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Slash (\) permutation</span>===
 
[[Image:Diag2cornerswap.png|110px|]]
 
[[Image:Diag2cornerswap.png|110px|]]
{{Alg5|wca=Rw2 f2 U2 Fw2 D Rw2 U2 Fw2 U' Fw2 L2 U2 B2 Lw2 U
+
{{Alg6|wca=Rw2 f2 U2 Fw2 D Rw2 U2 Fw2 U' Fw2 L2 U2 B2 Lw2 U
 
|sign=r2 2F2 U2 f2 D r2 U2 f2 U' f2 L2 U2 B2 l2 U
 
|sign=r2 2F2 U2 f2 D r2 U2 f2 U' f2 L2 U2 B2 l2 U
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=Rw2 f2 U2 Bw2 D' Rw2 U2 Bw2 U Fw2 R2 D2 B2 Lw2 U
+
{{Alg6|wca=Rw2 f2 U2 Bw2 D' Rw2 U2 Bw2 U Fw2 R2 D2 B2 Lw2 U
 
|sign=r2 2F2 U2 b2 D' r2 U2 b2 U f2 R2 D2 B2 l2 U
 
|sign=r2 2F2 U2 b2 D' r2 U2 b2 U f2 R2 D2 B2 l2 U
 
|length=(27,15)|name=v1
 
|length=(27,15)|name=v1
Line 1,469: Line 1,725:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U
+
{{Alg6|wca=Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U
 
|sign=r2 2F2 U2 f2 U' r2 U2 f2 U f2 R2 U2 F2 r2 U
 
|sign=r2 2F2 U2 f2 U' r2 U2 f2 U f2 R2 U2 F2 r2 U
 
|length=(27,15)|name=v2
 
|length=(27,15)|name=v2
 
|wide=N|author=Michael Fung
 
|wide=N|author=Michael Fung
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31349
+
|url=https://web.archive.org/web/20191022173528/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31349?guccounter=1
 
}}
 
}}
{{Alg5|wca=Rw2 f2 D2 Fw2 U' Rw2 U2 Bw2 U Bw2 R2 U2 F2 Rw2 U'
+
{{Alg6|wca=Rw2 f2 D2 Fw2 U' Rw2 U2 Bw2 U Bw2 R2 U2 F2 Rw2 U'
 
|sign=r2 2F2 D2 f2 U' r2 U2 b2 U b2 R2 U2 F2 r2 U'
 
|sign=r2 2F2 D2 f2 U' r2 U2 b2 U b2 R2 U2 F2 r2 U'
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 f2 D2 Fw2 D' Rw2 U2 Bw2 U Bw2 L2 U2 B2 Lw2 U
+
{{Alg6|wca=Rw2 f2 D2 Fw2 D' Rw2 U2 Bw2 U Bw2 L2 U2 B2 Lw2 U
 
|sign=r2 2F2 D2 f2 D' r2 U2 b2 U b2 L2 U2 B2 l2 U
 
|sign=r2 2F2 D2 f2 D' r2 U2 b2 U b2 L2 U2 B2 l2 U
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 f2 D2 Bw2 U Rw2 U2 Fw2 U' Bw2 L2 D2 F2 Rw2 U'
+
{{Alg6|wca=Rw2 f2 D2 Bw2 U Rw2 U2 Fw2 U' Bw2 L2 D2 F2 Rw2 U'
 
|sign=r2 2F2 D2 b2 U r2 U2 f2 U' b2 L2 D2 F2 r2 U'
 
|sign=r2 2F2 D2 b2 U r2 U2 f2 U' b2 L2 D2 F2 r2 U'
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Fw2 r2 D2 Lw2 U Bw2 D2 Lw2 D' Rw2 B2 U2 L2 Bw2 U'
+
{{Alg6|wca=Fw2 r2 D2 Lw2 U Bw2 D2 Lw2 D' Rw2 B2 U2 L2 Bw2 U'
 
|sign=f2 2R2 D2 l2 U b2 D2 l2 D' r2 B2 U2 L2 b2 U'
 
|sign=f2 2R2 D2 l2 U b2 D2 l2 D' r2 B2 U2 L2 b2 U'
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Fw2 r2 D2 Rw2 U Bw2 D2 Rw2 D' Rw2 F2 D2 L2 Bw2 U
+
{{Alg6|wca=Fw2 r2 D2 Rw2 U Bw2 D2 Rw2 D' Rw2 F2 D2 L2 Bw2 U
 
|sign=f2 2R2 D2 r2 U b2 D2 r2 D' r2 F2 D2 L2 b2 U
 
|sign=f2 2R2 D2 r2 U b2 D2 r2 D' r2 F2 D2 L2 b2 U
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|length=(27,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U
+
{{Alg6|wca=Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U
 
|sign=r2 F2 U2 y r2 U' r2 U D l2' U' l2' y' 2R2 U2 F2 r2 U
 
|sign=r2 F2 U2 y r2 U' r2 U D l2' U' l2' y' 2R2 U2 F2 r2 U
 
|length=(27,16)|name=|wide=N|author=Christopher Mowla
 
|length=(27,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-415410
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-415410
 
}}
 
}}
{{Alg5|wca=Rw2 F2 U2 y Lw2' U Lw2' U' D' Rw2 U Rw2 y' r2 U2 F2 Rw2 U
+
{{Alg6|wca=Rw2 F2 U2 y Lw2' U Lw2' U' D' Rw2 U Rw2 y' r2 U2 F2 Rw2 U
 
|sign=r2 F2 U2 y l2' U l2' U' D' r2 U r2 y' 2R2 U2 F2 r2 U
 
|sign=r2 F2 U2 y l2' U l2' U' D' r2 U r2 y' 2R2 U2 F2 r2 U
 
|length=(27,16)|name=|wide=N|author=Christopher Mowla
 
|length=(27,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 L' U2 Lw2 F2 R' D2 R2 U2 B2 R D2 B2 Rw2 U2
+
{{Alg6|wca=r2 F2 L' U2 Lw2 F2 R' D2 R2 U2 B2 R D2 B2 Rw2 U2
 
|sign=2R2 F2 L' U2 l2 F2 R' D2 R2 U2 B2 R D2 B2 r2 U2
 
|sign=2R2 F2 L' U2 l2 F2 R' D2 R2 U2 B2 R D2 B2 r2 U2
 
|length=(29,16)|name=|wide=Y|author=Clément Gallet
 
|length=(29,16)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' z (R2' Uw2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' Uw2' R2 3Dw' R2) Uw2 U2 x
+
{{Alg6|wca=y' z (R2' Uw2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' Uw2' R2 3Dw' R2) Uw2 U2 x
 
|sign=y' z (R2' u2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' u2' R2 (d' 2U) R2) u2 U2 x
 
|sign=y' z (R2' u2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' u2' R2 (d' 2U) R2) u2 U2 x
 
|length=(29,16)|name=reCornerX(BD) v1
 
|length=(29,16)|name=reCornerX(BD) v1
Line 1,521: Line 1,777:
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-532598
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-532598
 
}}
 
}}
{{Alg5|wca=y' U2 Rw2 U2 R U2 F2 R2 F2 R' F2 U2 Rw2 U2 R' F2 r2 y
+
{{Alg6|wca=y' U2 Rw2 U2 R U2 F2 R2 F2 R' F2 U2 Rw2 U2 R' F2 r2 y
 
|sign=y' U2 r2 U2 R U2 F2 R2 F2 R' F2 U2 r2 U2 R' F2 2R2 y
 
|sign=y' U2 r2 U2 R U2 F2 R2 F2 R' F2 U2 r2 U2 R' F2 2R2 y
 
|length=(29,16)|name=reCornerX(BD) v2
 
|length=(29,16)|name=reCornerX(BD) v2
Line 1,527: Line 1,783:
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-531815
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-531815
 
}}
 
}}
{{Alg5|wca=y' Rw' r' S2 U R U' B2 D L' D Lw l D2 F2 Lw l D2 z2 y
+
{{Alg6|wca=y' Rw' r' S2 U R U' B2 D L' D Lw l D2 F2 Lw l D2 z2 y
 
|sign=y' r' 2R' s2 U R U' B2 D L' D l 2L D2 F2 l 2L D2 z2 y
 
|sign=y' r' 2R' s2 U R U' B2 D L' D l 2L D2 F2 l 2L D2 z2 y
 
|length=(22,17)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|length=(22,17)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' R2 D Rw2 U2' B2 r2 B2 U2' Lw2 R U' 3Lw U2 3Rw' U 3Rw U2 x' y
+
{{Alg6|wca=y' R2 D Rw2 U2' B2 r2 B2 U2' Lw2 R U' 3Lw U2 3Rw' U 3Rw U2 x' y
 
|sign=y' R2 D r2 U2' B2 2R2 B2 U2' l2 R U' 3l U2 3r' U 3r U2 x' y
 
|sign=y' R2 D r2 U2' B2 2R2 B2 U2' l2 R U' 3l U2 3r' U 3r U2 x' y
 
|length=(26,17)|name=|wide=N|author=Mario Laurent
 
|length=(26,17)|name=|wide=N|author=Mario Laurent
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-532688
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-532688
 
}}
 
}}
{{Alg5|wca=F2 L' U2 L R U2 R' F2 Lw2 F2 U2 Lw2' L' U2 F2 Lw2 U2
+
{{Alg6|wca=F2 L' U2 L R U2 R' F2 Lw2 F2 U2 Lw2' L' U2 F2 Lw2 U2
 
|sign=F2 L' U2 L R U2 R' F2 l2 F2 U2 l2' L' U2 F2 l2 U2
 
|sign=F2 L' U2 L R U2 R' F2 l2 F2 U2 l2' L' U2 F2 l2 U2
 
|length=(28,17)|name=|wide=Y|author=Clément Gallet
 
|length=(28,17)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 y
+
{{Alg6|wca=y' r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 y
 
|sign=y' 2R2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 r' 2R' U2 F2 r2 U2 y
 
|sign=y' 2R2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 r' 2R' U2 F2 r2 U2 y
 
|length=(30,17)|name=|wide=N|author=Christopher Mowla
 
|length=(30,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2 y
+
{{Alg6|wca=y' r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2 y
 
|sign=y' 2R2 B2 R' U2 r2 U2 B2 R' B2 2R2 U2 r2 B2 U2 R' U2 r2 y
 
|sign=y' 2R2 B2 R' U2 r2 U2 B2 R' B2 2R2 U2 r2 B2 U2 R' U2 r2 y
 
|length=(31,17)|name=|wide=N|author=Christopher Mowla
 
|length=(31,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-530611
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-530611
 
}}
 
}}
{{Alg5|wca=L2 u2 F2 U2 L2 u2 F2 U' F2 L2 U2 L2 U L2 U2 F2 u2 U
+
{{Alg6|wca=L2 u2 F2 U2 L2 u2 F2 U' F2 L2 U2 L2 U L2 U2 F2 u2 U
 
|sign=L2 2U2 F2 U2 L2 2U2 F2 U' F2 L2 U2 L2 U L2 U2 F2 2U2 U
 
|sign=L2 2U2 F2 U2 L2 2U2 F2 U' F2 L2 U2 L2 U L2 U2 F2 2U2 U
 
|length=(32,18)|name=|wide=N|author=Clément Gallet
 
|length=(32,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' R Rw2 F2 L U L' B D L D' B2 U B r2 U2 F2 Rw2 R' U2 y
+
{{Alg6|wca=y' R Rw2 F2 L U L' B D L D' B2 U B r2 U2 F2 Rw2 R' U2 y
 
|sign=y' R r2 F2 L U L' B D L D' B2 U B 2R2 U2 F2 r2 R' U2 y
 
|sign=y' R r2 F2 L U L' B D L D' B2 U B 2R2 U2 F2 r2 R' U2 y
 
|length=(25,19)|name=FB14
 
|length=(25,19)|name=FB14
Line 1,563: Line 1,819:
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
|url=http://frederickbadie.free.fr/444PLLparity.html
 
}}
 
}}
{{Alg5|wca=y' r2 U2 r2 Uw2 r2 Uw2 L' U R' U2 L U' L' R U R' U2 L U' R U y
+
{{Alg6|wca=y' r2 U2 r2 Uw2 r2 Uw2 L' U R' U2 L U' L' R U R' U2 L U' R U y
 
|sign=y' 2R2 U2 2R2 u2 2R2 u2 L' U R' U2 L U' L' R U R' U2 L U' R U y
 
|sign=y' 2R2 U2 2R2 u2 2R2 u2 L' U R' U2 L U' L' R U R' U2 L U' R U y
 
|length=(29,21)|name=|wide=N|author=|url=
 
|length=(29,21)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R U2 R U2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' Rw2
+
{{Alg6|wca=Rw2 R U2 R U2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' Rw2
 
|sign=r2 R U2 R U2 R' U2 r U2 r2 U2 r2 U2 L r U2 R' U2 R U2 L' r2
 
|sign=r2 R U2 R U2 R' U2 r U2 r2 U2 r2 U2 L r U2 R' U2 R U2 L' r2
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R U2 R U2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' Rw2
+
{{Alg6|wca=Rw2 R U2 R U2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' Rw2
 
|sign=r2 R U2 R U2 R' U2 r' U2 r2 U2 r2 U2 L r' U2 R' U2 R U2 L' r2
 
|sign=r2 R U2 R U2 R' U2 r' U2 r2 U2 r2 U2 L r' U2 R' U2 R U2 L' r2
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-413961
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-413961
 
}}
 
}}
{{Alg5|wca=l2 U2 F2 l R U2 R' U2 L2 F2 L F2 Lw F2 U2 Lw2 U2 F2 U2 F2 L' U2
+
{{Alg6|wca=l2 U2 F2 l R U2 R' U2 L2 F2 L F2 Lw F2 U2 Lw2 U2 F2 U2 F2 L' U2
 
|sign=2L2 U2 F2 2L R U2 R' U2 L2 F2 L F2 l F2 U2 l2 U2 F2 U2 F2 L' U2
 
|sign=2L2 U2 F2 2L R U2 R' U2 L2 F2 L F2 l F2 U2 l2 U2 F2 U2 F2 L' U2
 
|length=(38,22)|name=|wide=N|author=Christopher Mowla
 
|length=(38,22)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-774005
 
|url=https://www.speedsolving.com/forum/threads/new-two-corner-swap-algorithm-technique-for-big-even-cubes-pll-parity.21725/page-2#post-774005
 
}}
 
}}
{{Alg5|wca=(F R U') (R' U' R U) (R' F') U r2 U2 r2 Uw2 r2 Uw2 U (R U R' U') (R' F R F')
+
{{Alg6|wca=(F R U') (R' U' R U) (R' F') U r2 U2 r2 Uw2 r2 Uw2 U (R U R' U') (R' F R F')
 
|sign=(F R U') (R' U' R U) (R' F') U 2R2 U2 2R2 u2 2R2 u2 U (R U R' U') (R' F R F')
 
|sign=(F R U') (R' U' R U) (R' F') U 2R2 U2 2R2 u2 2R2 u2 U (R U R' U') (R' F R F')
 
|length=(30,25)|name=|wide=N|author=Stefan Lidström
 
|length=(30,25)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F' (Rw U' L' U Rw' U' L U2)9 F
+
{{Alg6|wca=F' (Rw U' L' U Rw' U' L U2)9 F
 
|sign=F' (r U' L' U r' U' L U2)9 F
 
|sign=F' (r U' L' U r' U' L U2)9 F
 
|length=(83,74)|name=|wide=N|author=Christopher Mowla
 
|length=(83,74)|name=|wide=N|author=Christopher Mowla
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374983#p374983
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374983#p374983
 
}}
 
}}
 +
{{br|b=1}}
  
==Two corner swaps (only 2 supercube center piece exchange)==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Two corner swaps (only 2 supercube center piece exchange)</span>==
===Adjacent===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Underscore ( _ ) permutation</span>===
 
[[Image:Adj2crnrsp.png|110px|]]
 
[[Image:Adj2crnrsp.png|110px|]]
{{Alg5|wca=U Rw2 Bw2 Rw F Rw' Bw2 Rw F' L2 r U' b2 U L' F' L U' b2 U L' F M x
+
{{Alg6|wca=x' Uw l S' D2 B d2 B' D2 S L F l2 F' D' Fw' D' Fw D2 Lw' Uw' Rw F' Lw'
 +
|sign=x' u 2L s' D2 B 2D2 B' D2 s L F 2L2 F' D' f' D' f D2 l' u' r F' l'
 +
|length=(28,23)|name=|wide=N|author=Tom Rokicki
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=410523#p410523
 +
}}
 +
{{Alg6|wca=U Rw2 Bw2 Rw F Rw' Bw2 Rw F' L2 r U' b2 U L' F' L U' b2 U L' F M x
 
|sign=U r2 b2 r F r' b2 r F' L2 2R U' 2B2 U L' F' L U' 2B2 U L' F m x
 
|sign=U r2 b2 r F r' b2 r F' L2 2R U' 2B2 U L' F' L U' 2B2 U L' F m x
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4-algorithm.4659/page-2#post-436800
 
|url=https://www.speedsolving.com/forum/threads/4x4-algorithm.4659/page-2#post-436800
 
}}
 
}}
{{Alg5|wca=z' Fw' L2 Uw F' U R U' F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L z
+
{{Alg6|wca=z' Fw' L2 Uw F' U R U' F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L z
 
|sign=z' f' L2 u F' U R U' F 2R2 F' U R' U' F 2R2 f u' L u f' u' L f L z
 
|sign=z' f' L2 u F' U R U' F 2R2 F' U R' U' F 2R2 f u' L u f' u' L f L z
 
|length=(27,24)|name=|wide=N|author=Christopher Mowla
 
|length=(27,24)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' Fw' L2 Uw r2 F' U R U' F r2 F' U R' U' F Fw Uw' L Uw Fw' Uw' L Fw L z
+
{{Alg6|wca=z' Fw' L2 Uw r2 F' U R U' F r2 F' U R' U' F Fw Uw' L Uw Fw' Uw' L Fw L z
 
|sign=z' f' L2 u 2R2 F' U R U' F 2R2 F' U R' U' F f u' L u f' u' L f L z
 
|sign=z' f' L2 u 2R2 F' U R U' F 2R2 F' U R' U' F f u' L u f' u' L f L z
 
|length=(27,24)|name=|wide=N|author=Christopher Mowla
 
|length=(27,24)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' (Rw' R2 U' R' U R' Rw U' R U2' R' U' R' Rw U R Rw' U' Rw' F Rw2 U' Rw' U') (Rw U Rw' F') y
+
{{Alg6|wca=y' (Rw' R2 U' R' U R' Rw U' R U2' R' U' R' Rw U R Rw' U' Rw' F Rw2 U' Rw' U') (Rw U Rw' F') y
 
|sign=y' (r' R2 U' R' U R' r U' R U2' R' U' R' r U R r' U' r' F r2 U' r' U') (r U r' F') y
 
|sign=y' (r' R2 U' R' U R' r U' R U2' R' U' R' r U R r' U' r' F r2 U' r' U') (r U r' F') y
 
|length=(27,25)|name=|wide=Y|author=Robert Yau
 
|length=(27,25)|name=|wide=Y|author=Robert Yau
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' Rw' F Rw2 U' Rw' U' y
+
{{Alg6|wca=y' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' Rw' F Rw2 U' Rw' U' y
 
|sign=y' r' U' R U 2R U' R' U R2 U R' U' 2R U 2R' F' r U r' U' r' F r2 U' r' U' y
 
|sign=y' r' U' R U 2R U' R' U R2 U R' U' 2R U 2R' F' r U r' U' r' F r2 U' r' U' y
 
|length=(28,26)|name=|wide=N|author=Robert Yau
 
|length=(28,26)|name=|wide=N|author=Robert Yau
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771910
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771910
 
}}
 
}}
{{Alg5|wca=y' Rw' U' R U r U' R' U R2 U R' U' r U r' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' y
+
{{Alg6|wca=y' Rw' U' R U r U' R' U R2 U R' U' r U r' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' y
 
|sign=y' r' U' R U 2R U' R' U R2 U R' U' 2R U 2R' U' r' F r2 U' r' U' r U r' F' y
 
|sign=y' r' U' R U 2R U' R' U R2 U R' U' 2R U 2R' U' r' F r2 U' r' U' r U r' F' y
 
|length=(28,26)|name=|wide=N|author=Robert Yau
 
|length=(28,26)|name=|wide=N|author=Robert Yau
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771910
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771910
 
}}
 
}}
{{Alg5|wca=y' Rw' U' R U r U' R' U R2 U R' U' r U R U' Lw Uw2 Rw' U' Rw Dw2 Rw' U Rw' F' x y'
+
{{Alg6|wca=y' Rw' U' R U r U' R' U R2 U R' U' r U R U' Lw Uw2 Rw' U' Rw Dw2 Rw' U Rw' F' x y'
 
|sign=y' r' U' R U 2R U' R' U R2 U R' U' 2R U R U' l u2 r' U' r d2 r' U r' F' x y'
 
|sign=y' r' U' R U 2R U' R' U R2 U R' U' 2R U R U' l u2 r' U' r d2 r' U r' F' x y'
 
|length=(29,26)|name=|wide=N|author=Robert Yau
 
|length=(29,26)|name=|wide=N|author=Robert Yau
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771910
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771910
 
}}
 
}}
{{Alg5|wca=U Rw2 Bw2 Rw F Rw' Bw2 Rw F' D' f' D F2 D' f D F2 Rw L F' L' f' L F L' f
+
{{Alg6|wca=U Rw2 Bw2 Rw F Rw' Bw2 Rw F' D' f' D F2 D' f D F2 Rw L F' L' f' L F L' f
 
|sign=U r2 b2 r F r' b2 r F' D' 2F' D F2 D' 2F D F2 r L F' L' 2F' L F L' 2F
 
|sign=U r2 b2 r F r' b2 r F' D' 2F' D F2 D' 2F D F2 r L F' L' 2F' L F L' 2F
 
|length=(31,26)|name=|wide=N|author=Chris Hardwick
 
|length=(31,26)|name=|wide=N|author=Chris Hardwick
 
|url=https://www.speedsolving.com/forum/threads/4x4-algorithm.4659/page-2#post-207072
 
|url=https://www.speedsolving.com/forum/threads/4x4-algorithm.4659/page-2#post-207072
 
}}
 
}}
{{Alg5|wca=y' Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' R' F' r' F R F' r2 B' R B r' B' R' B y
+
{{Alg6|wca=y' Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' R' F' r' F R F' r2 B' R B r' B' R' B y
 
|sign=y' r U r' U' r' F r2 U' r' U' r U r' R' F' 2R' F R F' 2R2 B' R B 2R' B' R' B y
 
|sign=y' r U r' U' r' F r2 U' r' U' r U r' R' F' 2R' F R F' 2R2 B' R B 2R' B' R' B y
 
|length=(29,27)|name=|wide=N|author=|url=
 
|length=(29,27)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=y' Rw U R' U' r' U R U' R2 U' R U r' U' R' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U y
+
{{Alg6|wca=y' Rw U R' U' r' U R U' R2 U' R U r' U' R' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U y
 
|sign=y' r U R' U' 2R' U R U' R2 U' R U 2R' U' R' l U l' U' r U l U' l' r' U r U y
 
|sign=y' r U R' U' 2R' U R U' R2 U' R U 2R' U' R' l U l' U' r U l U' l' r' U r U y
 
|length=(29,28)|name=|wide=N|author=Christopher Mowla
 
|length=(29,28)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771998
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771998
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Slash (\) permutation</span>===
===Opposite/diagonal===
 
 
[[Image:Diag2cornerswap.png|110px|]]
 
[[Image:Diag2cornerswap.png|110px|]]
{{Alg5|wca=F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L Fw' L2 Uw F' U R U'
+
{{Alg6|wca=F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L Fw' L2 Uw F' U R U'
 
|sign=F 2R2 F' U R' U' F 2R2 f u' L u f' u' L f L f' L2 u F' U R U'
 
|sign=F 2R2 F' U R' U' F 2R2 f u' L u f' u' L f L f' L2 u F' U R U'
 
|length=(27,24)|name=|wide=N|author=Christopher Mowla
 
|length=(27,24)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F Rw' F Rw2 U' Rw' U' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' F'
+
{{Alg6|wca=Fw R Fw' U' Fw2 Rw2 Fw' R' Fw Rw2 Fw' U2 R2 U Fw L2 Fw' U' R2 U' R' Fw L2 Fw2
 +
|sign=f R f' U' f2 r2 f' R' f r2 f' U2 R2 U f L2 f' U' R2 U' R' f L2 f2
 +
|length=(33,24)|name=|wide=N|author=Tom Rokicki
 +
|url=http://twistypuzzles.com/forum/viewtopic.php?p=410552#p410552
 +
}}
 +
{{Alg6|wca=F Rw' F Rw2 U' Rw' U' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' F'
 
|sign=F r' F r2 U' r' U' r' U' R U 2R U' R' U R2 U R' U' 2R U 2R' F' r U r' U' F'
 
|sign=F r' F r2 U' r' U' r' U' R U 2R U' R' U R2 U R' U' 2R U 2R' F' r U r' U' F'
 
|length=(30,28)|name=|wide=N|author=Robert Yau
 
|length=(30,28)|name=|wide=N|author=Robert Yau
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771998
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771998
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Two X-center piece swap algorithms</span>===
===Two X-center piece swap algorithms===
 
 
[[Image:2xcentpswp.png|110px|]]
 
[[Image:2xcentpswp.png|110px|]]
 
*These algorithms, and other algorithms like them, are used to make two corner swap algorithms which only swap two X-center pieces on the 4x4x4 supercube.
 
*These algorithms, and other algorithms like them, are used to make two corner swap algorithms which only swap two X-center pieces on the 4x4x4 supercube.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=y Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U y'
{{Alg5|wca=y Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U y'
 
 
|sign=y r U' l u2 r' U r u2 x r2 U y'
 
|sign=y r U' l u2 r' U r u2 x r2 U y'
 
|length=(13,10)|name=|wide=Y|author=|url=
 
|length=(13,10)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U'
+
{{Alg6|wca=Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U'
 
|sign=f' U' r f r' U' r f' r' U2 f U'
 
|sign=f' U' r f r' U' r f' r' U2 f U'
 
|length=(13,12)|name=|wide=Y|author=Christopher Mowla
 
|length=(13,12)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'
+
{{Alg6|wca=Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'
 
|sign=r U r' U' r' F r2 U' r' U' r U r' F'
 
|sign=r U r' U' r' F r2 U' r' U' r U r' F'
 
|length=(15,14)|name=|wide=Y|author=|url=
 
|length=(15,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U
+
{{Alg6|wca=Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U
 
|sign=r' U' l U l' U' r U l U' l' r' U r U
 
|sign=r' U' l U l' U' r U l U' l' r' U r U
 
|length=(15,15)|name=|wide=Y|author=Christopher Mowla
 
|length=(15,15)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Two corner swap and a dedge 3-cycle</span>==
==Two corner swap and a dedge 3-cycle==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">D permutation</span>===
===D permutation===
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Da</span>====
====Da====
 
 
[[Image:PLL_Parity13.png|110px|]][[Image:Da Perm Diagram.png|110px|]]
 
[[Image:PLL_Parity13.png|110px|]][[Image:Da Perm Diagram.png|110px|]]
{{Alg5|wca=z2 F2 R2 Dw2 F2 U' R2 Uw2 U R2 U F2 Uw2 U M2 F2 U'
+
{{Alg6|wca=z2 F2 R2 Dw2 F2 U' R2 Uw2 U R2 U F2 Uw2 U M2 F2 U'
 
|sign=z2 F2 R2 d2 F2 U' R2 u2 U R2 U F2 u2 U m2 F2 U'
 
|sign=z2 F2 R2 d2 F2 U' R2 u2 U R2 U F2 u2 U m2 F2 U'
 
|length=(25,16)|name=|wide=Y|author=Clément Gallet
 
|length=(25,16)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 U Rw2 U' B2 U' F2 U B2 U' r2 F2 U2 Rw2 U' F2 U'
+
{{Alg6|wca=F2 U Rw2 U' B2 U' F2 U B2 U' r2 F2 U2 Rw2 U' F2 U'
 
|sign=F2 U r2 U' B2 U' F2 U B2 U' 2R2 F2 U2 r2 U' F2 U'
 
|sign=F2 U r2 U' B2 U' F2 U B2 U' 2R2 F2 U2 r2 U' F2 U'
 
|length=(27,17)|name=FB07
 
|length=(27,17)|name=FB07
Line 1,701: Line 1,965:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 U' R2 b2 l2 Fw2 l2 F2 r2 L D L' B2 L D' L' F2 R2
+
{{Alg6|wca=y2 U' R2 b2 l2 Fw2 l2 F2 r2 L D L' B2 L D' L' F2 R2
 
|sign=y2 U' R2 2B2 2L2 f2 2L2 F2 2R2 L D L' B2 L D' L' F2 R2
 
|sign=y2 U' R2 2B2 2L2 f2 2L2 F2 2R2 L D L' B2 L D' L' F2 R2
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 U' f2 D2 L2 b2 D' R2 D L2 D' R2 D' f2 U R2 U'
+
{{Alg6|wca=R2 U' f2 D2 L2 b2 D' R2 D L2 D' R2 D' f2 U R2 U'
 
|sign=R2 U' 2F2 D2 L2 2B2 D' R2 D L2 D' R2 D' 2F2 U R2 U'
 
|sign=R2 U' 2F2 D2 L2 2B2 D' R2 D L2 D' R2 D' 2F2 U R2 U'
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 U' Uw' R U R' Uw' Rw2 U2' Rw2 R D' R U R' D R U Rw2 Uw R U' R' Uw y2
+
{{Alg6|wca=y2 U' Uw' R U R' Uw' Rw2 U2' Rw2 R D' R U R' D R U Rw2 Uw R U' R' Uw y2
 
|sign=y2 U' u' R U R' u' r2 U2 r2 R D' R U R' D R U r2 u R U' R' u y2
 
|sign=y2 U' u' R U R' u' r2 U2 r2 R D' R U R' D R U r2 u R U' R' u y2
 
|length=(27,23)|name=|wide=N|author=xyzzy
 
|length=(27,23)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
}}
 
}}
 
+
{{br|b=1}}
====Db====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Db</span>====
 
[[Image:PLL_Parity12.png|110px|]][[Image:Db_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity12.png|110px|]][[Image:Db_Perm_Diagram.png|110px|]]
{{Alg5|wca=U F2 M2 Uw2 U' F2 U' R2 Uw2 U' R2 U F2 Dw2 R2 F2 z2
+
{{Alg6|wca=U F2 M2 Uw2 U' F2 U' R2 Uw2 U' R2 U F2 Dw2 R2 F2 z2
 
|sign=U F2 m2 u2 U' F2 U' R2 u2 U' R2 U F2 d2 R2 F2 z2
 
|sign=U F2 m2 u2 U' F2 U' R2 u2 U' R2 U F2 d2 R2 F2 z2
 
|length=(25,16)|name=|wide=Y|author=Clément Gallet
 
|length=(25,16)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U F2 U Rw2 U2 F2 r2 U B2 U' F2 U B2 U Rw2 U' F2
+
{{Alg6|wca=U F2 U Rw2 U2 F2 r2 U B2 U' F2 U B2 U Rw2 U' F2
 
|sign=U F2 U r2 U2 F2 2R2 U B2 U' F2 U B2 U r2 U' F2
 
|sign=U F2 U r2 U2 F2 2R2 U B2 U' F2 U B2 U r2 U' F2
 
|length=(27,17)|name=FB07
 
|length=(27,17)|name=FB07
Line 1,730: Line 1,994:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 F2 L D L' B2 L D' L' r2 F2 l2 Fw2 l2 b2 R2 U y2
+
{{Alg6|wca=R2 F2 L D L' B2 L D' L' r2 F2 l2 Fw2 l2 b2 R2 U y2
 
|sign=R2 F2 L D L' B2 L D' L' 2R2 F2 2L2 f2 2L2 2B2 R2 U y2
 
|sign=R2 F2 L D L' B2 L D' L' 2R2 F2 2L2 f2 2L2 2B2 R2 U y2
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U R2 U' f2 D R2 D L2 D' R2 D b2 L2 D2 f2 U R2
+
{{Alg6|wca=U R2 U' f2 D R2 D L2 D' R2 D b2 L2 D2 f2 U R2
 
|sign=U R2 U' 2F2 D R2 D L2 D' R2 D 2B2 L2 D2 2F2 U R2
 
|sign=U R2 U' 2F2 D R2 D L2 D' R2 D 2B2 L2 D2 2F2 U R2
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|length=(27,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 Uw' R U R' Uw' Rw2 U' R' D' R U' R' D R' Rw2 U2 Rw2 Uw R U' R' Uw U y2
+
{{Alg6|wca=y2 Uw' R U R' Uw' Rw2 U' R' D' R U' R' D R' Rw2 U2 Rw2 Uw R U' R' Uw U y2
 
|sign=y2 u' R U R' u' r2 U' R' D' R U' R' D R' r2 U2 r2 u R U' R' u U y2
 
|sign=y2 u' R U R' u' r2 U' R' D' R U' R' D R' r2 U2 r2 u R U' R' u U y2
 
|length=(27,23)|name=|wide=N|author=xyzzy
 
|length=(27,23)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
 
}}
 
}}
 
+
{{br|b=1}}
===K permutation===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">K permutation</span>===
====Ka====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Ka</span>====
 
[[Image:PLL_Parity10.png|110px|]][[Image:Ka_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity10.png|110px|]][[Image:Ka_Perm_Diagram.png|110px|]]
{{Alg5|wca=U R U' L U2 R' U L l2 F2 Lw2 Fw2 l2 Fw2
+
{{Alg6|wca=U R U' L U2 R' U L l2 F2 Lw2 Fw2 l2 Fw2
 
|sign=U R U' L U2 R' U L 2L2 F2 l2 f2 2L2 f2
 
|sign=U R U' L U2 R' U L 2L2 F2 l2 f2 2L2 f2
 
|length=(20,14)|name=|wide=N|author=Clément Gallet
 
|length=(20,14)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw2 R2 D B2 Dw2 D' B2 D' R2 Dw2 D' B2 L2 U' L2
+
{{Alg6|wca=Dw2 R2 D B2 Dw2 D' B2 D' R2 Dw2 D' B2 L2 U' L2
 
|sign=d2 R2 D B2 d2 D' B2 D' R2 d2 D' B2 L2 U' L2
 
|sign=d2 R2 D B2 d2 D' B2 D' R2 d2 D' B2 L2 U' L2
 
|length=(23,15)|name=|wide=Y|author=Clément Gallet
 
|length=(23,15)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=u2 r2 Uw2 r2 U2 Rw2 D R D' R F2 L' U L F2
+
{{Alg6|wca=u2 r2 Uw2 r2 U2 Rw2 D R D' R F2 L' U L F2
 
|sign=2U2 2R2 u2 2R2 U2 r2 D R D' R F2 L' U L F2
 
|sign=2U2 2R2 u2 2R2 U2 r2 D R D' R F2 L' U L F2
 
|length=(23,15)|name=PKF06
 
|length=(23,15)|name=PKF06
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050
+
|url=https://web.archive.org/web/20191022173219/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050?guccounter=1
 
}}
 
}}
{{Alg5|wca=d2 D' B2 L2 U d2 L2 D' B2 U R2 U R2 Dw2 L2
+
{{Alg6|wca=d2 D' B2 L2 U d2 L2 D' B2 U R2 U R2 Dw2 L2
 
|sign=2D2 D' B2 L2 U 2D2 L2 D' B2 U R2 U R2 d2 L2
 
|sign=2D2 D' B2 L2 U 2D2 L2 D' B2 U R2 U R2 d2 L2
 
|length=(24,15)|name=|wide=N|author=Clément Gallet
 
|length=(24,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y (Rw2' D' Rw U2 Rw' D Rw U2 Rw) U (Rw U2 Rw D Rw' U2 Rw D' Rw2') U2 y'  
+
{{Alg6|wca=y (Rw2' D' Rw U2 Rw' D Rw U2 Rw) U (Rw U2 Rw D Rw' U2 Rw D' Rw2') U2 y'
 
|sign=y (r2' D' r U2 r' D r U2 r) U (r U2 r D r' U2 r D' r2') U2 y'
 
|sign=y (r2' D' r U2 r' D r U2 r) U (r U2 r D r' U2 r D' r2') U2 y'
 
|length=(27,20)|name=|wide=Y|author=Daniel Sheppard
 
|length=(27,20)|name=|wide=Y|author=Daniel Sheppard
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-83#post-1049939
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-83#post-1049939
 
}}
 
}}
{{Alg5|wca=R U R' F' R U R' U' R' F R2 U' R' U (r2 U2 r2 Uw2 r2 Uw2)
+
{{Alg6|wca=R U R' F' R U R' U' R' F R2 U' R' U (r2 U2 r2 Uw2 r2 Uw2)
 
|sign=R U R' F' R U R' U' R' F R2 U' R' U (2R2 U2 2R2 u2 2R2 u2)
 
|sign=R U R' F' R U R' U' R' F R2 U' R' U (2R2 U2 2R2 u2 2R2 u2)
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Kb</span>====
====Kb====
 
 
[[Image:PLL_Parity11.png|110px|]][[Image:Kb_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity11.png|110px|]][[Image:Kb_Perm_Diagram.png|110px|]]
{{Alg5|wca=Fw2 l2 Fw2 Lw2 F2 l2 L' U' R U2 L' U R' U'
+
{{Alg6|wca=Fw2 l2 Fw2 Lw2 F2 l2 L' U' R U2 L' U R' U'
 
|sign=f2 2L2 f2 l2 F2 2L2 L' U' R U2 L' U R' U'
 
|sign=f2 2L2 f2 l2 F2 2L2 L' U' R U2 L' U R' U'
 
|length=(20,14)|name=|wide=N|author=Clément Gallet
 
|length=(20,14)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=L2 U L2 B2 Dw2 D R2 D B2 Dw2 D B2 D' R2 Dw2
+
{{Alg6|wca=L2 U L2 B2 Dw2 D R2 D B2 Dw2 D B2 D' R2 Dw2
 
|sign=L2 U L2 B2 d2 D R2 D B2 d2 D B2 D' R2 d2
 
|sign=L2 U L2 B2 d2 D R2 D B2 d2 D B2 D' R2 d2
 
|length=(23,15)|name=|wide=Y|author=Clément Gallet
 
|length=(23,15)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 L' U' L F2 R' D R' D' Rw2 U2 r2 Uw2 r2 u2
+
{{Alg6|wca=F2 L' U' L F2 R' D R' D' Rw2 U2 r2 Uw2 r2 u2
 
|sign=F2 L' U' L F2 R' D R' D' r2 U2 2R2 u2 2R2 2U2
 
|sign=F2 L' U' L F2 R' D R' D' r2 U2 2R2 u2 2R2 2U2
 
|length=(23,15)|name=PKF06
 
|length=(23,15)|name=PKF06
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050
+
|url=https://web.archive.org/web/20191022173219/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050?guccounter=1
 
}}
 
}}
{{Alg5|wca=L2 Dw2 R2 U' R2 U' B2 D L2 d2 U' L2 B2 D d2
+
{{Alg6|wca=L2 Dw2 R2 U' R2 U' B2 D L2 d2 U' L2 B2 D d2
 
|sign=L2 d2 R2 U' R2 U' B2 D L2 2D2 U' L2 B2 D 2D2
 
|sign=L2 d2 R2 U' R2 U' B2 D L2 2D2 U' L2 B2 D 2D2
 
|length=(24,15)|name=|wide=N|author=Clément Gallet
 
|length=(24,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' (Rw2 D Rw' U2 Rw D' Rw' U2 Rw') U' (Rw' U2 Rw' D' Rw U2 Rw' D Rw2') y U2
+
{{Alg6|wca=y' (Rw2 D Rw' U2 Rw D' Rw' U2 Rw') U' (Rw' U2 Rw' D' Rw U2 Rw' D Rw2') y U2
 
|sign=y' (r2 D r' U2 r D' r' U2 r') U' (r' U2 r' D' r U2 r' D r2') y U2
 
|sign=y' (r2 D r' U2 r D' r' U2 r') U' (r' U2 r' D' r U2 r' D r2') y U2
 
|length=(27,20)|name=|wide=Y|author=Daniel Sheppard
 
|length=(27,20)|name=|wide=Y|author=Daniel Sheppard
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-83#post-1049939
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-83#post-1049939
 
}}
 
}}
{{Alg5|wca=(r2 U2 r2 Uw2 r2 Uw2 U2) R U R' F' R U R' U' R' F R2 U' R' U'
+
{{Alg6|wca=(r2 U2 r2 Uw2 r2 Uw2 U2) R U R' F' R U R' U' R' F R2 U' R' U'
 
|sign=(2R2 U2 2R2 u2 2R2 u2 U2) R U R' F' R U R' U' R' F R2 U' R' U'
 
|sign=(2R2 U2 2R2 u2 2R2 u2 U2) R U R' F' R U R' U' R' F R2 U' R' U'
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">P permutation</span>===
===P permutation===
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Pa</span>====
====Pa====
 
 
[[Image:PLL_Parity8.png|110px|]][[Image:Pa_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity8.png|110px|]][[Image:Pa_Perm_Diagram.png|110px|]]
{{Alg5|wca=U' z' U2 B2 Lw2 U2 L' B2 Lw2' L B2 L U2 Lw2' L U2 z
+
{{Alg6|wca=U' z' U2 B2 Lw2 U2 L' B2 Lw2' L B2 L U2 Lw2' L U2 z
 
|sign=U' z' U2 B2 l2 U2 L' B2 l2' L B2 L U2 l2' L U2 z
 
|sign=U' z' U2 B2 l2 U2 L' B2 l2' L B2 L U2 l2' L U2 z
 
|length=(23,15)|name=CG05
 
|length=(23,15)|name=CG05
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=y U L2 3Uw' L2 U L2 y u2 l2 Uw2 l2 U2 Lw2 3Uw L2 U' L2 y2
+
{{Alg6|wca=y U L2 3Uw' L2 U L2 y u2 l2 Uw2 l2 U2 Lw2 3Uw L2 U' L2 y2
 
|sign=y U L2 3u' L2 U L2 y 2U2 2L2 u2 2L2 U2 l2 3u L2 U' L2 y2
 
|sign=y U L2 3u' L2 U L2 y 2U2 2L2 u2 2L2 U2 l2 3u L2 U' L2 y2
 
|length=(27,16)|name=
 
|length=(27,16)|name=
 
|wide=N|author=Stefan Pochmann
 
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
+
|url=https://web.archive.org/web/20191022173629/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347?guccounter=1
 
}}
 
}}
{{Alg5|wca=R2 U R2 U' R2 F2 U' (Fw2 r2)2 F2 r2 D R2 D'
+
{{Alg6|wca=R2 U R2 U' R2 F2 U' (Fw2 r2)2 F2 r2 D R2 D'
 
|sign=R2 U R2 U' R2 F2 U' (f2 2R2)2 F2 2R2 D R2 D'
 
|sign=R2 U R2 U' R2 F2 U' (f2 2R2)2 F2 2R2 D R2 D'
 
|length=(27,16)|name=PKF05
 
|length=(27,16)|name=PKF05
Line 1,838: Line 2,100:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 L' U' L U L F' L2 U L (r2 U2 r2 Uw2 r2 Uw2) U' L' U' L F y2
+
{{Alg6|wca=y2 L' U' L U L F' L2 U L (r2 U2 r2 Uw2 r2 Uw2) U' L' U' L F y2
 
|sign=y2 L' U' L U L F' L2 U L (2R2 U2 2R2 u2 2R2 u2) U' L' U' L F y2
 
|sign=y2 L' U' L U L F' L2 U L (2R2 U2 2R2 u2 2R2 u2) U' L' U' L F y2
 
|length=(26,20)|name=|wide=N|author=Stefan Lidström
 
|length=(26,20)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Pb</span>====
====Pb====
 
 
[[Image:PLL_Parity9.png|110px|]][[Image:Pb_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity9.png|110px|]][[Image:Pb_Perm_Diagram.png|110px|]]
{{Alg5|wca=z' U2 Lw2 L' U2 L' B2 Lw2' L' B2 L U2 Lw2' B2 U2 z U
+
{{Alg6|wca=z' U2 Lw2 L' U2 L' B2 Lw2' L' B2 L U2 Lw2' B2 U2 z U
 
|sign=z' U2 l2 L' U2 L' B2 l2' L' B2 L U2 l2' B2 U2 z U
 
|sign=z' U2 l2 L' U2 L' B2 l2' L' B2 L U2 l2' B2 U2 z U
 
|length=(23,15)|name=CG05
 
|length=(23,15)|name=CG05
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=y2 L2 U L2 3Uw' Lw2 U2 l2 Uw2 l2 u2 y' L2 U' L2 3Uw L2 U' y'
+
{{Alg6|wca=y2 L2 U L2 3Uw' Lw2 U2 l2 Uw2 l2 u2 y' L2 U' L2 3Uw L2 U' y'
 
|sign=y2 L2 U L2 3u' l2 U2 2L2 u2 2L2 2U2 y' L2 U' L2 3u L2 U' y'
 
|sign=y2 L2 U L2 3u' l2 U2 2L2 u2 2L2 2U2 y' L2 U' L2 3u L2 U' y'
 
|length=(27,16)|name=
 
|length=(27,16)|name=
 
|wide=N|author=Stefan Pochmann
 
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
+
|url=https://web.archive.org/web/20191022173629/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347?guccounter=1
 
}}
 
}}
{{Alg5|wca=R2 D' r2 F2 (r2 Fw2)2 U F2 R2 U R2 U' R2 D
+
{{Alg6|wca=R2 D' r2 F2 (r2 Fw2)2 U F2 R2 U R2 U' R2 D
 
|sign=R2 D' 2R2 F2 (2R2 f2)2 U F2 R2 U R2 U' R2 D
 
|sign=R2 D' 2R2 F2 (2R2 f2)2 U F2 R2 U R2 U' R2 D
 
|length=(27,16)|name=PKF05
 
|length=(27,16)|name=PKF05
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31043
+
|url=https://web.archive.org/web/20191022173918/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31043?guccounter=1
 
}}
 
}}
{{Alg5|wca=R U R' U (r2 U2 r2 Uw2 r2 Uw2) R' F R2 U' R' U' R U R' F'
+
{{Alg6|wca=R U R' U (r2 U2 r2 Uw2 r2 Uw2) R' F R2 U' R' U' R U R' F'
 
|sign=R U R' U (2R2 U2 2R2 u2 2R2 u2) R' F R2 U' R' U' R U R' F'
 
|sign=R U R' U (2R2 U2 2R2 u2 2R2 u2) R' F R2 U' R' U' R U R' F'
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">b permutation</span>===
====Pc====
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Ba</span>====
 
[[Image:PLL_Parity7.png|110px|]][[Image:Pc_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity7.png|110px|]][[Image:Pc_Perm_Diagram.png|110px|]]
{{Alg5|wca=z' U2 Lw2' L U2 L F2 Lw2' L F2 L' U2 Lw2 F2 U2 z U'
+
{{Alg6|wca=z' U2 Lw2' L U2 L F2 Lw2' L F2 L' U2 Lw2 F2 U2 z U'
 
|sign=z' U2 l2' L U2 L F2 l2' L F2 L' U2 l2 F2 U2 z U'
 
|sign=z' U2 l2' L U2 L F2 l2' L F2 L' U2 l2 F2 U2 z U'
 
|length=(23,15)|name=CG05
 
|length=(23,15)|name=CG05
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=R2' U' R2 3Uw Rw2 U2 r2 Uw2 r2 u2 y R2 U R2' 3Uw' R2 U y'
+
{{Alg6|wca=R2' U' R2 3Uw Rw2 U2 r2 Uw2 r2 u2 y R2 U R2' 3Uw' R2 U y'
 
|sign=R2' U' R2 3u r2 U2 2R2 u2 2R2 2U2 y R2 U R2' 3u' R2 U y'
 
|sign=R2' U' R2 3u r2 U2 2R2 u2 2R2 2U2 y R2 U R2' 3u' R2 U y'
 
|length=(27,16)|name=
 
|length=(27,16)|name=
 
|wide=N|author=Stefan Pochmann
 
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
+
|url=https://web.archive.org/web/20191022173629/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347?guccounter=1
 
}}
 
}}
{{Alg5|wca=R2 D r2 B2 (r2 Bw2)2 U' B2 R2 U' R2 U R2 D'
+
{{Alg6|wca=R2 D r2 B2 (r2 Bw2)2 U' B2 R2 U' R2 U R2 D'
 
|sign=R2 D 2R2 B2 (2R2 b2)2 U' B2 R2 U' R2 U R2 D'
 
|sign=R2 D 2R2 B2 (2R2 b2)2 U' B2 R2 U' R2 U R2 D'
 
|length=(27,16)|name=PKF05
 
|length=(27,16)|name=PKF05
Line 1,892: Line 2,153:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 L' U' L U' (r2 U2 r2 Uw2 r2 Uw2) L F' L2 U L U L' U' L F y2
+
{{Alg6|wca=y2 L' U' L U' (r2 U2 r2 Uw2 r2 Uw2) L F' L2 U L U L' U' L F y2
 
|sign=y2 L' U' L U' (2R2 U2 2R2 u2 2R2 u2) L F' L2 U L U L' U' L F y2
 
|sign=y2 L' U' L U' (2R2 U2 2R2 u2 2R2 u2) L F' L2 U L U L' U' L F y2
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|length=(27,20)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Bb</span>====
====Pd====
 
 
[[Image:PLL_Parity6.png|110px|]][[Image:Pd_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity6.png|110px|]][[Image:Pd_Perm_Diagram.png|110px|]]
{{Alg5|wca=U z' U2 F2 Lw2' U2 L F2 Lw2 L' F2 L' U2 Lw2 L' U2 z
+
{{Alg6|wca=U z' U2 F2 Lw2' U2 L F2 Lw2 L' F2 L' U2 Lw2 L' U2 z
 
|sign=U z' U2 F2 l2' U2 L F2 l2 L' F2 L' U2 l2 L' U2 z
 
|sign=U z' U2 F2 l2' U2 L F2 l2 L' F2 L' U2 l2 L' U2 z
 
|length=(23,15)|name=CG05
 
|length=(23,15)|name=CG05
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
|url=https://web.archive.org/web/20191022171306/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340?guccounter=1
 
}}
 
}}
{{Alg5|wca=y U' R2 3Uw R2 U' R2 y' u2 r2 Uw2 r2 U2 Rw2 3Uw' R2 U R2
+
{{Alg6|wca=y U' R2 3Uw R2 U' R2 y' u2 r2 Uw2 r2 U2 Rw2 3Uw' R2 U R2
 
|sign=y U' R2 3u R2 U' R2 y' 2U2 2R2 u2 2R2 U2 r2 3u' R2 U R2
 
|sign=y U' R2 3u R2 U' R2 y' 2U2 2R2 u2 2R2 U2 r2 3u' R2 U R2
 
|length=(27,16)|name=
 
|length=(27,16)|name=
 
|wide=N|author=Stefan Pochmann
 
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
+
|url=https://web.archive.org/web/20191022173629/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347?guccounter=1
 
}}
 
}}
{{Alg5|wca=R2 U' R2 U R2 B2 U (Bw2 r2)2 B2 r2 D' R2 D
+
{{Alg6|wca=R2 U' R2 U R2 B2 U (Bw2 r2)2 B2 r2 D' R2 D
 
|sign=R2 U' R2 U R2 B2 U (b2 2R2)2 B2 2R2 D' R2 D
 
|sign=R2 U' R2 U R2 B2 U (b2 2R2)2 B2 2R2 D' R2 D
 
|length=(27,16)|name=PKF05
 
|length=(27,16)|name=PKF05
Line 1,919: Line 2,179:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R U R' U' R' F R2 U' R' (r2 U2 r2 Uw2 r2 Uw2) U R U R' F'
+
{{Alg6|wca=R U R' U' R' F R2 U' R' (r2 U2 r2 Uw2 r2 Uw2) U R U R' F'
 
|sign=R U R' U' R' F R2 U' R' (2R2 U2 2R2 u2 2R2 u2) U R U R' F'
 
|sign=R U R' U' R' F R2 U' R' (2R2 U2 2R2 u2 2R2 u2) U R U R' F'
 
|length=(25,20)|name=|wide=N|author=Stefan Lidström
 
|length=(25,20)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Q permutation</span>===
===Q permutation===
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Qa</span>====
====Qa====
 
 
[[Image:PLL_Parity18.png|110px|]][[Image:Qa_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity18.png|110px|]][[Image:Qa_Perm_Diagram.png|110px|]]
{{Alg5|wca=y' z U2 R' U2 Rw2 B2 R U2 Rw2 R' U2 R2 B2 Rw2 R U2 z' y U
+
{{Alg6|wca=y' z U2 R' U2 Rw2 B2 R U2 Rw2 R' U2 R2 B2 Rw2 R U2 z' y U
 
|sign=y' z U2 R' U2 r2 B2 R U2 r2 R' U2 R2 B2 r2 R U2 z' y U
 
|sign=y' z U2 R' U2 r2 B2 R U2 r2 R' U2 R2 B2 r2 R U2 z' y U
 
|length=(25,16)|name=CG11
 
|length=(25,16)|name=CG11
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31343
+
|url=https://web.archive.org/web/20191022174058/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31343?guccounter=1
 
}}
 
}}
{{Alg5|wca=B2 L2 U2 L2 d2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2
+
{{Alg6|wca=B2 L2 U2 L2 d2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2
 
|sign=B2 L2 U2 L2 2D2 D' R2 U2 F2 2D2 D B2 U2 R2 U L2 R2 2U2
 
|sign=B2 L2 U2 L2 2D2 D' R2 U2 F2 2D2 D B2 U2 R2 U L2 R2 2U2
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=B2 d2 L2 U2 L2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2
+
{{Alg6|wca=B2 d2 L2 U2 L2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2
 
|sign=B2 2D2 L2 U2 L2 D' R2 U2 F2 2D2 D B2 U2 R2 U L2 R2 2U2
 
|sign=B2 2D2 L2 U2 L2 D' R2 U2 F2 2D2 D B2 U2 R2 U L2 R2 2U2
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R' U' R F2 R' U R U F2 U' F2 U' Fw2 U2 f2 Uw2 f2 u2
+
{{Alg6|wca=R' U' R F2 R' U R U F2 U' F2 U' Fw2 U2 f2 Uw2 f2 u2
 
|sign=R' U' R F2 R' U R U F2 U' F2 U' f2 U2 2F2 u2 2F2 2U2
 
|sign=R' U' R F2 R' U R U F2 U' F2 U' f2 U2 2F2 u2 2F2 2U2
 
|length=(27,18)|name=PKF11
 
|length=(27,18)|name=PKF11
Line 1,951: Line 2,210:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y F' U' F L2 F' U F U L2 U' L2 U' Lw2 U2 l2 Uw2 l2 u2 y'
+
{{Alg6|wca=y F' U' F L2 F' U F U L2 U' L2 U' Lw2 U2 l2 Uw2 l2 u2 y'
 
|sign=y F' U' F L2 F' U F U L2 U' L2 U' l2 U2 2L2 u2 2L2 2U2 y'
 
|sign=y F' U' F L2 F' U F U L2 U' L2 U' l2 U2 2L2 u2 2L2 2U2 y'
 
|length=(27,18)|name=
 
|length=(27,18)|name=
Line 1,957: Line 2,216:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Qb</span>====
====Qb====
 
 
[[Image:PLL_Parity19.png|110px|]][[Image:Qb_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity19.png|110px|]][[Image:Qb_Perm_Diagram.png|110px|]]
{{Alg5|wca=y' z U2 R U2 Rw2 F2 R' U2 Rw2 R U2 R2 F2 Rw2 R' U2 z' y U
+
{{Alg6|wca=y' z U2 R U2 Rw2 F2 R' U2 Rw2 R U2 R2 F2 Rw2 R' U2 z' y U
 
|sign=y' z U2 R U2 r2 F2 R' U2 r2 R U2 R2 F2 r2 R' U2 z' y U
 
|sign=y' z U2 R U2 r2 F2 R' U2 r2 R U2 R2 F2 r2 R' U2 z' y U
 
|length=(25,16)|name=CG11
 
|length=(25,16)|name=CG11
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31343
+
|url=https://web.archive.org/web/20191022174058/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31343?guccounter=1
 
}}
 
}}
{{Alg5|wca=u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' d2 F2 U2 F2 R2
+
{{Alg6|wca=u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' d2 F2 U2 F2 R2
 
|sign=2U2 F2 B2 U B2 U2 R2 D 2D2 L2 U2 B2 D' 2D2 F2 U2 F2 R2
 
|sign=2U2 F2 B2 U B2 U2 R2 D 2D2 L2 U2 B2 D' 2D2 F2 U2 F2 R2
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' F2 U2 F2 d2 R2
+
{{Alg6|wca=u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' F2 U2 F2 d2 R2
 
|sign=2U2 F2 B2 U B2 U2 R2 D 2D2 L2 U2 B2 D' F2 U2 F2 2D2 R2
 
|sign=2U2 F2 B2 U B2 U2 R2 D 2D2 L2 U2 B2 D' F2 U2 F2 2D2 R2
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|length=(30,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=u2 l2 Uw2 l2 U2 Lw2 U' L2 U' L2 3Dw L U L' F2 L U' L' y
+
{{Alg6|wca=u2 l2 Uw2 l2 U2 Lw2 U' L2 U' L2 3Dw L U L' F2 L U' L' y
 
|sign=2U2 2L2 u2 2L2 U2 l2 U' L2 U' L2 3d L U L' F2 L U' L' y
 
|sign=2U2 2L2 u2 2L2 U2 l2 U' L2 U' L2 3d L U L' F2 L U' L' y
 
|length=(27,18)|name=PKF11
 
|length=(27,18)|name=PKF11
Line 1,983: Line 2,241:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y2 u2 r2 Uw2 r2 U2 Rw2 U' R2 U' R2 U F U F' R2 F U' F' y2
+
{{Alg6|wca=y2 u2 r2 Uw2 r2 U2 Rw2 U' R2 U' R2 U F U F' R2 F U' F' y2
 
|sign=y2 2U2 2R2 u2 2R2 U2 r2 U' R2 U' R2 U F U F' R2 F U' F' y2
 
|sign=y2 2U2 2R2 u2 2R2 U2 r2 U' R2 U' R2 U F U F' R2 F U' F' y2
 
|length=(27,18)|name=
 
|length=(27,18)|name=
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31055
+
|url=https://web.archive.org/web/20191022174208/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31055?guccounter=1
 
}}
 
}}
 +
{{br|b=1}}
  
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Two corner swap and a dedge 2 2-cycle</span>==
==Two corner swap and a dedge 2 2-cycle==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">C permutation</span>===
===C permutation===
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Ca</span>====
====Ca====
 
 
[[Image:PLL_Parity15.png|110px|]][[Image:Ca_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity15.png|110px|]][[Image:Ca_Perm_Diagram.png|110px|]]
{{Alg5|wca=y' Rw2 F2 U2 r2 U' B2 U' F2 U B2 U' Rw2 U y
+
{{Alg6|wca=y' Rw2 F2 U2 r2 U' B2 U' F2 U B2 U' Rw2 U y
 
|sign=y' r2 F2 U2 2R2 U' B2 U' F2 U B2 U' r2 U y
 
|sign=y' r2 F2 U2 2R2 U' B2 U' F2 U B2 U' r2 U y
 
|length=(21,13)|name=|wide=N|author=Clément Gallet
 
|length=(21,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw2 U F2 U' B2 U F2 U l2 U2 B2 Lw2 U'
+
{{Alg6|wca=Lw2 U F2 U' B2 U F2 U l2 U2 B2 Lw2 U'
 
|sign=l2 U F2 U' B2 U F2 U 2L2 U2 B2 l2 U'
 
|sign=l2 U F2 U' B2 U F2 U 2L2 U2 B2 l2 U'
 
|length=(21,13)|name=AO09
 
|length=(21,13)|name=AO09
 
|wide=N|author=Alexander Ooms
 
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30880
+
|url=https://web.archive.org/web/20191022174335/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30880?guccounter=1
 
}}
 
}}
{{Alg5|wca=U Lw2 B2 U2 l2 U' F2 U' B2 U F2 U' Lw2
+
{{Alg6|wca=U Lw2 B2 U2 l2 U' F2 U' B2 U F2 U' Lw2
 
|sign=U l2 B2 U2 2L2 U' F2 U' B2 U F2 U' l2
 
|sign=U l2 B2 U2 2L2 U' F2 U' B2 U F2 U' l2
 
|length=(21,13)|name=Inv of AO09
 
|length=(21,13)|name=Inv of AO09
 
|wide=N|author=Alexander Ooms
 
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30880
+
|url=https://web.archive.org/web/20191022174335/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30880?guccounter=1
 
}}
 
}}
{{Alg5|wca=y' Rw r B' R F2 R' B R U2 r2 U2 F2 Rw2 U y
+
{{Alg6|wca=y' Rw r B' R F2 R' B R U2 r2 U2 F2 Rw2 U y
 
|sign=y' r 2R B' R F2 R' B R U2 2R2 U2 F2 r2 U y
 
|sign=y' r 2R B' R F2 R' B R U2 2R2 U2 F2 r2 U y
 
|length=(20,14)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|length=(20,14)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 R2 D2 l2 D L2 D R2 D' L2 D F2 r2 U'
+
{{Alg6|wca=r2 F2 R2 D2 l2 D L2 D R2 D' L2 D F2 r2 U'
 
|sign=2R2 F2 R2 D2 2L2 D L2 D R2 D' L2 D F2 2R2 U'
 
|sign=2R2 F2 R2 D2 2L2 D L2 D R2 D' L2 D F2 2R2 U'
 
|length=(25,15)|name=|wide=N|author=Clément Gallet
 
|length=(25,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Dw2 Lw2 B2 U F2 U' B2 U F2 U l2 U2 Lw2 Dw2
+
{{Alg6|wca=U Dw2 Lw2 B2 U F2 U' B2 U F2 U l2 U2 Lw2 Dw2
 
|sign=U d2 l2 B2 U F2 U' B2 U F2 U 2L2 U2 l2 d2
 
|sign=U d2 l2 B2 U F2 U' B2 U F2 U 2L2 U2 l2 d2
 
|length=(24,15)|name=|wide=N|author=Frédérick Badie
 
|length=(24,15)|name=|wide=N|author=Frédérick Badie
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30854
+
|url=https://web.archive.org/web/20191022174506/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30854?guccounter=1
 
}}
 
}}
{{Alg5|wca=l r U2 x U' L U' R2 U L' U' Rw2 U2 x' U2 l' r' U'
+
{{Alg6|wca=l r U2 x U' L U' R2 U L' U' Rw2 U2 x' U2 l' r' U'
 
|sign=2L 2R U2 x U' L U' R2 U L' U' r2 U2 x' U2 2L' 2R' U'
 
|sign=2L 2R U2 x U' L U' R2 U L' U' r2 U2 x' U2 2L' 2R' U'
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Cb</span>====
====Cb====
 
 
[[Image:PLL_Parity16.png|110px|]][[Image:Cb_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity16.png|110px|]][[Image:Cb_Perm_Diagram.png|110px|]]
{{Alg5|wca=y Rw2 B2 U2 r2 U F2 U B2 U' F2 U Rw2 U' y'
+
{{Alg6|wca=y Rw2 B2 U2 r2 U F2 U B2 U' F2 U Rw2 U' y'
 
|sign=y r2 B2 U2 2R2 U F2 U B2 U' F2 U r2 U' y'
 
|sign=y r2 B2 U2 2R2 U F2 U B2 U' F2 U r2 U' y'
 
|length=(21,13)|name=|wide=N|author=Clément Gallet
 
|length=(21,13)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw2 U' B2 U F2 U' B2 U' l2 U2 F2 Lw2 U
+
{{Alg6|wca=Lw2 U' B2 U F2 U' B2 U' l2 U2 F2 Lw2 U
 
|sign=l2 U' B2 U F2 U' B2 U' 2L2 U2 F2 l2 U
 
|sign=l2 U' B2 U F2 U' B2 U' 2L2 U2 F2 l2 U
 
|length=(21,13)|name=AO09
 
|length=(21,13)|name=AO09
 
|wide=N|author=Alexander Ooms
 
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30877
+
|url=https://web.archive.org/web/20191022174612/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30877?guccounter=1
 
}}
 
}}
{{Alg5|wca=U' Lw2 F2 U2 l2 U B2 U F2 U' B2 U Lw2
+
{{Alg6|wca=U' Lw2 F2 U2 l2 U B2 U F2 U' B2 U Lw2
 
|sign=U' l2 F2 U2 2L2 U B2 U F2 U' B2 U l2
 
|sign=U' l2 F2 U2 2L2 U B2 U F2 U' B2 U l2
 
|length=(21,13)|name=Inv of AO09
 
|length=(21,13)|name=Inv of AO09
 
|wide=N|author=Alexander Ooms
 
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30877
+
|url=https://web.archive.org/web/20191022174612/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30877?guccounter=1
 
}}
 
}}
{{Alg5|wca=y Rw2 R F R' B2 R F' R' U2 r2 U2 B2 Rw2 U' y'
+
{{Alg6|wca=y Rw2 R F R' B2 R F' R' U2 r2 U2 B2 Rw2 U' y'
 
|sign=y r2 R F R' B2 R F' R' U2 2R2 U2 B2 r2 U' y'
 
|sign=y r2 R F R' B2 R F' R' U2 2R2 U2 B2 r2 U' y'
 
|length=(20,14)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|length=(20,14)|name=|wide=N|author=Frédérick Badie &Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30994
+
|url=https://web.archive.org/web/20191022174746/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30994?guccounter=1
 
}}
 
}}
{{Alg5|wca=r2 B2 R2 D2 l2 D' L2 D' R2 D L2 D' B2 r2 U
+
{{Alg6|wca=r2 B2 R2 D2 l2 D' L2 D' R2 D L2 D' B2 r2 U
 
|sign=2R2 B2 R2 D2 2L2 D' L2 D' R2 D L2 D' B2 2R2 U
 
|sign=2R2 B2 R2 D2 2L2 D' L2 D' R2 D L2 D' B2 2R2 U
 
|length=(25,15)|name=|wide=N|author=Clément Gallet
 
|length=(25,15)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Dw2 Rw2 B2 U' F2 U B2 U' F2 U' r2 U2 Rw2 u2 y2
+
{{Alg6|wca=U Dw2 Rw2 B2 U' F2 U B2 U' F2 U' r2 U2 Rw2 u2 y2
 
|sign=U d2 r2 B2 U' F2 U B2 U' F2 U' 2R2 U2 r2 2U2 y2
 
|sign=U d2 r2 B2 U' F2 U B2 U' F2 U' 2R2 U2 r2 2U2 y2
 
|length=(24,15)|name=|wide=N|author=Frédérick Badie
 
|length=(24,15)|name=|wide=N|author=Frédérick Badie
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30854
+
|url=https://web.archive.org/web/20191022174506/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30854?guccounter=1
 
}}
 
}}
{{Alg5|wca=l' r' U2 x' U L' U R2 U' L U Rw2 U2 x U2 l r U
+
{{Alg6|wca=l' r' U2 x' U L' U R2 U' L U Rw2 U2 x U2 l r U
 
|sign=2L' 2R' U2 x' U L' U R2 U' L U r2 U2 x U2 2L 2R U
 
|sign=2L' 2R' U2 x' U L' U R2 U' L U r2 U2 x U2 2L 2R U
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">H permutation</span>===
===I permutation===
 
 
[[Image:PLL_Parity14.png|110px|]][[Image:I_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity14.png|110px|]][[Image:I_Perm_Diagram.png|110px|]]
{{Alg5|wca=L2 Uw2 L2 U' L2 D' B2 R2 d2 U' R2 D B2 u2 U
+
{{Alg6|wca=L2 Uw2 L2 U' L2 D' B2 R2 d2 U' R2 D B2 u2 U
 
|sign=L2 u2 L2 U' L2 D' B2 R2 2D2 U' R2 D B2 2U2 U
 
|sign=L2 u2 L2 U' L2 D' B2 R2 2D2 U' R2 D B2 2U2 U
 
|length=(24,15)|name=|wide=N|author=Clément Gallet
 
|length=(24,15)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31344
+
|url=https://web.archive.org/web/20191022174842/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31344?guccounter=1
 
}}
 
}}
{{Alg5|wca=L2 Uw2 L2 U L2 3Uw L2 F2 U z l2 F2 L' U2 Lw2 z' U y
+
{{Alg6|wca=L2 Uw2 L2 U L2 3Uw L2 F2 U z l2 F2 L' U2 Lw2 z' U y
 
|sign=L2 u2 L2 U L2 3u L2 F2 U z 2L2 F2 L' U2 l2 z' U y
 
|sign=L2 u2 L2 U L2 3u L2 F2 U z 2L2 F2 L' U2 l2 z' U y
 
|length=(25,15)|name=CG08
 
|length=(25,15)|name=CG08
Line 2,088: Line 2,344:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 D' F2 D R2 B2 D L2 D' Bw2 U2 b2 Uw2 b2 Uw2 U'
+
{{Alg6|wca=R2 D' F2 D R2 B2 D L2 D' Bw2 U2 b2 Uw2 b2 Uw2 U'
 
|sign=R2 D' F2 D R2 B2 D L2 D' b2 U2 2B2 u2 2B2 u2 U'
 
|sign=R2 D' F2 D R2 B2 D L2 D' b2 U2 2B2 u2 2B2 u2 U'
 
|length=(26,16)|name=|wide=N|author=Kenneth Gustavsson
 
|length=(26,16)|name=|wide=N|author=Kenneth Gustavsson
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30906
+
|url=https://web.archive.org/web/20191022174946/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30906?guccounter=1
 
}}
 
}}
{{Alg5|wca=Lw2 U F2 L D' L D L' U L U' L' U l2 U2 F2 Lw2
+
{{Alg6|wca=Lw2 U F2 L D' L D L' U L U' L' U l2 U2 F2 Lw2
 
|sign=l2 U F2 L D' L D L' U L U' L' U 2L2 U2 F2 l2
 
|sign=l2 U F2 L D' L D L' U L U' L' U 2L2 U2 F2 l2
 
|length=(23,17)|name=AO08
 
|length=(23,17)|name=AO08
 
|wide=N|author=Alexander Ooms
 
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31012
+
|url=https://web.archive.org/web/20191022175042/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31012?guccounter=1
 
}}
 
}}
{{Alg5|wca=Rw2 U2 r2 Uw2 r2 u2 D' F2 U F2 R2 U R2 U' R2 D
+
{{Alg6|wca=Rw2 U2 r2 Uw2 r2 u2 D' F2 U F2 R2 U R2 U' R2 D
 
|sign=r2 U2 2R2 u2 2R2 2U2 D' F2 U F2 R2 U R2 U' R2 D
 
|sign=r2 U2 2R2 u2 2R2 2U2 D' F2 U F2 R2 U R2 U' R2 D
 
|length=(27,16)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(27,16)|name=|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31043
+
|url=https://web.archive.org/web/20191022173918/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31043?guccounter=1
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Theta (θ) permutation</span>===
===Theta (θ) permutation===
 
 
[[Image:PLL_Parity20.png|110px|]][[Image:Theta_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity20.png|110px|]][[Image:Theta_Perm_Diagram.png|110px|]]
{{Alg5|wca=R2 U B2 Uw2 R2 U' B2 Uw2 U B2 U2 R2 Uw2 U' R2 U'
+
{{Alg6|wca=R2 U B2 Uw2 R2 U' B2 Uw2 U B2 U2 R2 Uw2 U' R2 U'
 
|sign=R2 U B2 u2 R2 U' B2 u2 U B2 U2 R2 u2 U' R2 U'
 
|sign=R2 U B2 u2 R2 U' B2 u2 U B2 U2 R2 u2 U' R2 U'
 
|length=(25,16)|name=|wide=Y|author=Clément Gallet
 
|length=(25,16)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z F2 Rw2 R' F2 R2 U2 Rw2 R U2 R' F2 Rw2 U2 R F2 z' U
+
{{Alg6|wca=z F2 Rw2 R' F2 R2 U2 Rw2 R U2 R' F2 Rw2 U2 R F2 z' U
 
|sign=z F2 r2 R' F2 R2 U2 r2 R U2 R' F2 r2 U2 R F2 z' U
 
|sign=z F2 r2 R' F2 R2 U2 r2 R U2 R' F2 r2 U2 R F2 z' U
 
|length=(25,16)|name=CG12
 
|length=(25,16)|name=CG12
 
|wide=Y|author=Clément Gallet
 
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31346
+
|url=https://web.archive.org/web/20191022175142/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31346?guccounter=1
 
}}
 
}}
{{Alg5|wca=u2 D F2 U R2 U2 u2 F2 D' F2 U L2 D2 B2 U' u2 R2 y2
+
{{Alg6|wca=u2 D F2 U R2 U2 u2 F2 D' F2 U L2 D2 B2 U' u2 R2 y2
 
|sign=2U2 D F2 U R2 U2 2U2 F2 D' F2 U L2 D2 B2 U' 2U2 R2 y2
 
|sign=2U2 D F2 U R2 U2 2U2 F2 D' F2 U L2 D2 B2 U' 2U2 R2 y2
 
|length=(29,17)|name=|wide=N|author=Clément Gallet
 
|length=(29,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R' B' R F D' R' D B R Fw' f' R2 f2 Rw2 f2 Rw2 U R2
+
{{Alg6|wca=R' B' R F D' R' D B R Fw' f' R2 f2 Rw2 f2 Rw2 U R2
 
|sign=R' B' R F D' R' D B R f' 2F' R2 2F2 r2 2F2 r2 U R2
 
|sign=R' B' R F D' R' D B R f' 2F' R2 2F2 r2 2F2 r2 U R2
 
|length=(24,18)|name=|wide=N|author=Per Kristen Fredlund &Clément Gallet
 
|length=(24,18)|name=|wide=N|author=Per Kristen Fredlund &Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F U F' R2 F U' F' U' R2 U f2 R2 (f2 Rw2)2 U R2
+
{{Alg6|wca=F U F' R2 F U' F' U' R2 U f2 R2 (f2 Rw2)2 U R2
 
|sign=F U F' R2 F U' F' U' R2 U 2F2 R2 (2F2 r2)2 U R2
 
|sign=F U F' R2 F U' F' U' R2 U 2F2 R2 (2F2 r2)2 U R2
 
|length=(27,18)|name=PKF12
 
|length=(27,18)|name=PKF12
 
|wide=N|author=Per Kristen Fredlund
 
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31055
+
|url=https://web.archive.org/web/20191022174208/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31055?guccounter=1
 
}}
 
}}
{{Alg5|wca=F R U' R' U' R U R' F' (r2 U2 r2 Uw2 r2 u2) R U R' U' R' F R F'
+
{{Alg6|wca=F R U' R' U' R U R' F' (r2 U2 r2 Uw2 r2 u2) R U R' U' R' F R F'
 
|sign=F R U' R' U' R U R' F' (2R2 U2 2R2 u2 2R2 2U2) R U R' U' R' F R F'
 
|sign=F R U' R' U' R U R' F' (2R2 U2 2R2 u2 2R2 2U2) R U R' U' R' F R F'
 
|length=(29,23)|name=|wide=N|author=Stefan Lidström
 
|length=(29,23)|name=|wide=N|author=Stefan Lidström
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Xi (Ξ) permutation</span>===
===Xi (Ξ) permutation===
 
 
[[Image:PLL_Parity21.png|110px|]][[Image:Xi_Perm_Diagram.png|110px|]]
 
[[Image:PLL_Parity21.png|110px|]][[Image:Xi_Perm_Diagram.png|110px|]]
{{Alg5|wca=Uw d B2 D M2 U L2 B2 U B2 Uw2 R2 D F2 Uw2 3Lw2 y'
+
{{Alg6|wca=Uw d B2 D M2 U L2 B2 U B2 Uw2 R2 D F2 Uw2 3Lw2 y'
 
|sign=u 2D B2 D m2 U L2 B2 U B2 u2 R2 D F2 u2 3l2 y'
 
|sign=u 2D B2 D m2 U L2 B2 U B2 u2 R2 D F2 u2 3l2 y'
 
|length=(26,16)|name=|wide=N|author=Clément Gallet
 
|length=(26,16)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 Uw2 U' M2 U R2 F2 Uw2 U' F2 U2 3Rw2 Uw2 U' F2 U2 R2 U
+
{{Alg6|wca=R2 Uw2 U' M2 U R2 F2 Uw2 U' F2 U2 3Rw2 Uw2 U' F2 U2 R2 U
 
|sign=R2 u2 U' m2 U R2 F2 u2 U' F2 U2 3r2 u2 U' F2 U2 R2 U
 
|sign=R2 u2 U' m2 U R2 F2 u2 U' F2 U2 3r2 u2 U' F2 U2 R2 U
 
|length=(28,18)|name=|wide=Y|author=Clément Gallet
 
|length=(28,18)|name=|wide=Y|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw2 Lw2 U' B' U B U2 F U' F' U F' L2 F Lw2 U2 Lw2 Uw2 U'
+
{{Alg6|wca=Uw2 Lw2 U' B' U B U2 F U' F' U F' L2 F Lw2 U2 Lw2 Uw2 U'
 
|sign=u2 l2 U' B' U B U2 F U' F' U F' L2 F l2 U2 l2 u2 U'
 
|sign=u2 l2 U' B' U B U2 F U' F' U F' L2 F l2 U2 l2 u2 U'
 
|length=(26,19)|name=FB13
 
|length=(26,19)|name=FB13
Line 2,160: Line 2,414:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U L2 U2 F2 D B2 u2 D' F2 L2 F2 D B2 D u2 R2 D2 F2 d2
+
{{Alg6|wca=U L2 U2 F2 D B2 u2 D' F2 L2 F2 D B2 D u2 R2 D2 F2 d2
 
|sign=U L2 U2 F2 D B2 2U2 D' F2 L2 F2 D B2 D 2U2 R2 D2 F2 2D2
 
|sign=U L2 U2 F2 D B2 2U2 D' F2 L2 F2 D B2 D 2U2 R2 D2 F2 2D2
 
|length=(33,19)|name=|wide=N|author=Clément Gallet
 
|length=(33,19)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw2 l' r' F' L' B' L F L' R' F' R B R' F' l2 F2 Lw2 Bw2 F' x
+
{{Alg6|wca=Dw2 l' r' F' L' B' L F L' R' F' R B R' F' l2 F2 Lw2 Bw2 F' x
 
|sign=d2 2L' 2R' F' L' B' L F L' R' F' R B R' F' 2L2 F2 l2 b2 F' x
 
|sign=d2 2L' 2R' F' L' B' L F L' R' F' R B R' F' 2L2 F2 l2 b2 F' x
 
|length=(24,20)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|length=(24,20)|name=|wide=N|author=Frédérick Badie &Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U Uw2 Rw2 U2 Rw2 R' D R' U' R (U2 D') R' D' R U2 R' (U' D) Rw2 Uw2
+
{{Alg6|wca=U Uw2 Rw2 U2 Rw2 R' D R' U' R (U2 D') R' D' R U2 R' (U' D) Rw2 Uw2
 
|sign=U u2 r2 U2 r2 R' D R' U' R (U2 D') R' D' R U2 R' (U' D) r2 u2
 
|sign=U u2 r2 U2 r2 R' D R' U' R (U2 D') R' D' R U2 R' (U' D) r2 u2
 
|length=(25,20)|name=|wide=N|author=xyzzy
 
|length=(25,20)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/4x4-discussion.29791/page-75#post-1292325
 
|url=https://www.speedsolving.com/forum/threads/4x4-discussion.29791/page-75#post-1292325
 
}}
 
}}
{{Alg5|wca=z Uw2 r2 Uw2 r2 U2 (Lw' Rw' z') U R' U R U' R B2 R' U R' U' R U B2 U y'
+
{{Alg6|wca=z Uw2 r2 Uw2 r2 U2 (Lw' Rw' z') U R' U R U' R B2 R' U R' U' R U B2 U y'
 
|sign=z u2 2R2 u2 2R2 U2 (l' r' z') U R' U R U' R B2 R' U R' U' R U B2 U y'
 
|sign=z u2 2R2 u2 2R2 U2 (l' r' z') U R' U R U' R B2 R' U R' U' R U B2 U y'
 
|length=(29,21)|name=|wide=N|author=Matthew Sheerin
 
|length=(29,21)|name=|wide=N|author=Matthew Sheerin
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-63#post-915705
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-63#post-915705
 
}}
 
}}
{{Alg5|wca=z Uw2 r2 Uw2 r2 U2 (Lw' Rw' z') U R' U R U' R B2 R' U R' U' R (z 3Lw) U2 z' U
+
{{Alg6|wca=z Uw2 r2 Uw2 r2 U2 (Lw' Rw' z') U R' U R U' R B2 R' U R' U' R (z 3Lw) U2 z' U
 
|sign=z u2 2R2 u2 2R2 U2 (l' r' z') U R' U R U' R B2 R' U R' U' R (z 3l) U2 z' U
 
|sign=z u2 2R2 u2 2R2 U2 (l' r' z') U R' U R U' R B2 R' U R' U' R (z 3l) U2 z' U
 
|length=(29,21)|name=|wide=N|author=Matthew Sheerin
 
|length=(29,21)|name=|wide=N|author=Matthew Sheerin
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-63#post-915705
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-63#post-915705
 
}}
 
}}
 +
{{br|b=1}}
  
==The shortest PLL parity fixes in BQTM==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">The shortest PLL parity fixes in BQTM</span>==
 
*Note that these are the only PLL parity algorithms in this section which only contain two inner layer slice quarter turns.
 
*Note that these are the only PLL parity algorithms in this section which only contain two inner layer slice quarter turns.
**[https://www.speedsolving.com/forum/threads/pseudo-3x3-shorter-than-3x3.43996/#post-937678 This alg set] is for theoretical purposes only, as they scramble the pseudo 3x3x3 state of the 4x4x4.
+
**{{LinkColorE|u=https://www.speedsolving.com/forum/threads/pseudo-3x3-shorter-than-3x3.43996/#post-937678|c=rgb(229,148,0)|t=This alg set}} is for theoretical purposes only, as they scramble the pseudo 3x3x3 state of the 4x4x4.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=Rw U D L2 U D S2 Rw
{{Alg5|wca=Rw U D L2 U D S2 Rw
 
 
|sign=r U D L2 U D s2 r
 
|sign=r U D L2 U D s2 r
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U D L2 U D S2 Rw'
+
{{Alg6|wca=Rw' U D L2 U D S2 Rw'
 
|sign=r' U D L2 U D s2 r'
 
|sign=r' U D L2 U D s2 r'
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' D' L2 U' D' S2 Rw
+
{{Alg6|wca=Rw U' D' L2 U' D' S2 Rw
 
|sign=r U' D' L2 U' D' s2 r
 
|sign=r U' D' L2 U' D' s2 r
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' D' L2 U' D' S2 Rw'
+
{{Alg6|wca=Rw' U' D' L2 U' D' S2 Rw'
 
|sign=r' U' D' L2 U' D' s2 r'
 
|sign=r' U' D' L2 U' D' s2 r'
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U D R2 U D S2 Rw
+
{{Alg6|wca=Rw U D R2 U D S2 Rw
 
|sign=r U D R2 U D s2 r
 
|sign=r U D R2 U D s2 r
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U D R2 U D S2 Rw'
+
{{Alg6|wca=Rw' U D R2 U D S2 Rw'
 
|sign=r' U D R2 U D s2 r'
 
|sign=r' U D R2 U D s2 r'
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' D' R2 U' D' S2 Rw
+
{{Alg6|wca=Rw U' D' R2 U' D' S2 Rw
 
|sign=r U' D' R2 U' D' s2 r
 
|sign=r U' D' R2 U' D' s2 r
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' D' R2 U' D' S2 Rw'
+
{{Alg6|wca=Rw' U' D' R2 U' D' S2 Rw'
 
|sign=r' U' D' R2 U' D' s2 r'
 
|sign=r' U' D' R2 U' D' s2 r'
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-935545
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-935545
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw U D S2 U' D' S2 Rw'
+
{{Alg6|wca=Rw U D S2 U' D' S2 Rw'
 
|sign=r U D s2 U' D' s2 r'
 
|sign=r U D s2 U' D' s2 r'
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U D S2 U' D' S2 Rw
+
{{Alg6|wca=Rw' U D S2 U' D' S2 Rw
 
|sign=r' U D s2 U' D' s2 r
 
|sign=r' U D s2 U' D' s2 r
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' D' S2 U D S2 Rw'
+
{{Alg6|wca=Rw U' D' S2 U D S2 Rw'
 
|sign=r U' D' s2 U D s2 r'
 
|sign=r U' D' s2 U D s2 r'
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' D' S2 U D S2 Rw
+
{{Alg6|wca=Rw' U' D' S2 U D S2 Rw
 
|sign=r' U' D' s2 U D s2 r
 
|sign=r' U' D' s2 U D s2 r
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 
*Taking the first algorithm, for example, and solving back the outer layers, we see that these short parity fixes were made from a supercube safe unoriented 4-cycle of dedges in M:
 
*Taking the first algorithm, for example, and solving back the outer layers, we see that these short parity fixes were made from a supercube safe unoriented 4-cycle of dedges in M:
 
+
{{br|b=1}}
{{Alg5|wca=r U D L2 U D S2 r S2 D' U' L2 D' U'
+
{{Alg6|wca=r U D L2 U D S2 r S2 D' U' L2 D' U'
 
|sign=2R U D L2 U D s2 2R s2 D' U' L2 D' U'
 
|sign=2R U D L2 U D s2 2R s2 D' U' L2 D' U'
 
|length=(18,14)|name=|wide=N|author=Christopher Mowla
 
|length=(18,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 
*However, note that this is not the shortest solution to this 4x4x4 position, as the following is a shorter supercube safe algorithm.
 
*However, note that this is not the shortest solution to this 4x4x4 position, as the following is a shorter supercube safe algorithm.
 
+
{{br|b=1}}
{{Alg5|wca=(l E2 r' E2)3//Safe
+
{{Alg6|wca=(l E2 r' E2)3 //Safe
 
|sign=(2L e2 2R' e2)3
 
|sign=(2L e2 2R' e2)3
 
|length=(18,12)|name=|wide=N|author=Christopher Mowla
 
|length=(18,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 +
=<span style="font-family:Georgia;color:rgb(0,200,0);">Pure Flips (Single Parity)</span>=
 +
*All algorithms in this "pure flips" section are <i>single parity</i> algorithms.
 +
{{br|b=1}}
 +
==<span style="font-family:Georgia;color:rgb(0,200,0);">One dedge flip</span>==
 +
[[Image:One_Dedge_Flip.png|110px|]]
 +
{{br|b=1}}
 +
===<span style="font-family:Georgia;color:rgb(0,200,0);">Shortest half turn move algorithms</span>===
  
 +
*It turns out that the shortest algorithms in the half turn move metric (in both the single slice turn metric and the block turn metric) have a length of 15.
  
=Pure Flips (Single Parity)=
+
*There are exactly 288 algorithms (with a length of 15 half turns) which flip the upper front dedge and affect the top or front centers of the 4x4x4 supercube.
*All algorithms in this "pure flips" section are <b>single parity</b> algorithms.
+
:They all happen to be 25 BQTM and <u>single slice turn-based</u> algorithms (algorithms which predominately consist of single slice turns).
 +
{{br|b=1}}
 +
<ul><ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
All 288 (25,15) algorithms can be obtained by running the {{LinkColorE|u=https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2|c=rgb(229,148,0)|t=3x3x3 Classic Setup}} through a 3x3x3 solver like {{LinkColorE|u=http://kociemba.org/cube.htm|c=rgb(229,148,0)|t=Cube Explorer}} and choosing all outputted 15f algorithms which are confined to the move set <U2,F2,D2,B2,L,R>.<br>
 +
:Simply convert the turns of the L and R faces into their corresponding inner slice turns and select the resulting algorithms which flip a single dedge on the 4x4x4.</ul></ul>
 +
{{br|b=1}}
 +
*These 288 (25,15) algorithms have been divided into 36 clusters.  There are exactly 8 algorithms in each cluster.
 +
*Every cluster essentially represents a single <u>unique algorithm</u> path, as move <u>transformations</u> (from cube rotations, mirrors, and inverses) can be done to any algorithm in a given cluster to obtain the 7 other algorithms in its cluster.  To avoid human error, a {{LinkColorE|u=https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-15#post-983757|c=rgb(229,148,0)|t=custom program}} was written to perform these move transformations to the first algorithm listed in each cluster and to label the remaining 7 algorithms in its cluster as the transformation they are of the first algorithm.
 +
{{br|b=1}}
 +
*Even further, several of these clusters are categorized as being in the same group number.  This is because, although transformations are strictly restricted to being in the 36 clusters, some of these clusters of algorithms are directly related to each other by either conjugation and/or by <u>cyclic shifting</u> (a special type of conjugation).
  
 +
:Take for example the first algorithm in the first cluster under <b>Group 1</b> of non-symmetrical algorithms, r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2.
  
==One dedge flip==
+
::Shifting ("rotating the algorithm's moves") 5 times in a clockwise manner gives: {{LinkColorE|u=https://alg.cubing.net/?puzzle=4x4x4&alg=F2_2R2_U2_2R_U2_2R-_U2_F2_2R2_F2_2R-_U2_2L_F2_2L-|c=rgb(229,148,0)|t=F2 r2 U2 r U2 r' U2 F2 r2 F2 r' U2 l F2 l'}}.
[[Image:One_Dedge_Flip.png|110px|]]
 
  
 
+
::This is a single dedge flip of the upper back dedge.
===Shortest half turn move algorithms===
 
 
 
*It turns out that the shortest algorithms in the half turn move metric (in both the single slice turn metric and the block turn metric) have a length of 15.
 
 
 
*There are exactly 288 algorithms (with a length of 15 half turns) which flip the upper front dedge and affect the top or front centers of the 4x4x4 supercube.
 
:They all happen to be 25 BQTM as well; and they all happen to be <u>single slice turn-based</u> algorithms (algorithms which predominately consist of single slice turns).
 
 
 
 
 
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="fbfb8b" |
 
All 288 (25,15) algorithms can be obtained by running the [https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2 3x3x3 Classic Setup] through a 3x3x3 solver like [http://kociemba.org/cube.htm Cube Explorer] and choosing all outputted 15f algorithms which are confined to the move set <U2,F2,D2,B2,L,R>.
 
:Simply convert the turns of the L and R faces into their corresponding inner slice turns and select the resulting algorithms which flip a single dedge on the 4x4x4.
 
|}
 
 
 
 
 
*These 288 (25,15) algorithms have been divided into 36 clusters.  There are exactly 8 algorithms in each cluster.
 
 
 
*Every cluster essentially represents a single <u>unique algorithm</u> path, as move <u>transformations</u> (from cube rotations, mirrors, and inverses) can be done to any algorithm in a given cluster to obtain the 7 other algorithms in its cluster.  To avoid human error, a [https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-15#post-983757 custom program] was written to perform these move transformations to the first algorithm listed in each cluster and to label the remaining 7 algorithms in its cluster as the transformation they are of the first algorithm.
 
 
 
 
 
*Even further, several of these clusters are categorized as being in the same group number.  This is because, although transformations are strictly restricted to being in the 36 clusters, some of these clusters of algorithms are directly related to each other by either conjugation and/or by <b><u>cyclic shifting</u></b> (a special type of conjugation).
 
 
 
:Take for example the first algorithm in the first cluster under <b>Group 1</b> of non-symmetrical algorithms, r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2.
 
 
 
::Shifting ("rotating the algorithm's moves") 5 times in a clockwise manner gives: F2 r2 U2 r U2 r' U2 F2 r2 F2 r' U2 l F2 l' ([https://alg.cubing.net/?puzzle=4x4x4&alg=F2_2R2_U2_2R_U2_2R-_U2_F2_2R2_F2_2R-_U2_2L_F2_2L- animation]).
 
 
 
::This is a single dedge flip of the upper back dedge.
 
  
 
::Rotating about y2 gives B2 l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r', which is the third algorithm in the first cluster under <b>Group 3</b> of non-symmetrical algorithms.
 
::Rotating about y2 gives B2 l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r', which is the third algorithm in the first cluster under <b>Group 3</b> of non-symmetrical algorithms.
  
::*This is why <b>Group 3</b> is called "Group 3: Cyclic Shift of Group 1", for example.
+
::*This is why <i>Group 3</i> is called "Group 3: Cyclic Shift of Group 1", for example.
 
+
{{br|b=1}}
 
 
 
*Even further, all unique non-symmetrical algorithms are directly related to each other by transformations (resulting from inserting cube rotations in between moves of the algorithms).  The same holds true for all unique symmetrical algorithms.
 
*Even further, all unique non-symmetrical algorithms are directly related to each other by transformations (resulting from inserting cube rotations in between moves of the algorithms).  The same holds true for all unique symmetrical algorithms.
:*This implies that, despite that there are 288 15 half turn move algorithms which solve the upper front dedge pure flip case, <b>there are actually only two fundamentally unique (25,15) algorithm paths</b>: the symmetrical approach and the non-symmetrical approach.
+
:*This implies that, despite that there are 288 15 half turn move algorithms which solve the upper front dedge pure flip case, <u>there are actually only two fundamentally unique (25,15) algorithm paths</u>: the symmetrical approach and the non-symmetrical approach.
::*This was shown by Christopher Mowla in 2012.[https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-774938].
+
::*This was {{LinkColorE|u=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-774938|c=rgb(229,148,0)|t=shown by Christopher Mowla in 2012}}.
 
+
{{br|b=1}}
 
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 
+
<span style="font-family:Georgia;font-size:120%;"><center><b>Additional Terminology</b></center></span>
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
An algorithm is called <u>symmetrical</u> if its first and last moves are inverses of each other (or if it can be rewritten as such, should its first and/or last move cancel with the second and/or second to last move in the algorithm, respectively).  Symmetrical algorithms are {{LinkColorI|p=conjugate|c=rgb(229,148,0)|t=conjugates}}.
| bgcolor="fbfb8b" |
 
<center><b>Additional Terminology</b></center>
 
 
 
An algorithm is called <u>symmetrical</u> if its first and last moves are inverses of each other (or if it can be rewritten as such, should its first and/or last move cancel with the second and/or second to last move in the algorithm, respectively).  Symmetrical algorithms are [[conjugate]]s.
 
 
 
  
 
A clear example of a symmetrical algorithm is Stefan Pochmann's <i>n</i>x<i>n</i>x<i>n</i> opposite PLL parity algorithm, (Rw2 F2 U2) r2 (U2 F2 Rw2), where all moves in the algorithm are conjugate moves except for the one move in the middle.
 
A clear example of a symmetrical algorithm is Stefan Pochmann's <i>n</i>x<i>n</i>x<i>n</i> opposite PLL parity algorithm, (Rw2 F2 U2) r2 (U2 F2 Rw2), where all moves in the algorithm are conjugate moves except for the one move in the middle.
  
 
+
Although symmetrical algorithms are technically conjugates of non-symmetrical algorithms, <u>non-symmetrical algorithms</u> are algorithms which are <i>solely</i> the result of a composition of one or more <i>separate</i> algorithm pieces, which all together accomplish the desired task.  (No "conjugate assistance" is used.)
Although symmetrical algorithms are technically conjugates of non-symmetrical algorithms, <u>non-symmetrical algorithms</u> are algorithms which are <b>solely</b> the result of a composition of one or more <b>separate</b> algorithm pieces, which all together accomplish the desired task.  (No "conjugate assistance" is used.)
 
 
 
  
 
In practice, human creation of symmetrical algorithms requires more trial and error of different paths in both creation of the <u>base</u> (the <i>base</i> is defined as the move sequence B in A B A') and final setup moves, whereas the creation of non-symmetrical algorithms requires having knowledge of forming different pieces individually and knowing how to combine them.
 
In practice, human creation of symmetrical algorithms requires more trial and error of different paths in both creation of the <u>base</u> (the <i>base</i> is defined as the move sequence B in A B A') and final setup moves, whereas the creation of non-symmetrical algorithms requires having knowledge of forming different pieces individually and knowing how to combine them.
  
 
+
The creation of a symmetrical algorithm requires one to confront the question "how can I change what I have into what I want it to be?" ({{LinkColorE|u=https://www.youtube.com/watch?v=JlskMgBY0HA&index=2&list=PLCB1E32A6B432F0D8&t=3m15s|c=rgb(229,148,0)|t=video example}}), whereas the creation of a non-symmetrical algorithm requires one to confront the question "I have already achieved a portion of the task, but what is the missing piece?" ({{LinkColorE|u=https://www.speedsolving.com/forum/threads/4x4x4-with-only-two-algs.28003/page-2#post-545348|c=rgb(229,148,0)|t=written example}}).</ul>
The creation of a symmetrical algorithm requires one to confront the question "how can I change what I have into what I want it to be?" ([https://www.youtube.com/watch?v=JlskMgBY0HA&index=2&list=PLCB1E32A6B432F0D8&t=3m15s video example]), whereas the creation of a non-symmetrical algorithm requires one to confront the question "I have already achieved a portion of the task, but what is the missing piece?" ([https://www.speedsolving.com/forum/threads/4x4x4-with-only-two-algs.28003/page-2#post-545348 written example]).
+
{{br|b=1}}
|}
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">(Non-symmetrical algorithms)</span>====
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Group 1</span>=====
 
+
{{Alg6|wca=r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2
====(Non-symmetrical algorithms)====
 
=====Group 1=====
 
{{Alg5|wca=r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2
 
 
|sign=2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2
 
|sign=2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2
 
|length=(25,15)|name=Alg.1(v1)
 
|length=(25,15)|name=Alg.1(v1)
Line 2,346: Line 2,582:
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
 
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
 
}}
 
}}
{{Alg5|wca=l U2 r' F2 r F2 l2 U2 l' U2 l U2 F2 l2 F2
+
{{Alg6|wca=l U2 r' F2 r F2 l2 U2 l' U2 l U2 F2 l2 F2
 
|sign=2L U2 2R' F2 2R F2 2L2 U2 2L' U2 2L U2 F2 2L2 F2
 
|sign=2L U2 2R' F2 2R F2 2L2 U2 2L' U2 2L U2 F2 2L2 F2
 
|length=(25,15)|name=Mirror[Alg.1(v1)]
 
|length=(25,15)|name=Mirror[Alg.1(v1)]
Line 2,352: Line 2,588:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r2 F2 U2 r U2 r' U2 r2 F2 l F2 l' U2 r
+
{{Alg6|wca=F2 r2 F2 U2 r U2 r' U2 r2 F2 l F2 l' U2 r
 
|sign=F2 2R2 F2 U2 2R U2 2R' U2 2R2 F2 2L F2 2L' U2 2R
 
|sign=F2 2R2 F2 U2 2R U2 2R' U2 2R2 F2 2L F2 2L' U2 2R
 
|length=(25,15)|name=Inverse[Alg.1(v1)]
 
|length=(25,15)|name=Inverse[Alg.1(v1)]
Line 2,358: Line 2,594:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' F2 r U2 r' U2 l2 F2 l F2 l' F2 U2 l2 U2
+
{{Alg6|wca=l' F2 r U2 r' U2 l2 F2 l F2 l' F2 U2 l2 U2
 
|sign=2L' F2 2R U2 2R' U2 2L2 F2 2L F2 2L' F2 U2 2L2 U2
 
|sign=2L' F2 2R U2 2R' U2 2L2 F2 2L F2 2L' F2 U2 2L2 U2
 
|length=(25,15)|name=Rotation[Alg.1(v1)]
 
|length=(25,15)|name=Rotation[Alg.1(v1)]
Line 2,364: Line 2,600:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l'
+
{{Alg6|wca=F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l'
 
|sign=F2 2L2 F2 U2 2L' U2 2L U2 2L2 F2 2R' F2 2R U2 2L'
 
|sign=F2 2L2 F2 U2 2L' U2 2L U2 2L2 F2 2R' F2 2R U2 2L'
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v1)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v1)]]
Line 2,370: Line 2,606:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F2 l' U2 l U2 r2 F2 r' F2 r F2 U2 r2 U2
+
{{Alg6|wca=r F2 l' U2 l U2 r2 F2 r' F2 r F2 U2 r2 U2
 
|sign=2R F2 2L' U2 2L U2 2R2 F2 2R' F2 2R F2 U2 2R2 U2
 
|sign=2R F2 2L' U2 2L U2 2R2 F2 2R' F2 2R F2 U2 2R2 U2
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v1)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v1)]]
Line 2,376: Line 2,612:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 l2 U2 F2 l F2 l' F2 l2 U2 r U2 r' F2 l
+
{{Alg6|wca=U2 l2 U2 F2 l F2 l' F2 l2 U2 r U2 r' F2 l
 
|sign=U2 2L2 U2 F2 2L F2 2L' F2 2L2 U2 2R U2 2R' F2 2L
 
|sign=U2 2L2 U2 F2 2L F2 2L' F2 2L2 U2 2R U2 2R' F2 2L
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v1)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v1)]]
Line 2,382: Line 2,618:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 r2 U2 F2 r' F2 r F2 r2 U2 l' U2 l F2 r'
+
{{Alg6|wca=U2 r2 U2 F2 r' F2 r F2 r2 U2 l' U2 l F2 r'
 
|sign=U2 2R2 U2 F2 2R' F2 2R F2 2R2 U2 2L' U2 2L F2 2R'
 
|sign=U2 2R2 U2 F2 2R' F2 2R F2 2R2 U2 2L' U2 2L F2 2R'
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v1)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v1)]]]
Line 2,388: Line 2,624:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2
 
|sign=2R' U2 2R U2 2L' U2 2L2 F2 2R F2 2L' U2 F2 2R2 F2
 
|sign=2R' U2 2R U2 2L' U2 2L2 F2 2R F2 2L' U2 F2 2R2 F2
 
|length=(25,15)|name=Alg.1(v2)
 
|length=(25,15)|name=Alg.1(v2)
Line 2,395: Line 2,631:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l U2 l' U2 r U2 r2 F2 l' F2 r U2 F2 l2 F2
+
{{Alg6|wca=l U2 l' U2 r U2 r2 F2 l' F2 r U2 F2 l2 F2
 
|sign=2L U2 2L' U2 2R U2 2R2 F2 2L' F2 2R U2 F2 2L2 F2
 
|sign=2L U2 2L' U2 2R U2 2R2 F2 2L' F2 2R U2 F2 2L2 F2
 
|length=(25,15)|name=Mirror[Alg.1(v2)]
 
|length=(25,15)|name=Mirror[Alg.1(v2)]
Line 2,401: Line 2,637:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r2 F2 U2 l F2 r' F2 l2 U2 l U2 r' U2 r
+
{{Alg6|wca=F2 r2 F2 U2 l F2 r' F2 l2 U2 l U2 r' U2 r
 
|sign=F2 2R2 F2 U2 2L F2 2R' F2 2L2 U2 2L U2 2R' U2 2R
 
|sign=F2 2R2 F2 U2 2L F2 2R' F2 2L2 U2 2L U2 2R' U2 2R
 
|length=(25,15)|name=Inverse[Alg.1(v2)]
 
|length=(25,15)|name=Inverse[Alg.1(v2)]
Line 2,407: Line 2,643:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' F2 l F2 r' F2 r2 U2 l U2 r' F2 U2 l2 U2
+
{{Alg6|wca=l' F2 l F2 r' F2 r2 U2 l U2 r' F2 U2 l2 U2
 
|sign=2L' F2 2L F2 2R' F2 2R2 U2 2L U2 2R' F2 U2 2L2 U2
 
|sign=2L' F2 2L F2 2R' F2 2R2 U2 2L U2 2R' F2 U2 2L2 U2
 
|length=(25,15)|name=Rotation[Alg.1(v2)]
 
|length=(25,15)|name=Rotation[Alg.1(v2)]
Line 2,413: Line 2,649:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l2 F2 U2 r' F2 l F2 r2 U2 r' U2 l U2 l'
+
{{Alg6|wca=F2 l2 F2 U2 r' F2 l F2 r2 U2 r' U2 l U2 l'
 
|sign=F2 2L2 F2 U2 2R' F2 2L F2 2R2 U2 2R' U2 2L U2 2L'
 
|sign=F2 2L2 F2 U2 2R' F2 2L F2 2R2 U2 2R' U2 2L U2 2L'
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v2)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v2)]]
Line 2,419: Line 2,655:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F2 r' F2 l F2 l2 U2 r' U2 l F2 U2 r2 U2
+
{{Alg6|wca=r F2 r' F2 l F2 l2 U2 r' U2 l F2 U2 r2 U2
 
|sign=2R F2 2R' F2 2L F2 2L2 U2 2R' U2 2L F2 U2 2R2 U2
 
|sign=2R F2 2R' F2 2L F2 2L2 U2 2R' U2 2L F2 U2 2R2 U2
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v2)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v2)]]
Line 2,425: Line 2,661:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 l2 U2 F2 r U2 l' U2 r2 F2 r F2 l' F2 l
+
{{Alg6|wca=U2 l2 U2 F2 r U2 l' U2 r2 F2 r F2 l' F2 l
 
|sign=U2 2L2 U2 F2 2R U2 2L' U2 2R2 F2 2R F2 2L' F2 2L
 
|sign=U2 2L2 U2 F2 2R U2 2L' U2 2R2 F2 2R F2 2L' F2 2L
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v2)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v2)]]
Line 2,431: Line 2,667:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 r2 U2 F2 l' U2 r U2 l2 F2 l' F2 r F2 r'
+
{{Alg6|wca=U2 r2 U2 F2 l' U2 r U2 l2 F2 l' F2 r F2 r'
 
|sign=U2 2R2 U2 F2 2L' U2 2R U2 2L2 F2 2L' F2 2R F2 2R'
 
|sign=U2 2R2 U2 F2 2L' U2 2R U2 2L2 F2 2L' F2 2R F2 2R'
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v2)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v2)]]]
Line 2,437: Line 2,673:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2
+
{{Alg6|wca=r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2
 
|sign=2R B2 2R' U2 2R U2 2R2 F2 2R' D2 2L D2 B2 2R2 F2
 
|sign=2R B2 2R' U2 2R U2 2R2 F2 2R' D2 2L D2 B2 2R2 F2
 
|length=(25,15)|name=Alg.1(v3)
 
|length=(25,15)|name=Alg.1(v3)
Line 2,444: Line 2,680:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 l' U2 l2 F2 l D2 r' D2 B2 l2 F2
+
{{Alg6|wca=l' B2 l U2 l' U2 l2 F2 l D2 r' D2 B2 l2 F2
 
|sign=2L' B2 2L U2 2L' U2 2L2 F2 2L D2 2R' D2 B2 2L2 F2
 
|sign=2L' B2 2L U2 2L' U2 2L2 F2 2L D2 2R' D2 B2 2L2 F2
 
|length=(25,15)|name=Mirror[Alg.1(v3)]
 
|length=(25,15)|name=Mirror[Alg.1(v3)]
Line 2,450: Line 2,686:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r2 B2 D2 l' D2 r F2 r2 U2 r' U2 r B2 r'
+
{{Alg6|wca=F2 r2 B2 D2 l' D2 r F2 r2 U2 r' U2 r B2 r'
 
|sign=F2 2R2 B2 D2 2L' D2 2R F2 2R2 U2 2R' U2 2R B2 2R'
 
|sign=F2 2R2 B2 D2 2L' D2 2R F2 2R2 U2 2R' U2 2R B2 2R'
 
|length=(25,15)|name=Inverse[Alg.1(v3)]
 
|length=(25,15)|name=Inverse[Alg.1(v3)]
Line 2,456: Line 2,692:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l D2 l' F2 l F2 l2 U2 l' B2 r B2 D2 l2 U2
+
{{Alg6|wca=l D2 l' F2 l F2 l2 U2 l' B2 r B2 D2 l2 U2
 
|sign=2L D2 2L' F2 2L F2 2L2 U2 2L' B2 2R B2 D2 2L2 U2
 
|sign=2L D2 2L' F2 2L F2 2L2 U2 2L' B2 2R B2 D2 2L2 U2
 
|length=(25,15)|name=Rotation[Alg.1(v3)]
 
|length=(25,15)|name=Rotation[Alg.1(v3)]
Line 2,462: Line 2,698:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l2 B2 D2 r D2 l' F2 l2 U2 l U2 l' B2 l
+
{{Alg6|wca=F2 l2 B2 D2 r D2 l' F2 l2 U2 l U2 l' B2 l
 
|sign=F2 2L2 B2 D2 2R D2 2L' F2 2L2 U2 2L U2 2L' B2 2L
 
|sign=F2 2L2 B2 D2 2R D2 2L' F2 2L2 U2 2L U2 2L' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v3)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v3)]]
Line 2,468: Line 2,704:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 r F2 r' F2 r2 U2 r B2 l' B2 D2 r2 U2
+
{{Alg6|wca=r' D2 r F2 r' F2 r2 U2 r B2 l' B2 D2 r2 U2
 
|sign=2R' D2 2R F2 2R' F2 2R2 U2 2R B2 2L' B2 D2 2R2 U2
 
|sign=2R' D2 2R F2 2R' F2 2R2 U2 2R B2 2L' B2 D2 2R2 U2
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v3)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v3)]]
Line 2,474: Line 2,710:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 l2 D2 B2 r' B2 l U2 l2 F2 l' F2 l D2 l'
+
{{Alg6|wca=U2 l2 D2 B2 r' B2 l U2 l2 F2 l' F2 l D2 l'
 
|sign=U2 2L2 D2 B2 2R' B2 2L U2 2L2 F2 2L' F2 2L D2 2L'
 
|sign=U2 2L2 D2 B2 2R' B2 2L U2 2L2 F2 2L' F2 2L D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v3)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v3)]]
Line 2,480: Line 2,716:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 r2 D2 B2 l B2 r' U2 r2 F2 r F2 r' D2 r
+
{{Alg6|wca=U2 r2 D2 B2 l B2 r' U2 r2 F2 r F2 r' D2 r
 
|sign=U2 2R2 D2 B2 2L B2 2R' U2 2R2 F2 2R F2 2R' D2 2R
 
|sign=U2 2R2 D2 B2 2L B2 2R' U2 2R2 F2 2R F2 2R' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v3)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v3)]]]
Line 2,486: Line 2,722:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2
+
{{Alg6|wca=r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2
 
|sign=2R B2 2R' U2 2R U2 2L2 B2 2R' U2 2L U2 F2 2L2 F2
 
|sign=2R B2 2R' U2 2R U2 2L2 B2 2R' U2 2L U2 F2 2L2 F2
 
|length=(25,15)|name=Alg.1(v4)
 
|length=(25,15)|name=Alg.1(v4)
Line 2,493: Line 2,729:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 l' U2 r2 B2 l U2 r' U2 F2 r2 F2
+
{{Alg6|wca=l' B2 l U2 l' U2 r2 B2 l U2 r' U2 F2 r2 F2
 
|sign=2L' B2 2L U2 2L' U2 2R2 B2 2L U2 2R' U2 F2 2R2 F2
 
|sign=2L' B2 2L U2 2L' U2 2R2 B2 2L U2 2R' U2 F2 2R2 F2
 
|length=(25,15)|name=Mirror[Alg.1(v4)]
 
|length=(25,15)|name=Mirror[Alg.1(v4)]
Line 2,499: Line 2,735:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l2 F2 U2 l' U2 r B2 l2 U2 r' U2 r B2 r'
+
{{Alg6|wca=F2 l2 F2 U2 l' U2 r B2 l2 U2 r' U2 r B2 r'
 
|sign=F2 2L2 F2 U2 2L' U2 2R B2 2L2 U2 2R' U2 2R B2 2R'
 
|sign=F2 2L2 F2 U2 2L' U2 2R B2 2L2 U2 2R' U2 2R B2 2R'
 
|length=(25,15)|name=Inverse[Alg.1(v4)]
 
|length=(25,15)|name=Inverse[Alg.1(v4)]
Line 2,505: Line 2,741:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l D2 l' F2 l F2 r2 D2 l' F2 r F2 U2 r2 U2
+
{{Alg6|wca=l D2 l' F2 l F2 r2 D2 l' F2 r F2 U2 r2 U2
 
|sign=2L D2 2L' F2 2L F2 2R2 D2 2L' F2 2R F2 U2 2R2 U2
 
|sign=2L D2 2L' F2 2L F2 2R2 D2 2L' F2 2R F2 U2 2R2 U2
 
|length=(25,15)|name=Rotation[Alg.1(v4)]
 
|length=(25,15)|name=Rotation[Alg.1(v4)]
Line 2,511: Line 2,747:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r2 F2 U2 r U2 l' B2 r2 U2 l U2 l' B2 l
+
{{Alg6|wca=F2 r2 F2 U2 r U2 l' B2 r2 U2 l U2 l' B2 l
 
|sign=F2 2R2 F2 U2 2R U2 2L' B2 2R2 U2 2L U2 2L' B2 2L
 
|sign=F2 2R2 F2 U2 2R U2 2L' B2 2R2 U2 2L U2 2L' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v4)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v4)]]
Line 2,517: Line 2,753:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 r F2 r' F2 l2 D2 r F2 l' F2 U2 l2 U2
+
{{Alg6|wca=r' D2 r F2 r' F2 l2 D2 r F2 l' F2 U2 l2 U2
 
|sign=2R' D2 2R F2 2R' F2 2L2 D2 2R F2 2L' F2 U2 2L2 U2
 
|sign=2R' D2 2R F2 2R' F2 2L2 D2 2R F2 2L' F2 U2 2L2 U2
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v4)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v4)]]
Line 2,523: Line 2,759:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 r2 U2 F2 r' F2 l D2 r2 F2 l' F2 l D2 l'
+
{{Alg6|wca=U2 r2 U2 F2 r' F2 l D2 r2 F2 l' F2 l D2 l'
 
|sign=U2 2R2 U2 F2 2R' F2 2L D2 2R2 F2 2L' F2 2L D2 2L'
 
|sign=U2 2R2 U2 F2 2R' F2 2L D2 2R2 F2 2L' F2 2L D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v4)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v4)]]
Line 2,529: Line 2,765:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 l2 U2 F2 l F2 r' D2 l2 F2 r F2 r' D2 r
+
{{Alg6|wca=U2 l2 U2 F2 l F2 r' D2 l2 F2 r F2 r' D2 r
 
|sign=U2 2L2 U2 F2 2L F2 2R' D2 2L2 F2 2R F2 2R' D2 2R
 
|sign=U2 2L2 U2 F2 2L F2 2R' D2 2L2 F2 2R F2 2R' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v4)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v4)]]]
Line 2,535: Line 2,771:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2
+
{{Alg6|wca=r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2
 
|sign=2R B2 2L' B2 2L U2 2R2 F2 2L' F2 2R U2 F2 2L2 F2
 
|sign=2R B2 2L' B2 2L U2 2R2 F2 2L' F2 2R U2 F2 2L2 F2
 
|length=(25,15)|name=Alg.1(v5)
 
|length=(25,15)|name=Alg.1(v5)
Line 2,542: Line 2,778:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 r B2 r' U2 l2 F2 r F2 l' U2 F2 r2 F2
+
{{Alg6|wca=l' B2 r B2 r' U2 l2 F2 r F2 l' U2 F2 r2 F2
 
|sign=2L' B2 2R B2 2R' U2 2L2 F2 2R F2 2L' U2 F2 2R2 F2
 
|sign=2L' B2 2R B2 2R' U2 2L2 F2 2R F2 2L' U2 F2 2R2 F2
 
|length=(25,15)|name=Mirror[Alg.1(v5)]
 
|length=(25,15)|name=Mirror[Alg.1(v5)]
Line 2,548: Line 2,784:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 l2 F2 U2 r' F2 l F2 r2 U2 l' B2 l B2 r'
+
{{Alg6|wca=F2 l2 F2 U2 r' F2 l F2 r2 U2 l' B2 l B2 r'
 
|sign=F2 2L2 F2 U2 2R' F2 2L F2 2R2 U2 2L' B2 2L B2 2R'
 
|sign=F2 2L2 F2 U2 2R' F2 2L F2 2R2 U2 2L' B2 2L B2 2R'
 
|length=(25,15)|name=Inverse[Alg.1(v5)]
 
|length=(25,15)|name=Inverse[Alg.1(v5)]
Line 2,554: Line 2,790:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l D2 r' D2 r F2 l2 U2 r' U2 l F2 U2 r2 U2
+
{{Alg6|wca=l D2 r' D2 r F2 l2 U2 r' U2 l F2 U2 r2 U2
 
|sign=2L D2 2R' D2 2R F2 2L2 U2 2R' U2 2L F2 U2 2R2 U2
 
|sign=2L D2 2R' D2 2R F2 2L2 U2 2R' U2 2L F2 U2 2R2 U2
 
|length=(25,15)|name=Rotation[Alg.1(v5)]
 
|length=(25,15)|name=Rotation[Alg.1(v5)]
Line 2,560: Line 2,796:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F2 r2 F2 U2 l F2 r' F2 l2 U2 r B2 r' B2 l
+
{{Alg6|wca=F2 r2 F2 U2 l F2 r' F2 l2 U2 r B2 r' B2 l
 
|sign=F2 2R2 F2 U2 2L F2 2R' F2 2L2 U2 2R B2 2R' B2 2L
 
|sign=F2 2R2 F2 U2 2L F2 2R' F2 2L2 U2 2R B2 2R' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v5)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.1(v5)]]
Line 2,566: Line 2,802:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l D2 l' F2 r2 U2 l U2 r' F2 U2 l2 U2
+
{{Alg6|wca=r' D2 l D2 l' F2 r2 U2 l U2 r' F2 U2 l2 U2
 
|sign=2R' D2 2L D2 2L' F2 2R2 U2 2L U2 2R' F2 U2 2L2 U2
 
|sign=2R' D2 2L D2 2L' F2 2R2 U2 2L U2 2R' F2 U2 2L2 U2
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v5)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.1(v5)]]
Line 2,572: Line 2,808:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 r2 U2 F2 l' U2 r U2 l2 F2 r' D2 r D2 l'
+
{{Alg6|wca=U2 r2 U2 F2 l' U2 r U2 l2 F2 r' D2 r D2 l'
 
|sign=U2 2R2 U2 F2 2L' U2 2R U2 2L2 F2 2R' D2 2R D2 2L'
 
|sign=U2 2R2 U2 F2 2L' U2 2R U2 2L2 F2 2R' D2 2R D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v5)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.1(v5)]]
Line 2,578: Line 2,814:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 l2 U2 F2 r U2 l' U2 r2 F2 l D2 l' D2 r
+
{{Alg6|wca=U2 l2 U2 F2 r U2 l' U2 r2 F2 l D2 l' D2 r
 
|sign=U2 2L2 U2 F2 2R U2 2L' U2 2R2 F2 2L D2 2L' D2 2R
 
|sign=U2 2L2 U2 F2 2R U2 2L' U2 2R2 F2 2L D2 2L' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v5)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v5)]]]
Line 2,584: Line 2,820:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Group 2: F2 move conjugation + rotation of Group 1</span>=====
=====Group 2: F2 move conjugation + rotation of Group 1=====
+
{{Alg6|wca=r2 U2 B2 r B2 r' B2 r2 U2 l U2 l' B2 r U2
{{Alg5|wca=r2 U2 B2 r B2 r' B2 r2 U2 l U2 l' B2 r U2
 
 
|sign=2R2 U2 B2 2R B2 2R' B2 2R2 U2 2L U2 2L' B2 2R U2
 
|sign=2R2 U2 B2 2R B2 2R' B2 2R2 U2 2L U2 2L' B2 2R U2
 
|length=(25,15)|name=Alg.2(v1)
 
|length=(25,15)|name=Alg.2(v1)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 l' B2 l B2 l2 U2 r' U2 r B2 l' U2
+
{{Alg6|wca=l2 U2 B2 l' B2 l B2 l2 U2 r' U2 r B2 l' U2
 
|sign=2L2 U2 B2 2L' B2 2L B2 2L2 U2 2R' U2 2R B2 2L' U2
 
|sign=2L2 U2 B2 2L' B2 2L B2 2L2 U2 2R' U2 2R B2 2L' U2
 
|length=(25,15)|name=Mirror[Alg.2(v1)]
 
|length=(25,15)|name=Mirror[Alg.2(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r' B2 l U2 l' U2 r2 B2 r B2 r' B2 U2 r2
+
{{Alg6|wca=U2 r' B2 l U2 l' U2 r2 B2 r B2 r' B2 U2 r2
 
|sign=U2 2R' B2 2L U2 2L' U2 2R2 B2 2R B2 2R' B2 U2 2R2
 
|sign=U2 2R' B2 2L U2 2L' U2 2R2 B2 2R B2 2R' B2 U2 2R2
 
|length=(25,15)|name=Inverse[Alg.2(v1)]
 
|length=(25,15)|name=Inverse[Alg.2(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l D2 l' D2 l2 F2 r F2 r' D2 l F2
+
{{Alg6|wca=l2 F2 D2 l D2 l' D2 l2 F2 r F2 r' D2 l F2
 
|sign=2L2 F2 D2 2L D2 2L' D2 2L2 F2 2R F2 2R' D2 2L F2
 
|sign=2L2 F2 D2 2L D2 2L' D2 2L2 F2 2R F2 2R' D2 2L F2
 
|length=(25,15)|name=Rotation[Alg.2(v1)]
 
|length=(25,15)|name=Rotation[Alg.2(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 l B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2
+
{{Alg6|wca=U2 l B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2
 
|sign=U2 2L B2 2R' U2 2R U2 2L2 B2 2L' B2 2L B2 U2 2L2
 
|sign=U2 2L B2 2R' U2 2R U2 2L2 B2 2L' B2 2L B2 U2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v1)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 r' D2 r D2 r2 F2 l' F2 l D2 r' F2
+
{{Alg6|wca=r2 F2 D2 r' D2 r D2 r2 F2 l' F2 l D2 r' F2
 
|sign=2R2 F2 D2 2R' D2 2R D2 2R2 F2 2L' F2 2L D2 2R' F2
 
|sign=2R2 F2 D2 2R' D2 2R D2 2R2 F2 2L' F2 2L D2 2R' F2
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v1)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 l' D2 r F2 r' F2 l2 D2 l D2 l' D2 F2 l2
+
{{Alg6|wca=F2 l' D2 r F2 r' F2 l2 D2 l D2 l' D2 F2 l2
 
|sign=F2 2L' D2 2R F2 2R' F2 2L2 D2 2L D2 2L' D2 F2 2L2
 
|sign=F2 2L' D2 2R F2 2R' F2 2L2 D2 2L D2 2L' D2 F2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v1)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 r D2 l' F2 l F2 r2 D2 r' D2 r D2 F2 r2
+
{{Alg6|wca=F2 r D2 l' F2 l F2 r2 D2 r' D2 r D2 F2 r2
 
|sign=F2 2R D2 2L' F2 2L F2 2R2 D2 2R' D2 2R D2 F2 2R2
 
|sign=F2 2R D2 2L' F2 2L F2 2R2 D2 2R' D2 2R D2 F2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v1)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v1)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 U2 B2 l U2 r' U2 l2 B2 l B2 r' B2 r U2
+
{{Alg6|wca=r2 U2 B2 l U2 r' U2 l2 B2 l B2 r' B2 r U2
 
|sign=2R2 U2 B2 2L U2 2R' U2 2L2 B2 2L B2 2R' B2 2R U2
 
|sign=2R2 U2 B2 2L U2 2R' U2 2L2 B2 2L B2 2R' B2 2R U2
 
|length=(25,15)|name=Alg.2(v2)
 
|length=(25,15)|name=Alg.2(v2)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 r' U2 l U2 r2 B2 r' B2 l B2 l' U2
+
{{Alg6|wca=l2 U2 B2 r' U2 l U2 r2 B2 r' B2 l B2 l' U2
 
|sign=2L2 U2 B2 2R' U2 2L U2 2R2 B2 2R' B2 2L B2 2L' U2
 
|sign=2L2 U2 B2 2R' U2 2L U2 2R2 B2 2R' B2 2L B2 2L' U2
 
|length=(25,15)|name=Mirror[Alg.2(v2)]
 
|length=(25,15)|name=Mirror[Alg.2(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r' B2 r B2 l' B2 l2 U2 r U2 l' B2 U2 r2
+
{{Alg6|wca=U2 r' B2 r B2 l' B2 l2 U2 r U2 l' B2 U2 r2
 
|sign=U2 2R' B2 2R B2 2L' B2 2L2 U2 2R U2 2L' B2 U2 2R2
 
|sign=U2 2R' B2 2R B2 2L' B2 2L2 U2 2R U2 2L' B2 U2 2R2
 
|length=(25,15)|name=Inverse[Alg.2(v2)]
 
|length=(25,15)|name=Inverse[Alg.2(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r F2 l' F2 r2 D2 r D2 l' D2 l F2
+
{{Alg6|wca=l2 F2 D2 r F2 l' F2 r2 D2 r D2 l' D2 l F2
 
|sign=2L2 F2 D2 2R F2 2L' F2 2R2 D2 2R D2 2L' D2 2L F2
 
|sign=2L2 F2 D2 2R F2 2L' F2 2R2 D2 2R D2 2L' D2 2L F2
 
|length=(25,15)|name=Rotation[Alg.2(v2)]
 
|length=(25,15)|name=Rotation[Alg.2(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 l B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2
+
{{Alg6|wca=U2 l B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2
 
|sign=U2 2L B2 2L' B2 2R B2 2R2 U2 2L' U2 2R B2 U2 2L2
 
|sign=U2 2L B2 2L' B2 2R B2 2R2 U2 2L' U2 2R B2 U2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v2)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 l' F2 r F2 l2 D2 l' D2 r D2 r' F2
+
{{Alg6|wca=r2 F2 D2 l' F2 r F2 l2 D2 l' D2 r D2 r' F2
 
|sign=2R2 F2 D2 2L' F2 2R F2 2L2 D2 2L' D2 2R D2 2R' F2
 
|sign=2R2 F2 D2 2L' F2 2R F2 2L2 D2 2L' D2 2R D2 2R' F2
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v2)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 l' D2 l D2 r' D2 r2 F2 l F2 r' D2 F2 l2
+
{{Alg6|wca=F2 l' D2 l D2 r' D2 r2 F2 l F2 r' D2 F2 l2
 
|sign=F2 2L' D2 2L D2 2R' D2 2R2 F2 2L F2 2R' D2 F2 2L2
 
|sign=F2 2L' D2 2L D2 2R' D2 2R2 F2 2L F2 2R' D2 F2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v2)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 r D2 r' D2 l D2 l2 F2 r' F2 l D2 F2 r2
+
{{Alg6|wca=F2 r D2 r' D2 l D2 l2 F2 r' F2 l D2 F2 r2
 
|sign=F2 2R D2 2R' D2 2L D2 2L2 F2 2R' F2 2L D2 F2 2R2
 
|sign=F2 2R D2 2R' D2 2L D2 2L2 F2 2R' F2 2L D2 F2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v2)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v2)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 D2 F2 l' F2 r U2 r2 B2 r' B2 r D2 r' U2
+
{{Alg6|wca=r2 D2 F2 l' F2 r U2 r2 B2 r' B2 r D2 r' U2
 
|sign=2R2 D2 F2 2L' F2 2R U2 2R2 B2 2R' B2 2R D2 2R' U2
 
|sign=2R2 D2 F2 2L' F2 2R U2 2R2 B2 2R' B2 2R D2 2R' U2
 
|length=(25,15)|name=Alg.2(v3)
 
|length=(25,15)|name=Alg.2(v3)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 r F2 l' U2 l2 B2 l B2 l' D2 l U2
+
{{Alg6|wca=l2 D2 F2 r F2 l' U2 l2 B2 l B2 l' D2 l U2
 
|sign=2L2 D2 F2 2R F2 2L' U2 2L2 B2 2L B2 2L' D2 2L U2
 
|sign=2L2 D2 F2 2R F2 2L' U2 2L2 B2 2L B2 2L' D2 2L U2
 
|length=(25,15)|name=Mirror[Alg.2(v3)]
 
|length=(25,15)|name=Mirror[Alg.2(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r D2 r' B2 r B2 r2 U2 r' F2 l F2 D2 r2
+
{{Alg6|wca=U2 r D2 r' B2 r B2 r2 U2 r' F2 l F2 D2 r2
 
|sign=U2 2R D2 2R' B2 2R B2 2R2 U2 2R' F2 2L F2 D2 2R2
 
|sign=U2 2R D2 2R' B2 2R B2 2R2 U2 2R' F2 2L F2 D2 2R2
 
|length=(25,15)|name=Inverse[Alg.2(v3)]
 
|length=(25,15)|name=Inverse[Alg.2(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r' U2 l F2 l2 D2 l' D2 l B2 l' F2
+
{{Alg6|wca=l2 B2 U2 r' U2 l F2 l2 D2 l' D2 l B2 l' F2
 
|sign=2L2 B2 U2 2R' U2 2L F2 2L2 D2 2L' D2 2L B2 2L' F2
 
|sign=2L2 B2 U2 2R' U2 2L F2 2L2 D2 2L' D2 2L B2 2L' F2
 
|length=(25,15)|name=Rotation[Alg.2(v3)]
 
|length=(25,15)|name=Rotation[Alg.2(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 l' D2 l B2 l' B2 l2 U2 l F2 r' F2 D2 l2
+
{{Alg6|wca=U2 l' D2 l B2 l' B2 l2 U2 l F2 r' F2 D2 l2
 
|sign=U2 2L' D2 2L B2 2L' B2 2L2 U2 2L F2 2R' F2 D2 2L2
 
|sign=U2 2L' D2 2L B2 2L' B2 2L2 U2 2L F2 2R' F2 D2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v3)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 U2 l U2 r' F2 r2 D2 r D2 r' B2 r F2
+
{{Alg6|wca=r2 B2 U2 l U2 r' F2 r2 D2 r D2 r' B2 r F2
 
|sign=2R2 B2 U2 2L U2 2R' F2 2R2 D2 2R D2 2R' B2 2R F2
 
|sign=2R2 B2 U2 2L U2 2R' F2 2R2 D2 2R D2 2R' B2 2R F2
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v3)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 l B2 l' D2 l D2 l2 F2 l' U2 r U2 B2 l2
+
{{Alg6|wca=F2 l B2 l' D2 l D2 l2 F2 l' U2 r U2 B2 l2
 
|sign=F2 2L B2 2L' D2 2L D2 2L2 F2 2L' U2 2R U2 B2 2L2
 
|sign=F2 2L B2 2L' D2 2L D2 2L2 F2 2L' U2 2R U2 B2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v3)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 r' B2 r D2 r' D2 r2 F2 r U2 l' U2 B2 r2
+
{{Alg6|wca=F2 r' B2 r D2 r' D2 r2 F2 r U2 l' U2 B2 r2
 
|sign=F2 2R' B2 2R D2 2R' D2 2R2 F2 2R U2 2L' U2 B2 2R2
 
|sign=F2 2R' B2 2R D2 2R' D2 2R2 F2 2R U2 2L' U2 B2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v3)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v3)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 U2 B2 r B2 l' D2 r2 B2 l B2 l' D2 l U2
+
{{Alg6|wca=r2 U2 B2 r B2 l' D2 r2 B2 l B2 l' D2 l U2
 
|sign=2R2 U2 B2 2R B2 2L' D2 2R2 B2 2L B2 2L' D2 2L U2
 
|sign=2R2 U2 B2 2R B2 2L' D2 2R2 B2 2L B2 2L' D2 2L U2
 
|length=(25,15)|name=Alg.2(v4)
 
|length=(25,15)|name=Alg.2(v4)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 l' B2 r D2 l2 B2 r' B2 r D2 r' U2
+
{{Alg6|wca=l2 U2 B2 l' B2 r D2 l2 B2 r' B2 r D2 r' U2
 
|sign=2L2 U2 B2 2L' B2 2R D2 2L2 B2 2R' B2 2R D2 2R' U2
 
|sign=2L2 U2 B2 2L' B2 2R D2 2L2 B2 2R' B2 2R D2 2R' U2
 
|length=(25,15)|name=Mirror[Alg.2(v4)]
 
|length=(25,15)|name=Mirror[Alg.2(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 l' D2 l B2 l' B2 r2 D2 l B2 r' B2 U2 r2
+
{{Alg6|wca=U2 l' D2 l B2 l' B2 r2 D2 l B2 r' B2 U2 r2
 
|sign=U2 2L' D2 2L B2 2L' B2 2R2 D2 2L B2 2R' B2 U2 2R2
 
|sign=U2 2L' D2 2L B2 2L' B2 2R2 D2 2L B2 2R' B2 U2 2R2
 
|length=(25,15)|name=Inverse[Alg.2(v4)]
 
|length=(25,15)|name=Inverse[Alg.2(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l D2 r' B2 l2 D2 r D2 r' B2 r F2
+
{{Alg6|wca=l2 F2 D2 l D2 r' B2 l2 D2 r D2 r' B2 r F2
 
|sign=2L2 F2 D2 2L D2 2R' B2 2L2 D2 2R D2 2R' B2 2R F2
 
|sign=2L2 F2 D2 2L D2 2R' B2 2L2 D2 2R D2 2R' B2 2R F2
 
|length=(25,15)|name=Rotation[Alg.2(v4)]
 
|length=(25,15)|name=Rotation[Alg.2(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r D2 r' B2 r B2 l2 D2 r' B2 l B2 U2 l2
+
{{Alg6|wca=U2 r D2 r' B2 r B2 l2 D2 r' B2 l B2 U2 l2
 
|sign=U2 2R D2 2R' B2 2R B2 2L2 D2 2R' B2 2L B2 U2 2L2
 
|sign=U2 2R D2 2R' B2 2R B2 2L2 D2 2R' B2 2L B2 U2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v4)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 r' D2 l B2 r2 D2 l' D2 l B2 l' F2
+
{{Alg6|wca=r2 F2 D2 r' D2 l B2 r2 D2 l' D2 l B2 l' F2
 
|sign=2R2 F2 D2 2R' D2 2L B2 2R2 D2 2L' D2 2L B2 2L' F2
 
|sign=2R2 F2 D2 2R' D2 2L B2 2R2 D2 2L' D2 2L B2 2L' F2
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v4)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 r' B2 r D2 r' D2 l2 B2 r D2 l' D2 F2 l2
+
{{Alg6|wca=F2 r' B2 r D2 r' D2 l2 B2 r D2 l' D2 F2 l2
 
|sign=F2 2R' B2 2R D2 2R' D2 2L2 B2 2R D2 2L' D2 F2 2L2
 
|sign=F2 2R' B2 2R D2 2R' D2 2L2 B2 2R D2 2L' D2 F2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v4)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 l B2 l' D2 l D2 r2 B2 l' D2 r D2 F2 r2
+
{{Alg6|wca=F2 l B2 l' D2 l D2 r2 B2 l' D2 r D2 F2 r2
 
|sign=F2 2L B2 2L' D2 2L D2 2R2 B2 2L' D2 2R D2 F2 2R2
 
|sign=F2 2L B2 2L' D2 2L D2 2R2 B2 2L' D2 2R D2 F2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v4)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v4)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 U2 B2 l U2 r' U2 l2 B2 r D2 r' D2 l U2
+
{{Alg6|wca=r2 U2 B2 l U2 r' U2 l2 B2 r D2 r' D2 l U2
 
|sign=2R2 U2 B2 2L U2 2R' U2 2L2 B2 2R D2 2R' D2 2L U2
 
|sign=2R2 U2 B2 2L U2 2R' U2 2L2 B2 2R D2 2R' D2 2L U2
 
|length=(25,15)|name=Alg.2(v5)
 
|length=(25,15)|name=Alg.2(v5)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 r' U2 l U2 r2 B2 l' D2 l D2 r' U2
+
{{Alg6|wca=l2 U2 B2 r' U2 l U2 r2 B2 l' D2 l D2 r' U2
 
|sign=2L2 U2 B2 2R' U2 2L U2 2R2 B2 2L' D2 2L D2 2R' U2
 
|sign=2L2 U2 B2 2R' U2 2L U2 2R2 B2 2L' D2 2L D2 2R' U2
 
|length=(25,15)|name=Mirror[Alg.2(v5)]
 
|length=(25,15)|name=Mirror[Alg.2(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 l' D2 r D2 r' B2 l2 U2 r U2 l' B2 U2 r2
+
{{Alg6|wca=U2 l' D2 r D2 r' B2 l2 U2 r U2 l' B2 U2 r2
 
|sign=U2 2L' D2 2R D2 2R' B2 2L2 U2 2R U2 2L' B2 U2 2R2
 
|sign=U2 2L' D2 2R D2 2R' B2 2L2 U2 2R U2 2L' B2 U2 2R2
 
|length=(25,15)|name=Inverse[Alg.2(v5)]
 
|length=(25,15)|name=Inverse[Alg.2(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r F2 l' F2 r2 D2 l B2 l' B2 r F2
+
{{Alg6|wca=l2 F2 D2 r F2 l' F2 r2 D2 l B2 l' B2 r F2
 
|sign=2L2 F2 D2 2R F2 2L' F2 2R2 D2 2L B2 2L' B2 2R F2
 
|sign=2L2 F2 D2 2R F2 2L' F2 2R2 D2 2L B2 2L' B2 2R F2
 
|length=(25,15)|name=Rotation[Alg.2(v5)]
 
|length=(25,15)|name=Rotation[Alg.2(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r D2 l' D2 l B2 r2 U2 l' U2 r B2 U2 l2
+
{{Alg6|wca=U2 r D2 l' D2 l B2 r2 U2 l' U2 r B2 U2 l2
 
|sign=U2 2R D2 2L' D2 2L B2 2R2 U2 2L' U2 2R B2 U2 2L2
 
|sign=U2 2R D2 2L' D2 2L B2 2R2 U2 2L' U2 2R B2 U2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v5)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.2(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 l' F2 r F2 l2 D2 r' B2 r B2 l' F2
+
{{Alg6|wca=r2 F2 D2 l' F2 r F2 l2 D2 r' B2 r B2 l' F2
 
|sign=2R2 F2 D2 2L' F2 2R F2 2L2 D2 2R' B2 2R B2 2L' F2
 
|sign=2R2 F2 D2 2L' F2 2R F2 2L2 D2 2R' B2 2R B2 2L' F2
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v5)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.2(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 r' B2 l B2 l' D2 r2 F2 l F2 r' D2 F2 l2
+
{{Alg6|wca=F2 r' B2 l B2 l' D2 r2 F2 l F2 r' D2 F2 l2
 
|sign=F2 2R' B2 2L B2 2L' D2 2R2 F2 2L F2 2R' D2 F2 2L2
 
|sign=F2 2R' B2 2L B2 2L' D2 2R2 F2 2L F2 2R' D2 F2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v5)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.2(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=F2 l B2 r' B2 r D2 l2 F2 r' F2 l D2 F2 r2
+
{{Alg6|wca=F2 l B2 r' B2 r D2 l2 F2 r' F2 l D2 F2 r2
 
|sign=F2 2L B2 2R' B2 2R D2 2L2 F2 2R' F2 2L D2 F2 2R2
 
|sign=F2 2L B2 2R' B2 2R D2 2L2 F2 2R' F2 2L D2 F2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v5)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v5)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Group 3: cyclic shift of Group 1</span>=====
=====Group 3: cyclic shift of Group 1=====
+
{{Alg6|wca=r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2
{{Alg5|wca=r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2
 
 
|sign=2R B2 2R' U2 2L B2 2L2 B2 U2 2L U2 2L' U2 2L2 B2
 
|sign=2R B2 2R' U2 2L B2 2L2 B2 U2 2L U2 2L' U2 2L2 B2
 
|length=(25,15)|name=Alg.3(v1)
 
|length=(25,15)|name=Alg.3(v1)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2
+
{{Alg6|wca=l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2
 
|sign=2L' B2 2L U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 2R2 B2
 
|sign=2L' B2 2L U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 2R2 B2
 
|length=(25,15)|name=Mirror[Alg.3(v1)]
 
|length=(25,15)|name=Mirror[Alg.3(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r'
+
{{Alg6|wca=B2 l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r'
 
|sign=B2 2L2 U2 2L U2 2L' U2 B2 2L2 B2 2L' U2 2R B2 2R'
 
|sign=B2 2L2 U2 2L U2 2L' U2 B2 2L2 B2 2L' U2 2R B2 2R'
 
|length=(25,15)|name=Inverse[Alg.3(v1)]
 
|length=(25,15)|name=Inverse[Alg.3(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2 D2
+
{{Alg6|wca=l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2 D2
 
|sign=2L D2 2L' F2 2R D2 2R2 D2 F2 2R F2 2R' F2 2R2 D2
 
|sign=2L D2 2L' F2 2R D2 2R2 D2 F2 2R F2 2R' F2 2R2 D2
 
|length=(25,15)|name=Rotation[Alg.3(v1)]
 
|length=(25,15)|name=Rotation[Alg.3(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l
+
{{Alg6|wca=B2 r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l
 
|sign=B2 2R2 U2 2R' U2 2R U2 B2 2R2 B2 2R U2 2L' B2 2L
 
|sign=B2 2R2 U2 2R' U2 2R U2 B2 2R2 B2 2R U2 2L' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v1)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2 D2
+
{{Alg6|wca=r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2 D2
 
|sign=2R' D2 2R F2 2L' D2 2L2 D2 F2 2L' F2 2L F2 2L2 D2
 
|sign=2R' D2 2R F2 2L' D2 2L2 D2 F2 2L' F2 2L F2 2L2 D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v1)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l'
+
{{Alg6|wca=D2 r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l'
 
|sign=D2 2R2 F2 2R F2 2R' F2 D2 2R2 D2 2R' F2 2L D2 2L'
 
|sign=D2 2R2 F2 2R F2 2R' F2 D2 2R2 D2 2R' F2 2L D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v1)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r
+
{{Alg6|wca=D2 l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r
 
|sign=D2 2L2 F2 2L' F2 2L F2 D2 2L2 D2 2L F2 2R' D2 2R
 
|sign=D2 2L2 F2 2L' F2 2L F2 D2 2L2 D2 2L F2 2R' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v1)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v1)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2
+
{{Alg6|wca=r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2
 
|sign=2R B2 2R' U2 2R D2 2R2 U2 F2 2L F2 2R' D2 2R2 B2
 
|sign=2R B2 2R' U2 2R D2 2R2 U2 F2 2L F2 2R' D2 2R2 B2
 
|length=(25,15)|name=Alg.3(v2)
 
|length=(25,15)|name=Alg.3(v2)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2 B2
+
{{Alg6|wca=l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2 B2
 
|sign=2L' B2 2L U2 2L' D2 2L2 U2 F2 2R' F2 2L D2 2L2 B2
 
|sign=2L' B2 2L U2 2L' D2 2L2 U2 F2 2R' F2 2L D2 2L2 B2
 
|length=(25,15)|name=Mirror[Alg.3(v2)]
 
|length=(25,15)|name=Mirror[Alg.3(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r'
+
{{Alg6|wca=B2 r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r'
 
|sign=B2 2R2 D2 2R F2 2L' F2 U2 2R2 D2 2R' U2 2R B2 2R'
 
|sign=B2 2R2 D2 2R F2 2L' F2 U2 2R2 D2 2R' U2 2R B2 2R'
 
|length=(25,15)|name=Inverse[Alg.3(v2)]
 
|length=(25,15)|name=Inverse[Alg.3(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2 D2
+
{{Alg6|wca=l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2 D2
 
|sign=2L D2 2L' F2 2L B2 2L2 F2 U2 2R U2 2L' B2 2L2 D2
 
|sign=2L D2 2L' F2 2L B2 2L2 F2 U2 2R U2 2L' B2 2L2 D2
 
|length=(25,15)|name=Rotation[Alg.3(v2)]
 
|length=(25,15)|name=Rotation[Alg.3(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l
+
{{Alg6|wca=B2 l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l
 
|sign=B2 2L2 D2 2L' F2 2R F2 U2 2L2 D2 2L U2 2L' B2 2L
 
|sign=B2 2L2 D2 2L' F2 2R F2 U2 2L2 D2 2L U2 2L' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v2)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2 D2
+
{{Alg6|wca=r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2 D2
 
|sign=2R' D2 2R F2 2R' B2 2R2 F2 U2 2L' U2 2R B2 2R2 D2
 
|sign=2R' D2 2R F2 2R' B2 2R2 F2 U2 2L' U2 2R B2 2R2 D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v2)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l'
+
{{Alg6|wca=D2 l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l'
 
|sign=D2 2L2 B2 2L U2 2R' U2 F2 2L2 B2 2L' F2 2L D2 2L'
 
|sign=D2 2L2 B2 2L U2 2R' U2 F2 2L2 B2 2L' F2 2L D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v2)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r
+
{{Alg6|wca=D2 r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r
 
|sign=D2 2R2 B2 2R' U2 2L U2 F2 2R2 B2 2R F2 2R' D2 2R
 
|sign=D2 2R2 B2 2R' U2 2L U2 F2 2R2 B2 2R F2 2R' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v2)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v2)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2
+
{{Alg6|wca=r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2
 
|sign=2R B2 2R' U2 2R D2 2L2 D2 B2 2L B2 2R' U2 2L2 B2
 
|sign=2R B2 2R' U2 2R D2 2L2 D2 B2 2L B2 2R' U2 2L2 B2
 
|length=(25,15)|name=Alg.3(v3)
 
|length=(25,15)|name=Alg.3(v3)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2 B2
+
{{Alg6|wca=l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2 B2
 
|sign=2L' B2 2L U2 2L' D2 2R2 D2 B2 2R' B2 2L U2 2R2 B2
 
|sign=2L' B2 2L U2 2L' D2 2R2 D2 B2 2R' B2 2L U2 2R2 B2
 
|length=(25,15)|name=Mirror[Alg.3(v3)]
 
|length=(25,15)|name=Mirror[Alg.3(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r'
+
{{Alg6|wca=B2 l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r'
 
|sign=B2 2L2 U2 2R B2 2L' B2 D2 2L2 D2 2R' U2 2R B2 2R'
 
|sign=B2 2L2 U2 2R B2 2L' B2 D2 2L2 D2 2R' U2 2R B2 2R'
 
|length=(25,15)|name=Inverse[Alg.3(v3)]
 
|length=(25,15)|name=Inverse[Alg.3(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2 D2
+
{{Alg6|wca=l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2 D2
 
|sign=2L D2 2L' F2 2L B2 2R2 B2 D2 2R D2 2L' F2 2R2 D2
 
|sign=2L D2 2L' F2 2L B2 2R2 B2 D2 2R D2 2L' F2 2R2 D2
 
|length=(25,15)|name=Rotation[Alg.3(v3)]
 
|length=(25,15)|name=Rotation[Alg.3(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l
+
{{Alg6|wca=B2 r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l
 
|sign=B2 2R2 U2 2L' B2 2R B2 D2 2R2 D2 2L U2 2L' B2 2L
 
|sign=B2 2R2 U2 2L' B2 2R B2 D2 2R2 D2 2L U2 2L' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v3)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2 D2
+
{{Alg6|wca=r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2 D2
 
|sign=2R' D2 2R F2 2R' B2 2L2 B2 D2 2L' D2 2R F2 2L2 D2
 
|sign=2R' D2 2R F2 2R' B2 2L2 B2 D2 2L' D2 2R F2 2L2 D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v3)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l'
+
{{Alg6|wca=D2 r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l'
 
|sign=D2 2R2 F2 2L D2 2R' D2 B2 2R2 B2 2L' F2 2L D2 2L'
 
|sign=D2 2R2 F2 2L D2 2R' D2 B2 2R2 B2 2L' F2 2L D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v3)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r
+
{{Alg6|wca=D2 l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r
 
|sign=D2 2L2 F2 2R' D2 2L D2 B2 2L2 B2 2R F2 2R' D2 2R
 
|sign=D2 2L2 F2 2R' D2 2L D2 B2 2L2 B2 2R F2 2R' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v3)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v3)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2
+
{{Alg6|wca=r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2
 
|sign=2R B2 2L' B2 2L D2 2L2 D2 B2 2R D2 2L' D2 2R2 B2
 
|sign=2R B2 2L' B2 2L D2 2L2 D2 B2 2R D2 2L' D2 2R2 B2
 
|length=(25,15)|name=Alg.3(v4)
 
|length=(25,15)|name=Alg.3(v4)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2 B2
+
{{Alg6|wca=l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2 B2
 
|sign=2L' B2 2R B2 2R' D2 2R2 D2 B2 2L' D2 2R D2 2L2 B2
 
|sign=2L' B2 2R B2 2R' D2 2R2 D2 B2 2L' D2 2R D2 2L2 B2
 
|length=(25,15)|name=Mirror[Alg.3(v4)]
 
|length=(25,15)|name=Mirror[Alg.3(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r'
+
{{Alg6|wca=B2 r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r'
 
|sign=B2 2R2 D2 2L D2 2R' B2 D2 2L2 D2 2L' B2 2L B2 2R'
 
|sign=B2 2R2 D2 2L D2 2R' B2 D2 2L2 D2 2L' B2 2L B2 2R'
 
|length=(25,15)|name=Inverse[Alg.3(v4)]
 
|length=(25,15)|name=Inverse[Alg.3(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2 D2
+
{{Alg6|wca=l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2 D2
 
|sign=2L D2 2R' D2 2R B2 2R2 B2 D2 2L B2 2R' B2 2L2 D2
 
|sign=2L D2 2R' D2 2R B2 2R2 B2 D2 2L B2 2R' B2 2L2 D2
 
|length=(25,15)|name=Rotation[Alg.3(v4)]
 
|length=(25,15)|name=Rotation[Alg.3(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l
+
{{Alg6|wca=B2 l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l
 
|sign=B2 2L2 D2 2R' D2 2L B2 D2 2R2 D2 2R B2 2R' B2 2L
 
|sign=B2 2L2 D2 2R' D2 2L B2 D2 2R2 D2 2R B2 2R' B2 2L
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v4)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2 D2
+
{{Alg6|wca=r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2 D2
 
|sign=2R' D2 2L D2 2L' B2 2L2 B2 D2 2R' B2 2L B2 2R2 D2
 
|sign=2R' D2 2L D2 2L' B2 2L2 B2 D2 2R' B2 2L B2 2R2 D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v4)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l'
+
{{Alg6|wca=D2 l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l'
 
|sign=D2 2L2 B2 2R B2 2L' D2 B2 2R2 B2 2R' D2 2R D2 2L'
 
|sign=D2 2L2 B2 2R B2 2L' D2 B2 2R2 B2 2R' D2 2R D2 2L'
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v4)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r
+
{{Alg6|wca=D2 r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r
 
|sign=D2 2R2 B2 2L' B2 2R D2 B2 2L2 B2 2L D2 2L' D2 2R
 
|sign=D2 2R2 B2 2L' B2 2R D2 B2 2L2 B2 2L D2 2L' D2 2R
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v4)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v4)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2
+
{{Alg6|wca=r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2
 
|sign=2R' U2 2R U2 2L' D2 2R2 D2 B2 2L' D2 2R D2 2L2 B2
 
|sign=2R' U2 2R U2 2L' D2 2R2 D2 B2 2L' D2 2R D2 2L2 B2
 
|length=(25,15)|name=Alg.3(v5)
 
|length=(25,15)|name=Alg.3(v5)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2 B2
+
{{Alg6|wca=l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2 B2
 
|sign=2L U2 2L' U2 2R D2 2L2 D2 B2 2R D2 2L' D2 2R2 B2
 
|sign=2L U2 2L' U2 2R D2 2L2 D2 B2 2R D2 2L' D2 2R2 B2
 
|length=(25,15)|name=Mirror[Alg.3(v5)]
 
|length=(25,15)|name=Mirror[Alg.3(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r
+
{{Alg6|wca=B2 l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r
 
|sign=B2 2L2 D2 2R' D2 2L B2 D2 2R2 D2 2L U2 2R' U2 2R
 
|sign=B2 2L2 D2 2R' D2 2L B2 D2 2R2 D2 2L U2 2R' U2 2R
 
|length=(25,15)|name=Inverse[Alg.3(v5)]
 
|length=(25,15)|name=Inverse[Alg.3(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2 D2
+
{{Alg6|wca=l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2 D2
 
|sign=2L' F2 2L F2 2R' B2 2L2 B2 D2 2R' B2 2L B2 2R2 D2
 
|sign=2L' F2 2L F2 2R' B2 2L2 B2 D2 2R' B2 2L B2 2R2 D2
 
|length=(25,15)|name=Rotation[Alg.3(v5)]
 
|length=(25,15)|name=Rotation[Alg.3(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l'
+
{{Alg6|wca=B2 r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l'
 
|sign=B2 2R2 D2 2L D2 2R' B2 D2 2L2 D2 2R' U2 2L U2 2L'
 
|sign=B2 2R2 D2 2L D2 2R' B2 D2 2L2 D2 2R' U2 2L U2 2L'
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v5)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.3(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2 D2
+
{{Alg6|wca=r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2 D2
 
|sign=2R F2 2R' F2 2L B2 2R2 B2 D2 2L B2 2R' B2 2L2 D2
 
|sign=2R F2 2R' F2 2L B2 2R2 B2 D2 2L B2 2R' B2 2L2 D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v5)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.3(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l
+
{{Alg6|wca=D2 r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l
 
|sign=D2 2R2 B2 2L' B2 2R D2 B2 2L2 B2 2R F2 2L' F2 2L
 
|sign=D2 2R2 B2 2L' B2 2R D2 B2 2L2 B2 2R F2 2L' F2 2L
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v5)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.3(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r'
+
{{Alg6|wca=D2 l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r'
 
|sign=D2 2L2 B2 2R B2 2L' D2 B2 2R2 B2 2L' F2 2R F2 2R'
 
|sign=D2 2L2 B2 2R B2 2L' D2 B2 2R2 B2 2L' F2 2R F2 2R'
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v5)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v5)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Group 4: B2 move conjugation of Group 3</span>=====
=====Group 4: B2 move conjugation of Group 3=====
+
{{Alg6|wca=r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l B2
{{Alg5|wca=r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l B2
 
 
|sign=2R2 U2 2R' U2 2R U2 B2 2R2 B2 2R U2 2L' B2 2L B2
 
|sign=2R2 U2 2R' U2 2R U2 B2 2R2 B2 2R U2 2L' B2 2L B2
 
|length=(25,15)|name=Alg.4(v1)
 
|length=(25,15)|name=Alg.4(v1)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r' B2
+
{{Alg6|wca=l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r' B2
 
|sign=2L2 U2 2L U2 2L' U2 B2 2L2 B2 2L' U2 2R B2 2R' B2
 
|sign=2L2 U2 2L U2 2L' U2 B2 2L2 B2 2L' U2 2R B2 2R' B2
 
|length=(25,15)|name=Mirror[Alg.4(v1)]
 
|length=(25,15)|name=Mirror[Alg.4(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2
+
{{Alg6|wca=B2 l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2
 
|sign=B2 2L' B2 2L U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 2R2
 
|sign=B2 2L' B2 2L U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 2R2
 
|length=(25,15)|name=Inverse[Alg.4(v1)]
 
|length=(25,15)|name=Inverse[Alg.4(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r D2
+
{{Alg6|wca=l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r D2
 
|sign=2L2 F2 2L' F2 2L F2 D2 2L2 D2 2L F2 2R' D2 2R D2
 
|sign=2L2 F2 2L' F2 2L F2 D2 2L2 D2 2L F2 2R' D2 2R D2
 
|length=(25,15)|name=Rotation[Alg.4(v1)]
 
|length=(25,15)|name=Rotation[Alg.4(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2
+
{{Alg6|wca=B2 r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2
 
|sign=B2 2R B2 2R' U2 2L B2 2L2 B2 U2 2L U2 2L' U2 2L2
 
|sign=B2 2R B2 2R' U2 2L B2 2L2 B2 U2 2L U2 2L' U2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v1)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l' D2
+
{{Alg6|wca=r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l' D2
 
|sign=2R2 F2 2R F2 2R' F2 D2 2R2 D2 2R' F2 2L D2 2L' D2
 
|sign=2R2 F2 2R F2 2R' F2 D2 2R2 D2 2R' F2 2L D2 2L' D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v1)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2
+
{{Alg6|wca=D2 r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2
 
|sign=D2 2R' D2 2R F2 2L' D2 2L2 D2 F2 2L' F2 2L F2 2L2
 
|sign=D2 2R' D2 2R F2 2L' D2 2L2 D2 F2 2L' F2 2L F2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v1)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2
+
{{Alg6|wca=D2 l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2
 
|sign=D2 2L D2 2L' F2 2R D2 2R2 D2 F2 2R F2 2R' F2 2R2
 
|sign=D2 2L D2 2L' F2 2R D2 2R2 D2 F2 2R F2 2R' F2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v1)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v1)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r' B2
+
{{Alg6|wca=r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r' B2
 
|sign=2R2 D2 2R F2 2L' F2 U2 2R2 D2 2R' U2 2R B2 2R' B2
 
|sign=2R2 D2 2R F2 2L' F2 U2 2R2 D2 2R' U2 2R B2 2R' B2
 
|length=(25,15)|name=Alg.4(v2)
 
|length=(25,15)|name=Alg.4(v2)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l B2
+
{{Alg6|wca=l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l B2
 
|sign=2L2 D2 2L' F2 2R F2 U2 2L2 D2 2L U2 2L' B2 2L B2
 
|sign=2L2 D2 2L' F2 2R F2 U2 2L2 D2 2L U2 2L' B2 2L B2
 
|length=(25,15)|name=Mirror[Alg.4(v2)]
 
|length=(25,15)|name=Mirror[Alg.4(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2
+
{{Alg6|wca=B2 r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2
 
|sign=B2 2R B2 2R' U2 2R D2 2R2 U2 F2 2L F2 2R' D2 2R2
 
|sign=B2 2R B2 2R' U2 2R D2 2R2 U2 F2 2L F2 2R' D2 2R2
 
|length=(25,15)|name=Inverse[Alg.4(v2)]
 
|length=(25,15)|name=Inverse[Alg.4(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l' D2
+
{{Alg6|wca=l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l' D2
 
|sign=2L2 B2 2L U2 2R' U2 F2 2L2 B2 2L' F2 2L D2 2L' D2
 
|sign=2L2 B2 2L U2 2R' U2 F2 2L2 B2 2L' F2 2L D2 2L' D2
 
|length=(25,15)|name=Rotation[Alg.4(v2)]
 
|length=(25,15)|name=Rotation[Alg.4(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2
+
{{Alg6|wca=B2 l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2
 
|sign=B2 2L' B2 2L U2 2L' D2 2L2 U2 F2 2R' F2 2L D2 2L2
 
|sign=B2 2L' B2 2L U2 2L' D2 2L2 U2 F2 2R' F2 2L D2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v2)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r D2
+
{{Alg6|wca=r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r D2
 
|sign=2R2 B2 2R' U2 2L U2 F2 2R2 B2 2R F2 2R' D2 2R D2
 
|sign=2R2 B2 2R' U2 2L U2 F2 2R2 B2 2R F2 2R' D2 2R D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v2)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2
+
{{Alg6|wca=D2 l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2
 
|sign=D2 2L D2 2L' F2 2L B2 2L2 F2 U2 2R U2 2L' B2 2L2
 
|sign=D2 2L D2 2L' F2 2L B2 2L2 F2 U2 2R U2 2L' B2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v2)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2
+
{{Alg6|wca=D2 r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2
 
|sign=D2 2R' D2 2R F2 2R' B2 2R2 F2 U2 2L' U2 2R B2 2R2
 
|sign=D2 2R' D2 2R F2 2R' B2 2R2 F2 U2 2L' U2 2R B2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v2)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v2)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l B2
+
{{Alg6|wca=r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l B2
 
|sign=2R2 U2 2L' B2 2R B2 D2 2R2 D2 2L U2 2L' B2 2L B2
 
|sign=2R2 U2 2L' B2 2R B2 D2 2R2 D2 2L U2 2L' B2 2L B2
 
|length=(25,15)|name=Alg.4(v3)
 
|length=(25,15)|name=Alg.4(v3)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r' B2
+
{{Alg6|wca=l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r' B2
 
|sign=2L2 U2 2R B2 2L' B2 D2 2L2 D2 2R' U2 2R B2 2R' B2
 
|sign=2L2 U2 2R B2 2L' B2 D2 2L2 D2 2R' U2 2R B2 2R' B2
 
|length=(25,15)|name=Mirror[Alg.4(v3)]
 
|length=(25,15)|name=Mirror[Alg.4(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2
+
{{Alg6|wca=B2 l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2
 
|sign=B2 2L' B2 2L U2 2L' D2 2R2 D2 B2 2R' B2 2L U2 2R2
 
|sign=B2 2L' B2 2L U2 2L' D2 2R2 D2 B2 2R' B2 2L U2 2R2
 
|length=(25,15)|name=Inverse[Alg.4(v3)]
 
|length=(25,15)|name=Inverse[Alg.4(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r D2
+
{{Alg6|wca=l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r D2
 
|sign=2L2 F2 2R' D2 2L D2 B2 2L2 B2 2R F2 2R' D2 2R D2
 
|sign=2L2 F2 2R' D2 2L D2 B2 2L2 B2 2R F2 2R' D2 2R D2
 
|length=(25,15)|name=Rotation[Alg.4(v3)]
 
|length=(25,15)|name=Rotation[Alg.4(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2
+
{{Alg6|wca=B2 r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2
 
|sign=B2 2R B2 2R' U2 2R D2 2L2 D2 B2 2L B2 2R' U2 2L2
 
|sign=B2 2R B2 2R' U2 2R D2 2L2 D2 B2 2L B2 2R' U2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v3)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l' D2
+
{{Alg6|wca=r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l' D2
 
|sign=2R2 F2 2L D2 2R' D2 B2 2R2 B2 2L' F2 2L D2 2L' D2
 
|sign=2R2 F2 2L D2 2R' D2 B2 2R2 B2 2L' F2 2L D2 2L' D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v3)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2
+
{{Alg6|wca=D2 r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2
 
|sign=D2 2R' D2 2R F2 2R' B2 2L2 B2 D2 2L' D2 2R F2 2L2
 
|sign=D2 2R' D2 2R F2 2R' B2 2L2 B2 D2 2L' D2 2R F2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v3)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2
+
{{Alg6|wca=D2 l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2
 
|sign=D2 2L D2 2L' F2 2L B2 2R2 B2 D2 2R D2 2L' F2 2R2
 
|sign=D2 2L D2 2L' F2 2L B2 2R2 B2 D2 2R D2 2L' F2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v3)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v3)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r' B2
+
{{Alg6|wca=r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r' B2
 
|sign=2R2 D2 2L D2 2R' B2 D2 2L2 D2 2L' B2 2L B2 2R' B2
 
|sign=2R2 D2 2L D2 2R' B2 D2 2L2 D2 2L' B2 2L B2 2R' B2
 
|length=(25,15)|name=Alg.4(v4)
 
|length=(25,15)|name=Alg.4(v4)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l B2
+
{{Alg6|wca=l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l B2
 
|sign=2L2 D2 2R' D2 2L B2 D2 2R2 D2 2R B2 2R' B2 2L B2
 
|sign=2L2 D2 2R' D2 2L B2 D2 2R2 D2 2R B2 2R' B2 2L B2
 
|length=(25,15)|name=Mirror[Alg.4(v4)]
 
|length=(25,15)|name=Mirror[Alg.4(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2
+
{{Alg6|wca=B2 r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2
 
|sign=B2 2R B2 2L' B2 2L D2 2L2 D2 B2 2R D2 2L' D2 2R2
 
|sign=B2 2R B2 2L' B2 2L D2 2L2 D2 B2 2R D2 2L' D2 2R2
 
|length=(25,15)|name=Inverse[Alg.4(v4)]
 
|length=(25,15)|name=Inverse[Alg.4(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l' D2
+
{{Alg6|wca=l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l' D2
 
|sign=2L2 B2 2R B2 2L' D2 B2 2R2 B2 2R' D2 2R D2 2L' D2
 
|sign=2L2 B2 2R B2 2L' D2 B2 2R2 B2 2R' D2 2R D2 2L' D2
 
|length=(25,15)|name=Rotation[Alg.4(v4)]
 
|length=(25,15)|name=Rotation[Alg.4(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2
+
{{Alg6|wca=B2 l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2
 
|sign=B2 2L' B2 2R B2 2R' D2 2R2 D2 B2 2L' D2 2R D2 2L2
 
|sign=B2 2L' B2 2R B2 2R' D2 2R2 D2 B2 2L' D2 2R D2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v4)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r D2
+
{{Alg6|wca=r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r D2
 
|sign=2R2 B2 2L' B2 2R D2 B2 2L2 B2 2L D2 2L' D2 2R D2
 
|sign=2R2 B2 2L' B2 2R D2 B2 2L2 B2 2L D2 2L' D2 2R D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v4)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2
+
{{Alg6|wca=D2 l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2
 
|sign=D2 2L D2 2R' D2 2R B2 2R2 B2 D2 2L B2 2R' B2 2L2
 
|sign=D2 2L D2 2R' D2 2R B2 2R2 B2 D2 2L B2 2R' B2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v4)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2
+
{{Alg6|wca=D2 r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2
 
|sign=D2 2R' D2 2L D2 2L' B2 2L2 B2 D2 2R' B2 2L B2 2R2
 
|sign=D2 2R' D2 2L D2 2L' B2 2L2 B2 D2 2R' B2 2L B2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v4)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v4)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l' B2
+
{{Alg6|wca=r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l' B2
 
|sign=2R2 D2 2L D2 2R' B2 D2 2L2 D2 2R' U2 2L U2 2L' B2
 
|sign=2R2 D2 2L D2 2R' B2 D2 2L2 D2 2R' U2 2L U2 2L' B2
 
|length=(25,15)|name=Alg.4(v5)
 
|length=(25,15)|name=Alg.4(v5)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r B2
+
{{Alg6|wca=l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r B2
 
|sign=2L2 D2 2R' D2 2L B2 D2 2R2 D2 2L U2 2R' U2 2R B2
 
|sign=2L2 D2 2R' D2 2L B2 D2 2R2 D2 2L U2 2R' U2 2R B2
 
|length=(25,15)|name=Mirror[Alg.4(v5)]
 
|length=(25,15)|name=Mirror[Alg.4(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2
+
{{Alg6|wca=B2 l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2
 
|sign=B2 2L U2 2L' U2 2R D2 2L2 D2 B2 2R D2 2L' D2 2R2
 
|sign=B2 2L U2 2L' U2 2R D2 2L2 D2 B2 2R D2 2L' D2 2R2
 
|length=(25,15)|name=Inverse[Alg.4(v5)]
 
|length=(25,15)|name=Inverse[Alg.4(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r' D2
+
{{Alg6|wca=l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r' D2
 
|sign=2L2 B2 2R B2 2L' D2 B2 2R2 B2 2L' F2 2R F2 2R' D2
 
|sign=2L2 B2 2R B2 2L' D2 B2 2R2 B2 2L' F2 2R F2 2R' D2
 
|length=(25,15)|name=Rotation[Alg.4(v5)]
 
|length=(25,15)|name=Rotation[Alg.4(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=B2 r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2
+
{{Alg6|wca=B2 r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2
 
|sign=B2 2R' U2 2R U2 2L' D2 2R2 D2 B2 2L' D2 2R D2 2L2
 
|sign=B2 2R' U2 2R U2 2L' D2 2R2 D2 B2 2L' D2 2R D2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v5)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.4(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l D2
+
{{Alg6|wca=r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l D2
 
|sign=2R2 B2 2L' B2 2R D2 B2 2L2 B2 2R F2 2L' F2 2L D2
 
|sign=2R2 B2 2L' B2 2R D2 B2 2L2 B2 2R F2 2L' F2 2L D2
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v5)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.4(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2
+
{{Alg6|wca=D2 r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2
 
|sign=D2 2R F2 2R' F2 2L B2 2R2 B2 D2 2L B2 2R' B2 2L2
 
|sign=D2 2R F2 2R' F2 2L B2 2R2 B2 D2 2L B2 2R' B2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v5)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.4(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=D2 l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2
+
{{Alg6|wca=D2 l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2
 
|sign=D2 2L' F2 2L F2 2R' B2 2L2 B2 D2 2R' B2 2L B2 2R2
 
|sign=D2 2L' F2 2L F2 2R' B2 2L2 B2 D2 2R' B2 2L B2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v5)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v5)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
====<span style="font-family:Georgia;color:rgb(0,200,0);">Symmetrical algorithms</span>====
====Symmetrical algorithms====
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Group 1</span>=====
=====Group 1=====
 
 
*The first and last turns of each of these algorithms can be made wide turns to still achieve a single dedge flip.
 
*The first and last turns of each of these algorithms can be made wide turns to still achieve a single dedge flip.
{{Alg5|wca=r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
+
{{br|b=1}}
 +
{{Alg6|wca=r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
 
|sign=2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2
 
|sign=2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2
 
|length=(25,15)|name=Alg.5(v1)
 
|length=(25,15)|name=Alg.5(v1)
 
|wide=Y|author=|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
 
|wide=Y|author=|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r' U2 l U2 l' U2 F2 l' F2 r B2 l2
+
{{Alg6|wca=l2 B2 U2 r' U2 l U2 l' U2 F2 l' F2 r B2 l2
 
|sign=2L2 B2 U2 2R' U2 2L U2 2L' U2 F2 2L' F2 2R B2 2L2
 
|sign=2L2 B2 U2 2R' U2 2L U2 2L' U2 F2 2L' F2 2R B2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v1)]
 
|length=(25,15)|name=Mirror[Alg.5(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l F2 r' F2 U2 r' U2 r U2 l' U2 B2 r2
+
{{Alg6|wca=r2 B2 l F2 r' F2 U2 r' U2 r U2 l' U2 B2 r2
 
|sign=2R2 B2 2L F2 2R' F2 U2 2R' U2 2R U2 2L' U2 B2 2R2
 
|sign=2R2 B2 2L F2 2R' F2 U2 2R' U2 2R U2 2L' U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v1)]
 
|length=(25,15)|name=Inverse[Alg.5(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 r F2 l' F2 l F2 U2 l U2 r' D2 l2
+
{{Alg6|wca=l2 D2 F2 r F2 l' F2 l F2 U2 l U2 r' D2 l2
 
|sign=2L2 D2 F2 2R F2 2L' F2 2L F2 U2 2L U2 2R' D2 2L2
 
|sign=2L2 D2 F2 2R F2 2L' F2 2L F2 U2 2L U2 2R' D2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v1)]
 
|length=(25,15)|name=Rotation[Alg.5(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 r' F2 l F2 U2 l U2 l' U2 r U2 B2 l2
+
{{Alg6|wca=l2 B2 r' F2 l F2 U2 l U2 l' U2 r U2 B2 l2
 
|sign=2L2 B2 2R' F2 2L F2 U2 2L U2 2L' U2 2R U2 B2 2L2
 
|sign=2L2 B2 2R' F2 2L F2 U2 2L U2 2L' U2 2R U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v1)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 l' F2 r F2 r' F2 U2 r' U2 l D2 r2
+
{{Alg6|wca=r2 D2 F2 l' F2 r F2 r' F2 U2 r' U2 l D2 r2
 
|sign=2R2 D2 F2 2L' F2 2R F2 2R' F2 U2 2R' U2 2L D2 2R2
 
|sign=2R2 D2 F2 2L' F2 2R F2 2R' F2 U2 2R' U2 2L D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v1)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 r U2 l' U2 F2 l' F2 l F2 r' F2 D2 l2
+
{{Alg6|wca=l2 D2 r U2 l' U2 F2 l' F2 l F2 r' F2 D2 l2
 
|sign=2L2 D2 2R U2 2L' U2 F2 2L' F2 2L F2 2R' F2 D2 2L2
 
|sign=2L2 D2 2R U2 2L' U2 F2 2L' F2 2L F2 2R' F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v1)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 l' U2 r U2 F2 r F2 r' F2 l F2 D2 r2
+
{{Alg6|wca=r2 D2 l' U2 r U2 F2 r F2 r' F2 l F2 D2 r2
 
|sign=2R2 D2 2L' U2 2R U2 F2 2R F2 2R' F2 2L F2 D2 2R2
 
|sign=2R2 D2 2L' U2 2R U2 F2 2R F2 2R' F2 2L F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v1)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v1)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2
+
{{Alg6|wca=r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2
 
|sign=2R2 B2 U2 2L U2 2L' B2 2R B2 U2 2R U2 2R' B2 2R2
 
|sign=2R2 B2 U2 2L U2 2L' B2 2R B2 U2 2R U2 2R' B2 2R2
 
|length=(25,15)|name=Alg.5(v2)
 
|length=(25,15)|name=Alg.5(v2)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r' U2 r B2 l' B2 U2 l' U2 l B2 l2
+
{{Alg6|wca=l2 B2 U2 r' U2 r B2 l' B2 U2 l' U2 l B2 l2
 
|sign=2L2 B2 U2 2R' U2 2R B2 2L' B2 U2 2L' U2 2L B2 2L2
 
|sign=2L2 B2 U2 2R' U2 2R B2 2L' B2 U2 2L' U2 2L B2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v2)]
 
|length=(25,15)|name=Mirror[Alg.5(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2
+
{{Alg6|wca=r2 B2 r U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2
 
|sign=2R2 B2 2R U2 2R' U2 B2 2R' B2 2L U2 2L' U2 B2 2R2
 
|sign=2R2 B2 2R U2 2R' U2 B2 2R' B2 2L U2 2L' U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v2)]
 
|length=(25,15)|name=Inverse[Alg.5(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 r F2 r' D2 l D2 F2 l F2 l' D2 l2
+
{{Alg6|wca=l2 D2 F2 r F2 r' D2 l D2 F2 l F2 l' D2 l2
 
|sign=2L2 D2 F2 2R F2 2R' D2 2L D2 F2 2L F2 2L' D2 2L2
 
|sign=2L2 D2 F2 2R F2 2R' D2 2L D2 F2 2L F2 2L' D2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v2)]
 
|length=(25,15)|name=Rotation[Alg.5(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 l' U2 l U2 B2 l B2 r' U2 r U2 B2 l2
+
{{Alg6|wca=l2 B2 l' U2 l U2 B2 l B2 r' U2 r U2 B2 l2
 
|sign=2L2 B2 2L' U2 2L U2 B2 2L B2 2R' U2 2R U2 B2 2L2
 
|sign=2L2 B2 2L' U2 2L U2 B2 2L B2 2R' U2 2R U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v2)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 l' F2 l D2 r' D2 F2 r' F2 r D2 r2
+
{{Alg6|wca=r2 D2 F2 l' F2 l D2 r' D2 F2 r' F2 r D2 r2
 
|sign=2R2 D2 F2 2L' F2 2L D2 2R' D2 F2 2R' F2 2R D2 2R2
 
|sign=2R2 D2 F2 2L' F2 2L D2 2R' D2 F2 2R' F2 2R D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v2)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l F2 l' F2 D2 l' D2 r F2 r' F2 D2 l2
+
{{Alg6|wca=l2 D2 l F2 l' F2 D2 l' D2 r F2 r' F2 D2 l2
 
|sign=2L2 D2 2L F2 2L' F2 D2 2L' D2 2R F2 2R' F2 D2 2L2
 
|sign=2L2 D2 2L F2 2L' F2 D2 2L' D2 2R F2 2R' F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v2)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r' F2 r F2 D2 r D2 l' F2 l F2 D2 r2
+
{{Alg6|wca=r2 D2 r' F2 r F2 D2 r D2 l' F2 l F2 D2 r2
 
|sign=2R2 D2 2R' F2 2R F2 D2 2R D2 2L' F2 2L F2 D2 2R2
 
|sign=2R2 D2 2R' F2 2R F2 D2 2R D2 2L' F2 2L F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v2)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v2)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2
+
{{Alg6|wca=r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2
 
|sign=2R2 F2 D2 2R' D2 2R F2 2L' F2 D2 2L' D2 2L F2 2R2
 
|sign=2R2 F2 D2 2R' D2 2R F2 2L' F2 D2 2L' D2 2L F2 2R2
 
|length=(25,15)|name=Alg.5(v3)
 
|length=(25,15)|name=Alg.5(v3)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l D2 l' F2 r F2 D2 r D2 r' F2 l2
+
{{Alg6|wca=l2 F2 D2 l D2 l' F2 r F2 D2 r D2 r' F2 l2
 
|sign=2L2 F2 D2 2L D2 2L' F2 2R F2 D2 2R D2 2R' F2 2L2
 
|sign=2L2 F2 D2 2L D2 2L' F2 2R F2 D2 2R D2 2R' F2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v3)]
 
|length=(25,15)|name=Mirror[Alg.5(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l' D2 l D2 F2 l F2 r' D2 r D2 F2 r2
+
{{Alg6|wca=r2 F2 l' D2 l D2 F2 l F2 r' D2 r D2 F2 r2
 
|sign=2R2 F2 2L' D2 2L D2 F2 2L F2 2R' D2 2R D2 F2 2R2
 
|sign=2R2 F2 2L' D2 2L D2 F2 2L F2 2R' D2 2R D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v3)]
 
|length=(25,15)|name=Inverse[Alg.5(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 l' B2 l U2 r' U2 B2 r' B2 r U2 l2
+
{{Alg6|wca=l2 U2 B2 l' B2 l U2 r' U2 B2 r' B2 r U2 l2
 
|sign=2L2 U2 B2 2L' B2 2L U2 2R' U2 B2 2R' B2 2R U2 2L2
 
|sign=2L2 U2 B2 2L' B2 2L U2 2R' U2 B2 2R' B2 2R U2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v3)]
 
|length=(25,15)|name=Rotation[Alg.5(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 r D2 r' D2 F2 r' F2 l D2 l' D2 F2 l2
+
{{Alg6|wca=l2 F2 r D2 r' D2 F2 r' F2 l D2 l' D2 F2 l2
 
|sign=2L2 F2 2R D2 2R' D2 F2 2R' F2 2L D2 2L' D2 F2 2L2
 
|sign=2L2 F2 2R D2 2R' D2 F2 2R' F2 2L D2 2L' D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v3)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 r B2 r' U2 l U2 B2 l B2 l' U2 r2
+
{{Alg6|wca=r2 U2 B2 r B2 r' U2 l U2 B2 l B2 l' U2 r2
 
|sign=2R2 U2 B2 2R B2 2R' U2 2L U2 B2 2L B2 2L' U2 2R2
 
|sign=2R2 U2 B2 2R B2 2R' U2 2L U2 B2 2L B2 2L' U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v3)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r' B2 r B2 U2 r U2 l' B2 l B2 U2 l2
+
{{Alg6|wca=l2 U2 r' B2 r B2 U2 r U2 l' B2 l B2 U2 l2
 
|sign=2L2 U2 2R' B2 2R B2 U2 2R U2 2L' B2 2L B2 U2 2L2
 
|sign=2L2 U2 2R' B2 2R B2 U2 2R U2 2L' B2 2L B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v3)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l B2 l' B2 U2 l' U2 r B2 r' B2 U2 r2
+
{{Alg6|wca=r2 U2 l B2 l' B2 U2 l' U2 r B2 r' B2 U2 r2
 
|sign=2R2 U2 2L B2 2L' B2 U2 2L' U2 2R B2 2R' B2 U2 2R2
 
|sign=2R2 U2 2L B2 2L' B2 U2 2L' U2 2R B2 2R' B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v3)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v3)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2
+
{{Alg6|wca=r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2
 
|sign=2R2 F2 D2 2R' D2 2L D2 2L' D2 B2 2L' B2 2R F2 2R2
 
|sign=2R2 F2 D2 2R' D2 2L D2 2L' D2 B2 2L' B2 2R F2 2R2
 
|length=(25,15)|name=Alg.5(v4)
 
|length=(25,15)|name=Alg.5(v4)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l D2 r' D2 r D2 B2 r B2 l' F2 l2
+
{{Alg6|wca=l2 F2 D2 l D2 r' D2 r D2 B2 r B2 l' F2 l2
 
|sign=2L2 F2 D2 2L D2 2R' D2 2R D2 B2 2R B2 2L' F2 2L2
 
|sign=2L2 F2 D2 2L D2 2R' D2 2R D2 B2 2R B2 2L' F2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v4)]
 
|length=(25,15)|name=Mirror[Alg.5(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' B2 l B2 D2 l D2 l' D2 r D2 F2 r2
+
{{Alg6|wca=r2 F2 r' B2 l B2 D2 l D2 l' D2 r D2 F2 r2
 
|sign=2R2 F2 2R' B2 2L B2 D2 2L D2 2L' D2 2R D2 F2 2R2
 
|sign=2R2 F2 2R' B2 2L B2 D2 2L D2 2L' D2 2R D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v4)]
 
|length=(25,15)|name=Inverse[Alg.5(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 l' B2 r B2 r' B2 D2 r' D2 l U2 l2
+
{{Alg6|wca=l2 U2 B2 l' B2 r B2 r' B2 D2 r' D2 l U2 l2
 
|sign=2L2 U2 B2 2L' B2 2R B2 2R' B2 D2 2R' D2 2L U2 2L2
 
|sign=2L2 U2 B2 2L' B2 2R B2 2R' B2 D2 2R' D2 2L U2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v4)]
 
|length=(25,15)|name=Rotation[Alg.5(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 l B2 r' B2 D2 r' D2 r D2 l' D2 F2 l2
+
{{Alg6|wca=l2 F2 l B2 r' B2 D2 r' D2 r D2 l' D2 F2 l2
 
|sign=2L2 F2 2L B2 2R' B2 D2 2R' D2 2R D2 2L' D2 F2 2L2
 
|sign=2L2 F2 2L B2 2R' B2 D2 2R' D2 2R D2 2L' D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v4)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 r B2 l' B2 l B2 D2 l D2 r' U2 r2
+
{{Alg6|wca=r2 U2 B2 r B2 l' B2 l B2 D2 l D2 r' U2 r2
 
|sign=2R2 U2 B2 2R B2 2L' B2 2L B2 D2 2L D2 2R' U2 2R2
 
|sign=2R2 U2 B2 2R B2 2L' B2 2L B2 D2 2L D2 2R' U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v4)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l' D2 r D2 B2 r B2 r' B2 l B2 U2 l2
+
{{Alg6|wca=l2 U2 l' D2 r D2 B2 r B2 r' B2 l B2 U2 l2
 
|sign=2L2 U2 2L' D2 2R D2 B2 2R B2 2R' B2 2L B2 U2 2L2
 
|sign=2L2 U2 2L' D2 2R D2 B2 2R B2 2R' B2 2L B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v4)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r D2 l' D2 B2 l' B2 l B2 r' B2 U2 r2
+
{{Alg6|wca=r2 U2 r D2 l' D2 B2 l' B2 l B2 r' B2 U2 r2
 
|sign=2R2 U2 2R D2 2L' D2 B2 2L' B2 2L B2 2R' B2 U2 2R2
 
|sign=2R2 U2 2R D2 2L' D2 B2 2L' B2 2L B2 2R' B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v4)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v4)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2
+
{{Alg6|wca=r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2
 
|sign=2R2 B2 U2 2R B2 2R' B2 2L U2 F2 2R F2 2L' B2 2R2
 
|sign=2R2 B2 U2 2R B2 2R' B2 2L U2 F2 2R F2 2L' B2 2R2
 
|length=(25,15)|name=Alg.5(v5)
 
|length=(25,15)|name=Alg.5(v5)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 l' B2 l B2 r' U2 F2 l' F2 r B2 l2
+
{{Alg6|wca=l2 B2 U2 l' B2 l B2 r' U2 F2 l' F2 r B2 l2
 
|sign=2L2 B2 U2 2L' B2 2L B2 2R' U2 F2 2L' F2 2R B2 2L2
 
|sign=2L2 B2 U2 2L' B2 2L B2 2R' U2 F2 2L' F2 2R B2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v5)]
 
|length=(25,15)|name=Mirror[Alg.5(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l F2 r' F2 U2 l' B2 r B2 r' U2 B2 r2
+
{{Alg6|wca=r2 B2 l F2 r' F2 U2 l' B2 r B2 r' U2 B2 r2
 
|sign=2R2 B2 2L F2 2R' F2 U2 2L' B2 2R B2 2R' U2 B2 2R2
 
|sign=2R2 B2 2L F2 2R' F2 U2 2L' B2 2R B2 2R' U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v5)]
 
|length=(25,15)|name=Inverse[Alg.5(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 l D2 l' D2 r F2 U2 l U2 r' D2 l2
+
{{Alg6|wca=l2 D2 F2 l D2 l' D2 r F2 U2 l U2 r' D2 l2
 
|sign=2L2 D2 F2 2L D2 2L' D2 2R F2 U2 2L U2 2R' D2 2L2
 
|sign=2L2 D2 F2 2L D2 2L' D2 2R F2 U2 2L U2 2R' D2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v5)]
 
|length=(25,15)|name=Rotation[Alg.5(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 r' F2 l F2 U2 r B2 l' B2 l U2 B2 l2
+
{{Alg6|wca=l2 B2 r' F2 l F2 U2 r B2 l' B2 l U2 B2 l2
 
|sign=2L2 B2 2R' F2 2L F2 U2 2R B2 2L' B2 2L U2 B2 2L2
 
|sign=2L2 B2 2R' F2 2L F2 U2 2R B2 2L' B2 2L U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v5)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 r' D2 r D2 l' F2 U2 r' U2 l D2 r2
+
{{Alg6|wca=r2 D2 F2 r' D2 r D2 l' F2 U2 r' U2 l D2 r2
 
|sign=2R2 D2 F2 2R' D2 2R D2 2L' F2 U2 2R' U2 2L D2 2R2
 
|sign=2R2 D2 F2 2R' D2 2R D2 2L' F2 U2 2R' U2 2L D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v5)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 r U2 l' U2 F2 r' D2 l D2 l' F2 D2 l2
+
{{Alg6|wca=l2 D2 r U2 l' U2 F2 r' D2 l D2 l' F2 D2 l2
 
|sign=2L2 D2 2R U2 2L' U2 F2 2R' D2 2L D2 2L' F2 D2 2L2
 
|sign=2L2 D2 2R U2 2L' U2 F2 2R' D2 2L D2 2L' F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v5)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 l' U2 r U2 F2 l D2 r' D2 r F2 D2 r2
+
{{Alg6|wca=r2 D2 l' U2 r U2 F2 l D2 r' D2 r F2 D2 r2
 
|sign=2R2 D2 2L' U2 2R U2 F2 2L D2 2R' D2 2R F2 D2 2R2
 
|sign=2R2 D2 2L' U2 2R U2 F2 2L D2 2R' D2 2R F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v5)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v5)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2
+
{{Alg6|wca=r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2
 
|sign=2R2 F2 D2 2L' F2 2L F2 2R' D2 B2 2L' B2 2R F2 2R2
 
|sign=2R2 F2 D2 2L' F2 2L F2 2R' D2 B2 2L' B2 2R F2 2R2
 
|length=(25,15)|name=Alg.5(v6)
 
|length=(25,15)|name=Alg.5(v6)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r F2 r' F2 l D2 B2 r B2 l' F2 l2
+
{{Alg6|wca=l2 F2 D2 r F2 r' F2 l D2 B2 r B2 l' F2 l2
 
|sign=2L2 F2 D2 2R F2 2R' F2 2L D2 B2 2R B2 2L' F2 2L2
 
|sign=2L2 F2 D2 2R F2 2R' F2 2L D2 B2 2R B2 2L' F2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v6)]
 
|length=(25,15)|name=Mirror[Alg.5(v6)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' B2 l B2 D2 r F2 l' F2 l D2 F2 r2
+
{{Alg6|wca=r2 F2 r' B2 l B2 D2 r F2 l' F2 l D2 F2 r2
 
|sign=2R2 F2 2R' B2 2L B2 D2 2R F2 2L' F2 2L D2 F2 2R2
 
|sign=2R2 F2 2R' B2 2L B2 D2 2R F2 2L' F2 2L D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v6)]
 
|length=(25,15)|name=Inverse[Alg.5(v6)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 r' U2 r U2 l' B2 D2 r' D2 l U2 l2
+
{{Alg6|wca=l2 U2 B2 r' U2 r U2 l' B2 D2 r' D2 l U2 l2
 
|sign=2L2 U2 B2 2R' U2 2R U2 2L' B2 D2 2R' D2 2L U2 2L2
 
|sign=2L2 U2 B2 2R' U2 2R U2 2L' B2 D2 2R' D2 2L U2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v6)]
 
|length=(25,15)|name=Rotation[Alg.5(v6)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 l B2 r' B2 D2 l' F2 r F2 r' D2 F2 l2
+
{{Alg6|wca=l2 F2 l B2 r' B2 D2 l' F2 r F2 r' D2 F2 l2
 
|sign=2L2 F2 2L B2 2R' B2 D2 2L' F2 2R F2 2R' D2 F2 2L2
 
|sign=2L2 F2 2L B2 2R' B2 D2 2L' F2 2R F2 2R' D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v6)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v6)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 l U2 l' U2 r B2 D2 l D2 r' U2 r2
+
{{Alg6|wca=r2 U2 B2 l U2 l' U2 r B2 D2 l D2 r' U2 r2
 
|sign=2R2 U2 B2 2L U2 2L' U2 2R B2 D2 2L D2 2R' U2 2R2
 
|sign=2R2 U2 B2 2L U2 2L' U2 2R B2 D2 2L D2 2R' U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v6)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v6)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l' D2 r D2 B2 l U2 r' U2 r B2 U2 l2
+
{{Alg6|wca=l2 U2 l' D2 r D2 B2 l U2 r' U2 r B2 U2 l2
 
|sign=2L2 U2 2L' D2 2R D2 B2 2L U2 2R' U2 2R B2 U2 2L2
 
|sign=2L2 U2 2L' D2 2R D2 B2 2L U2 2R' U2 2R B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v6)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v6)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r D2 l' D2 B2 r' U2 l U2 l' B2 U2 r2
+
{{Alg6|wca=r2 U2 r D2 l' D2 B2 r' U2 l U2 l' B2 U2 r2
 
|sign=2R2 U2 2R D2 2L' D2 B2 2R' U2 2L U2 2L' B2 U2 2R2
 
|sign=2R2 U2 2R D2 2L' D2 B2 2R' U2 2L U2 2L' B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v6)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v6)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2
+
{{Alg6|wca=r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2
 
|sign=2R2 B2 U2 2R B2 2L' D2 2R D2 B2 2L U2 2R' B2 2R2
 
|sign=2R2 B2 U2 2R B2 2L' D2 2R D2 B2 2L U2 2R' B2 2R2
 
|length=(25,15)|name=Alg.5(v7)
 
|length=(25,15)|name=Alg.5(v7)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 l' B2 r D2 l' D2 B2 r' U2 l B2 l2
+
{{Alg6|wca=l2 B2 U2 l' B2 r D2 l' D2 B2 r' U2 l B2 l2
 
|sign=2L2 B2 U2 2L' B2 2R D2 2L' D2 B2 2R' U2 2L B2 2L2
 
|sign=2L2 B2 U2 2L' B2 2R D2 2L' D2 B2 2R' U2 2L B2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v7)]
 
|length=(25,15)|name=Mirror[Alg.5(v7)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 l' B2 D2 r' D2 l B2 r' U2 B2 r2
+
{{Alg6|wca=r2 B2 r U2 l' B2 D2 r' D2 l B2 r' U2 B2 r2
 
|sign=2R2 B2 2R U2 2L' B2 D2 2R' D2 2L B2 2R' U2 B2 2R2
 
|sign=2R2 B2 2R U2 2L' B2 D2 2R' D2 2L B2 2R' U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v7)]
 
|length=(25,15)|name=Inverse[Alg.5(v7)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 l D2 r' B2 l B2 D2 r F2 l' D2 l2
+
{{Alg6|wca=l2 D2 F2 l D2 r' B2 l B2 D2 r F2 l' D2 l2
 
|sign=2L2 D2 F2 2L D2 2R' B2 2L B2 D2 2R F2 2L' D2 2L2
 
|sign=2L2 D2 F2 2L D2 2R' B2 2L B2 D2 2R F2 2L' D2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v7)]
 
|length=(25,15)|name=Rotation[Alg.5(v7)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 l' U2 r B2 D2 l D2 r' B2 l U2 B2 l2
+
{{Alg6|wca=l2 B2 l' U2 r B2 D2 l D2 r' B2 l U2 B2 l2
 
|sign=2L2 B2 2L' U2 2R B2 D2 2L D2 2R' B2 2L U2 B2 2L2
 
|sign=2L2 B2 2L' U2 2R B2 D2 2L D2 2R' B2 2L U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v7)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v7)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 r' D2 l B2 r' B2 D2 l' F2 r D2 r2
+
{{Alg6|wca=r2 D2 F2 r' D2 l B2 r' B2 D2 l' F2 r D2 r2
 
|sign=2R2 D2 F2 2R' D2 2L B2 2R' B2 D2 2L' F2 2R D2 2R2
 
|sign=2R2 D2 F2 2R' D2 2L B2 2R' B2 D2 2L' F2 2R D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v7)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v7)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l F2 r' D2 B2 l' B2 r D2 l' F2 D2 l2
+
{{Alg6|wca=l2 D2 l F2 r' D2 B2 l' B2 r D2 l' F2 D2 l2
 
|sign=2L2 D2 2L F2 2R' D2 B2 2L' B2 2R D2 2L' F2 D2 2L2
 
|sign=2L2 D2 2L F2 2R' D2 B2 2L' B2 2R D2 2L' F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v7)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v7)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r' F2 l D2 B2 r B2 l' D2 r F2 D2 r2
+
{{Alg6|wca=r2 D2 r' F2 l D2 B2 r B2 l' D2 r F2 D2 r2
 
|sign=2R2 D2 2R' F2 2L D2 B2 2R B2 2L' D2 2R F2 D2 2R2
 
|sign=2R2 D2 2R' F2 2L D2 B2 2R B2 2L' D2 2R F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v7)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v7)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2
+
{{Alg6|wca=r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2
 
|sign=2R2 F2 D2 2L' F2 2R U2 2L' U2 F2 2R' D2 2L F2 2R2
 
|sign=2R2 F2 D2 2L' F2 2R U2 2L' U2 F2 2R' D2 2L F2 2R2
 
|length=(25,15)|name=Alg.5(v8)
 
|length=(25,15)|name=Alg.5(v8)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r F2 l' U2 r U2 F2 l D2 r' F2 l2
+
{{Alg6|wca=l2 F2 D2 r F2 l' U2 r U2 F2 l D2 r' F2 l2
 
|sign=2L2 F2 D2 2R F2 2L' U2 2R U2 F2 2L D2 2R' F2 2L2
 
|sign=2L2 F2 D2 2R F2 2L' U2 2R U2 F2 2L D2 2R' F2 2L2
 
|length=(25,15)|name=Mirror[Alg.5(v8)]
 
|length=(25,15)|name=Mirror[Alg.5(v8)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l' D2 r F2 U2 l U2 r' F2 l D2 F2 r2
+
{{Alg6|wca=r2 F2 l' D2 r F2 U2 l U2 r' F2 l D2 F2 r2
 
|sign=2R2 F2 2L' D2 2R F2 U2 2L U2 2R' F2 2L D2 F2 2R2
 
|sign=2R2 F2 2L' D2 2R F2 U2 2L U2 2R' F2 2L D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.5(v8)]
 
|length=(25,15)|name=Inverse[Alg.5(v8)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 r' U2 l F2 r' F2 U2 l' B2 r U2 l2
+
{{Alg6|wca=l2 U2 B2 r' U2 l F2 r' F2 U2 l' B2 r U2 l2
 
|sign=2L2 U2 B2 2R' U2 2L F2 2R' F2 U2 2L' B2 2R U2 2L2
 
|sign=2L2 U2 B2 2R' U2 2L F2 2R' F2 U2 2L' B2 2R U2 2L2
 
|length=(25,15)|name=Rotation[Alg.5(v8)]
 
|length=(25,15)|name=Rotation[Alg.5(v8)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 r D2 l' F2 U2 r' U2 l F2 r' D2 F2 l2
+
{{Alg6|wca=l2 F2 r D2 l' F2 U2 r' U2 l F2 r' D2 F2 l2
 
|sign=2L2 F2 2R D2 2L' F2 U2 2R' U2 2L F2 2R' D2 F2 2L2
 
|sign=2L2 F2 2R D2 2L' F2 U2 2R' U2 2L F2 2R' D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v8)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.5(v8)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 l U2 r' F2 l F2 U2 r B2 l' U2 r2
+
{{Alg6|wca=r2 U2 B2 l U2 r' F2 l F2 U2 r B2 l' U2 r2
 
|sign=2R2 U2 B2 2L U2 2R' F2 2L F2 U2 2R B2 2L' U2 2R2
 
|sign=2R2 U2 B2 2L U2 2R' F2 2L F2 U2 2R B2 2L' U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v8)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.5(v8)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r' B2 l U2 F2 r F2 l' U2 r B2 U2 l2
+
{{Alg6|wca=l2 U2 r' B2 l U2 F2 r F2 l' U2 r B2 U2 l2
 
|sign=2L2 U2 2R' B2 2L U2 F2 2R F2 2L' U2 2R B2 U2 2L2
 
|sign=2L2 U2 2R' B2 2L U2 F2 2R F2 2L' U2 2R B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v8)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.5(v8)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l B2 r' U2 F2 l' F2 r U2 l' B2 U2 r2
+
{{Alg6|wca=r2 U2 l B2 r' U2 F2 l' F2 r U2 l' B2 U2 r2
 
|sign=2R2 U2 2L B2 2R' U2 F2 2L' F2 2R U2 2L' B2 U2 2R2
 
|sign=2R2 U2 2L B2 2R' U2 F2 2L' F2 2R U2 2L' B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v8)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v8)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
=====<span style="font-family:Georgia;color:rgb(0,200,0);">Group 2: cyclic shift and re-conjugation of Group 1</span>=====
=====Group 2: cyclic shift and re-conjugation of Group 1=====
 
 
*The first and last turns of each of these algorithms can be made wide turns to still achieve a single dedge flip.
 
*The first and last turns of each of these algorithms can be made wide turns to still achieve a single dedge flip.
{{Alg5|wca=r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2
+
{{br|b=1}}
 +
{{Alg6|wca=r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2
 
|sign=2R2 B2 U2 2L' U2 2R U2 2R' U2 B2 2R' B2 2L B2 2R2
 
|sign=2R2 B2 U2 2L' U2 2R U2 2R' U2 B2 2R' B2 2L B2 2R2
 
|length=(25,15)|name=Alg.6(v1)
 
|length=(25,15)|name=Alg.6(v1)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r U2 l' U2 l U2 B2 l B2 r' B2 l2
+
{{Alg6|wca=l2 B2 U2 r U2 l' U2 l U2 B2 l B2 r' B2 l2
 
|sign=2L2 B2 U2 2R U2 2L' U2 2L U2 B2 2L B2 2R' B2 2L2
 
|sign=2L2 B2 U2 2R U2 2L' U2 2L U2 B2 2L B2 2R' B2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v1)]
 
|length=(25,15)|name=Mirror[Alg.6(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l' B2 r B2 U2 r U2 r' U2 l U2 B2 r2
+
{{Alg6|wca=r2 B2 l' B2 r B2 U2 r U2 r' U2 l U2 B2 r2
 
|sign=2R2 B2 2L' B2 2R B2 U2 2R U2 2R' U2 2L U2 B2 2R2
 
|sign=2R2 B2 2L' B2 2R B2 U2 2R U2 2R' U2 2L U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v1)]
 
|length=(25,15)|name=Inverse[Alg.6(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 r' F2 l F2 l' F2 D2 l' D2 r D2 l2
+
{{Alg6|wca=l2 D2 F2 r' F2 l F2 l' F2 D2 l' D2 r D2 l2
 
|sign=2L2 D2 F2 2R' F2 2L F2 2L' F2 D2 2L' D2 2R D2 2L2
 
|sign=2L2 D2 F2 2R' F2 2L F2 2L' F2 D2 2L' D2 2R D2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v1)]
 
|length=(25,15)|name=Rotation[Alg.6(v1)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 r B2 l' B2 U2 l' U2 l U2 r' U2 B2 l2
+
{{Alg6|wca=l2 B2 r B2 l' B2 U2 l' U2 l U2 r' U2 B2 l2
 
|sign=2L2 B2 2R B2 2L' B2 U2 2L' U2 2L U2 2R' U2 B2 2L2
 
|sign=2L2 B2 2R B2 2L' B2 U2 2L' U2 2L U2 2R' U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v1)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 l F2 r' F2 r F2 D2 r D2 l' D2 r2
+
{{Alg6|wca=r2 D2 F2 l F2 r' F2 r F2 D2 r D2 l' D2 r2
 
|sign=2R2 D2 F2 2L F2 2R' F2 2R F2 D2 2R D2 2L' D2 2R2
 
|sign=2R2 D2 F2 2L F2 2R' F2 2R F2 D2 2R D2 2L' D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v1)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 r' D2 l D2 F2 l F2 l' F2 r F2 D2 l2
+
{{Alg6|wca=l2 D2 r' D2 l D2 F2 l F2 l' F2 r F2 D2 l2
 
|sign=2L2 D2 2R' D2 2L D2 F2 2L F2 2L' F2 2R F2 D2 2L2
 
|sign=2L2 D2 2R' D2 2L D2 F2 2L F2 2L' F2 2R F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v1)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v1)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 l D2 r' D2 F2 r' F2 r F2 l' F2 D2 r2
+
{{Alg6|wca=r2 D2 l D2 r' D2 F2 r' F2 r F2 l' F2 D2 r2
 
|sign=2R2 D2 2L D2 2R' D2 F2 2R' F2 2R F2 2L' F2 D2 2R2
 
|sign=2R2 D2 2L D2 2R' D2 F2 2R' F2 2R F2 2L' F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v1)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v1)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2
+
{{Alg6|wca=r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2
 
|sign=2R2 B2 U2 2L' U2 2L F2 2R' F2 U2 2R' U2 2R B2 2R2
 
|sign=2R2 B2 U2 2L' U2 2L F2 2R' F2 U2 2R' U2 2R B2 2R2
 
|length=(25,15)|name=Alg.6(v2)
 
|length=(25,15)|name=Alg.6(v2)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r U2 r' F2 l F2 U2 l U2 l' B2 l2
+
{{Alg6|wca=l2 B2 U2 r U2 r' F2 l F2 U2 l U2 l' B2 l2
 
|sign=2L2 B2 U2 2R U2 2R' F2 2L F2 U2 2L U2 2L' B2 2L2
 
|sign=2L2 B2 U2 2R U2 2R' F2 2L F2 U2 2L U2 2L' B2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v2)]
 
|length=(25,15)|name=Mirror[Alg.6(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r' U2 r U2 F2 r F2 l' U2 l U2 B2 r2
+
{{Alg6|wca=r2 B2 r' U2 r U2 F2 r F2 l' U2 l U2 B2 r2
 
|sign=2R2 B2 2R' U2 2R U2 F2 2R F2 2L' U2 2L U2 B2 2R2
 
|sign=2R2 B2 2R' U2 2R U2 F2 2R F2 2L' U2 2L U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v2)]
 
|length=(25,15)|name=Inverse[Alg.6(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 r' F2 r U2 l' U2 F2 l' F2 l D2 l2
+
{{Alg6|wca=l2 D2 F2 r' F2 r U2 l' U2 F2 l' F2 l D2 l2
 
|sign=2L2 D2 F2 2R' F2 2R U2 2L' U2 F2 2L' F2 2L D2 2L2
 
|sign=2L2 D2 F2 2R' F2 2R U2 2L' U2 F2 2L' F2 2L D2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v2)]
 
|length=(25,15)|name=Rotation[Alg.6(v2)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 l U2 l' U2 F2 l' F2 r U2 r' U2 B2 l2
+
{{Alg6|wca=l2 B2 l U2 l' U2 F2 l' F2 r U2 r' U2 B2 l2
 
|sign=2L2 B2 2L U2 2L' U2 F2 2L' F2 2R U2 2R' U2 B2 2L2
 
|sign=2L2 B2 2L U2 2L' U2 F2 2L' F2 2R U2 2R' U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v2)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 l F2 l' U2 r U2 F2 r F2 r' D2 r2
+
{{Alg6|wca=r2 D2 F2 l F2 l' U2 r U2 F2 r F2 r' D2 r2
 
|sign=2R2 D2 F2 2L F2 2L' U2 2R U2 F2 2R F2 2R' D2 2R2
 
|sign=2R2 D2 F2 2L F2 2L' U2 2R U2 F2 2R F2 2R' D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v2)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l' F2 l F2 U2 l U2 r' F2 r F2 D2 l2
+
{{Alg6|wca=l2 D2 l' F2 l F2 U2 l U2 r' F2 r F2 D2 l2
 
|sign=2L2 D2 2L' F2 2L F2 U2 2L U2 2R' F2 2R F2 D2 2L2
 
|sign=2L2 D2 2L' F2 2L F2 U2 2L U2 2R' F2 2R F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v2)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v2)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r F2 r' F2 U2 r' U2 l F2 l' F2 D2 r2
+
{{Alg6|wca=r2 D2 r F2 r' F2 U2 r' U2 l F2 l' F2 D2 r2
 
|sign=2R2 D2 2R F2 2R' F2 U2 2R' U2 2L F2 2L' F2 D2 2R2
 
|sign=2R2 D2 2R F2 2R' F2 U2 2R' U2 2L F2 2L' F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v2)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v2)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2
+
{{Alg6|wca=r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2
 
|sign=2R2 F2 D2 2R D2 2R' B2 2L B2 D2 2L D2 2L' F2 2R2
 
|sign=2R2 F2 D2 2R D2 2R' B2 2L B2 D2 2L D2 2L' F2 2R2
 
|length=(25,15)|name=Alg.6(v3)
 
|length=(25,15)|name=Alg.6(v3)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l' D2 l B2 r' B2 D2 r' D2 r F2 l2
+
{{Alg6|wca=l2 F2 D2 l' D2 l B2 r' B2 D2 r' D2 r F2 l2
 
|sign=2L2 F2 D2 2L' D2 2L B2 2R' B2 D2 2R' D2 2R F2 2L2
 
|sign=2L2 F2 D2 2L' D2 2L B2 2R' B2 D2 2R' D2 2R F2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v3)]
 
|length=(25,15)|name=Mirror[Alg.6(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l D2 l' D2 B2 l' B2 r D2 r' D2 F2 r2
+
{{Alg6|wca=r2 F2 l D2 l' D2 B2 l' B2 r D2 r' D2 F2 r2
 
|sign=2R2 F2 2L D2 2L' D2 B2 2L' B2 2R D2 2R' D2 F2 2R2
 
|sign=2R2 F2 2L D2 2L' D2 B2 2L' B2 2R D2 2R' D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v3)]
 
|length=(25,15)|name=Inverse[Alg.6(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 l B2 l' D2 r D2 B2 r B2 r' U2 l2
+
{{Alg6|wca=l2 U2 B2 l B2 l' D2 r D2 B2 r B2 r' U2 l2
 
|sign=2L2 U2 B2 2L B2 2L' D2 2R D2 B2 2R B2 2R' U2 2L2
 
|sign=2L2 U2 B2 2L B2 2L' D2 2R D2 B2 2R B2 2R' U2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v3)]
 
|length=(25,15)|name=Rotation[Alg.6(v3)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 r' D2 r D2 B2 r B2 l' D2 l D2 F2 l2
+
{{Alg6|wca=l2 F2 r' D2 r D2 B2 r B2 l' D2 l D2 F2 l2
 
|sign=2L2 F2 2R' D2 2R D2 B2 2R B2 2L' D2 2L D2 F2 2L2
 
|sign=2L2 F2 2R' D2 2R D2 B2 2R B2 2L' D2 2L D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v3)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 r' B2 r D2 l' D2 B2 l' B2 l U2 r2
+
{{Alg6|wca=r2 U2 B2 r' B2 r D2 l' D2 B2 l' B2 l U2 r2
 
|sign=2R2 U2 B2 2R' B2 2R D2 2L' D2 B2 2L' B2 2L U2 2R2
 
|sign=2R2 U2 B2 2R' B2 2R D2 2L' D2 B2 2L' B2 2L U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v3)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r B2 r' B2 D2 r' D2 l B2 l' B2 U2 l2
+
{{Alg6|wca=l2 U2 r B2 r' B2 D2 r' D2 l B2 l' B2 U2 l2
 
|sign=2L2 U2 2R B2 2R' B2 D2 2R' D2 2L B2 2L' B2 U2 2L2
 
|sign=2L2 U2 2R B2 2R' B2 D2 2R' D2 2L B2 2L' B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v3)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v3)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' B2 l B2 D2 l D2 r' B2 r B2 U2 r2
+
{{Alg6|wca=r2 U2 l' B2 l B2 D2 l D2 r' B2 r B2 U2 r2
 
|sign=2R2 U2 2L' B2 2L B2 D2 2L D2 2R' B2 2R B2 U2 2R2
 
|sign=2R2 U2 2L' B2 2L B2 D2 2L D2 2R' B2 2R B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v3)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v3)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2
+
{{Alg6|wca=r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2
 
|sign=2R2 F2 D2 2R D2 2L' D2 2L D2 F2 2L F2 2R' F2 2R2
 
|sign=2R2 F2 D2 2R D2 2L' D2 2L D2 F2 2L F2 2R' F2 2R2
 
|length=(25,15)|name=Alg.6(v4)
 
|length=(25,15)|name=Alg.6(v4)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l' D2 r D2 r' D2 F2 r' F2 l F2 l2
+
{{Alg6|wca=l2 F2 D2 l' D2 r D2 r' D2 F2 r' F2 l F2 l2
 
|sign=2L2 F2 D2 2L' D2 2R D2 2R' D2 F2 2R' F2 2L F2 2L2
 
|sign=2L2 F2 D2 2L' D2 2R D2 2R' D2 F2 2R' F2 2L F2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v4)]
 
|length=(25,15)|name=Mirror[Alg.6(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r F2 l' F2 D2 l' D2 l D2 r' D2 F2 r2
+
{{Alg6|wca=r2 F2 r F2 l' F2 D2 l' D2 l D2 r' D2 F2 r2
 
|sign=2R2 F2 2R F2 2L' F2 D2 2L' D2 2L D2 2R' D2 F2 2R2
 
|sign=2R2 F2 2R F2 2L' F2 D2 2L' D2 2L D2 2R' D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v4)]
 
|length=(25,15)|name=Inverse[Alg.6(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 l B2 r' B2 r B2 U2 r U2 l' U2 l2
+
{{Alg6|wca=l2 U2 B2 l B2 r' B2 r B2 U2 r U2 l' U2 l2
 
|sign=2L2 U2 B2 2L B2 2R' B2 2R B2 U2 2R U2 2L' U2 2L2
 
|sign=2L2 U2 B2 2L B2 2R' B2 2R B2 U2 2R U2 2L' U2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v4)]
 
|length=(25,15)|name=Rotation[Alg.6(v4)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 l' F2 r F2 D2 r D2 r' D2 l D2 F2 l2
+
{{Alg6|wca=l2 F2 l' F2 r F2 D2 r D2 r' D2 l D2 F2 l2
 
|sign=2L2 F2 2L' F2 2R F2 D2 2R D2 2R' D2 2L D2 F2 2L2
 
|sign=2L2 F2 2L' F2 2R F2 D2 2R D2 2R' D2 2L D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v4)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 r' B2 l B2 l' B2 U2 l' U2 r U2 r2
+
{{Alg6|wca=r2 U2 B2 r' B2 l B2 l' B2 U2 l' U2 r U2 r2
 
|sign=2R2 U2 B2 2R' B2 2L B2 2L' B2 U2 2L' U2 2R U2 2R2
 
|sign=2R2 U2 B2 2R' B2 2L B2 2L' B2 U2 2L' U2 2R U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v4)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l U2 r' U2 B2 r' B2 r B2 l' B2 U2 l2
+
{{Alg6|wca=l2 U2 l U2 r' U2 B2 r' B2 r B2 l' B2 U2 l2
 
|sign=2L2 U2 2L U2 2R' U2 B2 2R' B2 2R B2 2L' B2 U2 2L2
 
|sign=2L2 U2 2L U2 2R' U2 B2 2R' B2 2R B2 2L' B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v4)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v4)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 l U2 B2 l B2 l' B2 r B2 U2 r2
+
{{Alg6|wca=r2 U2 r' U2 l U2 B2 l B2 l' B2 r B2 U2 r2
 
|sign=2R2 U2 2R' U2 2L U2 B2 2L B2 2L' B2 2R B2 U2 2R2
 
|sign=2R2 U2 2R' U2 2L U2 B2 2L B2 2L' B2 2R B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v4)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v4)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2
+
{{Alg6|wca=r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2
 
|sign=2R2 B2 U2 2R' F2 2R F2 2L' U2 B2 2R' B2 2L B2 2R2
 
|sign=2R2 B2 U2 2R' F2 2R F2 2L' U2 B2 2R' B2 2L B2 2R2
 
|length=(25,15)|name=Alg.6(v5)
 
|length=(25,15)|name=Alg.6(v5)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 l F2 l' F2 r U2 B2 l B2 r' B2 l2
+
{{Alg6|wca=l2 B2 U2 l F2 l' F2 r U2 B2 l B2 r' B2 l2
 
|sign=2L2 B2 U2 2L F2 2L' F2 2R U2 B2 2L B2 2R' B2 2L2
 
|sign=2L2 B2 U2 2L F2 2L' F2 2R U2 B2 2L B2 2R' B2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v5)]
 
|length=(25,15)|name=Mirror[Alg.6(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l' B2 r B2 U2 l F2 r' F2 r U2 B2 r2
+
{{Alg6|wca=r2 B2 l' B2 r B2 U2 l F2 r' F2 r U2 B2 r2
 
|sign=2R2 B2 2L' B2 2R B2 U2 2L F2 2R' F2 2R U2 B2 2R2
 
|sign=2R2 B2 2L' B2 2R B2 U2 2L F2 2R' F2 2R U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v5)]
 
|length=(25,15)|name=Inverse[Alg.6(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 l' U2 l U2 r' F2 D2 l' D2 r D2 l2
+
{{Alg6|wca=l2 D2 F2 l' U2 l U2 r' F2 D2 l' D2 r D2 l2
 
|sign=2L2 D2 F2 2L' U2 2L U2 2R' F2 D2 2L' D2 2R D2 2L2
 
|sign=2L2 D2 F2 2L' U2 2L U2 2R' F2 D2 2L' D2 2R D2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v5)]
 
|length=(25,15)|name=Rotation[Alg.6(v5)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 r B2 l' B2 U2 r' F2 l F2 l' U2 B2 l2
+
{{Alg6|wca=l2 B2 r B2 l' B2 U2 r' F2 l F2 l' U2 B2 l2
 
|sign=2L2 B2 2R B2 2L' B2 U2 2R' F2 2L F2 2L' U2 B2 2L2
 
|sign=2L2 B2 2R B2 2L' B2 U2 2R' F2 2L F2 2L' U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v5)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 r U2 r' U2 l F2 D2 r D2 l' D2 r2
+
{{Alg6|wca=r2 D2 F2 r U2 r' U2 l F2 D2 r D2 l' D2 r2
 
|sign=2R2 D2 F2 2R U2 2R' U2 2L F2 D2 2R D2 2L' D2 2R2
 
|sign=2R2 D2 F2 2R U2 2R' U2 2L F2 D2 2R D2 2L' D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v5)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 r' D2 l D2 F2 r U2 l' U2 l F2 D2 l2
+
{{Alg6|wca=l2 D2 r' D2 l D2 F2 r U2 l' U2 l F2 D2 l2
 
|sign=2L2 D2 2R' D2 2L D2 F2 2R U2 2L' U2 2L F2 D2 2L2
 
|sign=2L2 D2 2R' D2 2L D2 F2 2R U2 2L' U2 2L F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v5)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v5)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 l D2 r' D2 F2 l' U2 r U2 r' F2 D2 r2
+
{{Alg6|wca=r2 D2 l D2 r' D2 F2 l' U2 r U2 r' F2 D2 r2
 
|sign=2R2 D2 2L D2 2R' D2 F2 2L' U2 2R U2 2R' F2 D2 2R2
 
|sign=2R2 D2 2L D2 2R' D2 F2 2L' U2 2R U2 2R' F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v5)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v5)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2
+
{{Alg6|wca=r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2
 
|sign=2R2 B2 U2 2R' F2 2L D2 2R' D2 F2 2L' U2 2R B2 2R2
 
|sign=2R2 B2 U2 2R' F2 2L D2 2R' D2 F2 2L' U2 2R B2 2R2
 
|length=(25,15)|name=Alg.6(v6)
 
|length=(25,15)|name=Alg.6(v6)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 l F2 r' D2 l D2 F2 r U2 l' B2 l2
+
{{Alg6|wca=l2 B2 U2 l F2 r' D2 l D2 F2 r U2 l' B2 l2
 
|sign=2L2 B2 U2 2L F2 2R' D2 2L D2 F2 2R U2 2L' B2 2L2
 
|sign=2L2 B2 U2 2L F2 2R' D2 2L D2 F2 2R U2 2L' B2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v6)]
 
|length=(25,15)|name=Mirror[Alg.6(v6)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r' U2 l F2 D2 r D2 l' F2 r U2 B2 r2
+
{{Alg6|wca=r2 B2 r' U2 l F2 D2 r D2 l' F2 r U2 B2 r2
 
|sign=2R2 B2 2R' U2 2L F2 D2 2R D2 2L' F2 2R U2 B2 2R2
 
|sign=2R2 B2 2R' U2 2L F2 D2 2R D2 2L' F2 2R U2 B2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v6)]
 
|length=(25,15)|name=Inverse[Alg.6(v6)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 F2 l' U2 r B2 l' B2 U2 r' F2 l D2 l2
+
{{Alg6|wca=l2 D2 F2 l' U2 r B2 l' B2 U2 r' F2 l D2 l2
 
|sign=2L2 D2 F2 2L' U2 2R B2 2L' B2 U2 2R' F2 2L D2 2L2
 
|sign=2L2 D2 F2 2L' U2 2R B2 2L' B2 U2 2R' F2 2L D2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v6)]
 
|length=(25,15)|name=Rotation[Alg.6(v6)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 l U2 r' F2 D2 l' D2 r F2 l' U2 B2 l2
+
{{Alg6|wca=l2 B2 l U2 r' F2 D2 l' D2 r F2 l' U2 B2 l2
 
|sign=2L2 B2 2L U2 2R' F2 D2 2L' D2 2R F2 2L' U2 B2 2L2
 
|sign=2L2 B2 2L U2 2R' F2 D2 2L' D2 2R F2 2L' U2 B2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v6)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v6)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 F2 r U2 l' B2 r B2 U2 l F2 r' D2 r2
+
{{Alg6|wca=r2 D2 F2 r U2 l' B2 r B2 U2 l F2 r' D2 r2
 
|sign=2R2 D2 F2 2R U2 2L' B2 2R B2 U2 2L F2 2R' D2 2R2
 
|sign=2R2 D2 F2 2R U2 2L' B2 2R B2 U2 2L F2 2R' D2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v6)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v6)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l' F2 r U2 B2 l B2 r' U2 l F2 D2 l2
+
{{Alg6|wca=l2 D2 l' F2 r U2 B2 l B2 r' U2 l F2 D2 l2
 
|sign=2L2 D2 2L' F2 2R U2 B2 2L B2 2R' U2 2L F2 D2 2L2
 
|sign=2L2 D2 2L' F2 2R U2 B2 2L B2 2R' U2 2L F2 D2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v6)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v6)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r F2 l' U2 B2 r' B2 l U2 r' F2 D2 r2
+
{{Alg6|wca=r2 D2 r F2 l' U2 B2 r' B2 l U2 r' F2 D2 r2
 
|sign=2R2 D2 2R F2 2L' U2 B2 2R' B2 2L U2 2R' F2 D2 2R2
 
|sign=2R2 D2 2R F2 2L' U2 B2 2R' B2 2L U2 2R' F2 D2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v6)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v6)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2
+
{{Alg6|wca=r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2
 
|sign=2R2 F2 D2 2L B2 2R' U2 2L U2 B2 2R D2 2L' F2 2R2
 
|sign=2R2 F2 D2 2L B2 2R' U2 2L U2 B2 2R D2 2L' F2 2R2
 
|length=(25,15)|name=Alg.6(v7)
 
|length=(25,15)|name=Alg.6(v7)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r' B2 l U2 r' U2 B2 l' D2 r F2 l2
+
{{Alg6|wca=l2 F2 D2 r' B2 l U2 r' U2 B2 l' D2 r F2 l2
 
|sign=2L2 F2 D2 2R' B2 2L U2 2R' U2 B2 2L' D2 2R F2 2L2
 
|sign=2L2 F2 D2 2R' B2 2L U2 2R' U2 B2 2L' D2 2R F2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v7)]
 
|length=(25,15)|name=Mirror[Alg.6(v7)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l D2 r' B2 U2 l' U2 r B2 l' D2 F2 r2
+
{{Alg6|wca=r2 F2 l D2 r' B2 U2 l' U2 r B2 l' D2 F2 r2
 
|sign=2R2 F2 2L D2 2R' B2 U2 2L' U2 2R B2 2L' D2 F2 2R2
 
|sign=2R2 F2 2L D2 2R' B2 U2 2L' U2 2R B2 2L' D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v7)]
 
|length=(25,15)|name=Inverse[Alg.6(v7)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 r D2 l' F2 r F2 D2 l B2 r' U2 l2
+
{{Alg6|wca=l2 U2 B2 r D2 l' F2 r F2 D2 l B2 r' U2 l2
 
|sign=2L2 U2 B2 2R D2 2L' F2 2R F2 D2 2L B2 2R' U2 2L2
 
|sign=2L2 U2 B2 2R D2 2L' F2 2R F2 D2 2L B2 2R' U2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v7)]
 
|length=(25,15)|name=Rotation[Alg.6(v7)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 r' D2 l B2 U2 r U2 l' B2 r D2 F2 l2
+
{{Alg6|wca=l2 F2 r' D2 l B2 U2 r U2 l' B2 r D2 F2 l2
 
|sign=2L2 F2 2R' D2 2L B2 U2 2R U2 2L' B2 2R D2 F2 2L2
 
|sign=2L2 F2 2R' D2 2L B2 U2 2R U2 2L' B2 2R D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v7)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v7)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 l' D2 r F2 l' F2 D2 r' B2 l U2 r2
+
{{Alg6|wca=r2 U2 B2 l' D2 r F2 l' F2 D2 r' B2 l U2 r2
 
|sign=2R2 U2 B2 2L' D2 2R F2 2L' F2 D2 2R' B2 2L U2 2R2
 
|sign=2R2 U2 B2 2L' D2 2R F2 2L' F2 D2 2R' B2 2L U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v7)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v7)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r B2 l' D2 F2 r' F2 l D2 r' B2 U2 l2
+
{{Alg6|wca=l2 U2 r B2 l' D2 F2 r' F2 l D2 r' B2 U2 l2
 
|sign=2L2 U2 2R B2 2L' D2 F2 2R' F2 2L D2 2R' B2 U2 2L2
 
|sign=2L2 U2 2R B2 2L' D2 F2 2R' F2 2L D2 2R' B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v7)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v7)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' B2 r D2 F2 l F2 r' D2 l B2 U2 r2
+
{{Alg6|wca=r2 U2 l' B2 r D2 F2 l F2 r' D2 l B2 U2 r2
 
|sign=2R2 U2 2L' B2 2R D2 F2 2L F2 2R' D2 2L B2 U2 2R2
 
|sign=2R2 U2 2L' B2 2R D2 F2 2L F2 2R' D2 2L B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v7)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v7)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2
+
{{Alg6|wca=r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2
 
|sign=2R2 F2 D2 2L B2 2L' B2 2R D2 F2 2L F2 2R' F2 2R2
 
|sign=2R2 F2 D2 2L B2 2L' B2 2R D2 F2 2L F2 2R' F2 2R2
 
|length=(25,15)|name=Alg.6(v8)
 
|length=(25,15)|name=Alg.6(v8)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r' B2 r B2 l' D2 F2 r' F2 l F2 l2
+
{{Alg6|wca=l2 F2 D2 r' B2 r B2 l' D2 F2 r' F2 l F2 l2
 
|sign=2L2 F2 D2 2R' B2 2R B2 2L' D2 F2 2R' F2 2L F2 2L2
 
|sign=2L2 F2 D2 2R' B2 2R B2 2L' D2 F2 2R' F2 2L F2 2L2
 
|length=(25,15)|name=Mirror[Alg.6(v8)]
 
|length=(25,15)|name=Mirror[Alg.6(v8)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r F2 l' F2 D2 r' B2 l B2 l' D2 F2 r2
+
{{Alg6|wca=r2 F2 r F2 l' F2 D2 r' B2 l B2 l' D2 F2 r2
 
|sign=2R2 F2 2R F2 2L' F2 D2 2R' B2 2L B2 2L' D2 F2 2R2
 
|sign=2R2 F2 2R F2 2L' F2 D2 2R' B2 2L B2 2L' D2 F2 2R2
 
|length=(25,15)|name=Inverse[Alg.6(v8)]
 
|length=(25,15)|name=Inverse[Alg.6(v8)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 B2 r D2 r' D2 l B2 U2 r U2 l' U2 l2
+
{{Alg6|wca=l2 U2 B2 r D2 r' D2 l B2 U2 r U2 l' U2 l2
 
|sign=2L2 U2 B2 2R D2 2R' D2 2L B2 U2 2R U2 2L' U2 2L2
 
|sign=2L2 U2 B2 2R D2 2R' D2 2L B2 U2 2R U2 2L' U2 2L2
 
|length=(25,15)|name=Rotation[Alg.6(v8)]
 
|length=(25,15)|name=Rotation[Alg.6(v8)]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 l' F2 r F2 D2 l B2 r' B2 r D2 F2 l2
+
{{Alg6|wca=l2 F2 l' F2 r F2 D2 l B2 r' B2 r D2 F2 l2
 
|sign=2L2 F2 2L' F2 2R F2 D2 2L B2 2R' B2 2R D2 F2 2L2
 
|sign=2L2 F2 2L' F2 2R F2 D2 2L B2 2R' B2 2R D2 F2 2L2
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v8)]]
 
|length=(25,15)|name=Mirror[Inverse[Alg.6(v8)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 B2 l' D2 l D2 r' B2 U2 l' U2 r U2 r2
+
{{Alg6|wca=r2 U2 B2 l' D2 l D2 r' B2 U2 l' U2 r U2 r2
 
|sign=2R2 U2 B2 2L' D2 2L D2 2R' B2 U2 2L' U2 2R U2 2R2
 
|sign=2R2 U2 B2 2L' D2 2L D2 2R' B2 U2 2L' U2 2R U2 2R2
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v8)]]
 
|length=(25,15)|name=Mirror[Rotation[Alg.6(v8)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l U2 r' U2 B2 l' D2 r D2 r' B2 U2 l2
+
{{Alg6|wca=l2 U2 l U2 r' U2 B2 l' D2 r D2 r' B2 U2 l2
 
|sign=2L2 U2 2L U2 2R' U2 B2 2L' D2 2R D2 2R' B2 U2 2L2
 
|sign=2L2 U2 2L U2 2R' U2 B2 2L' D2 2R D2 2R' B2 U2 2L2
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v8)]]
 
|length=(25,15)|name=Inverse[Rotation[Alg.6(v8)]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 l U2 B2 r D2 l' D2 l B2 U2 r2
+
{{Alg6|wca=r2 U2 r' U2 l U2 B2 r D2 l' D2 l B2 U2 r2
 
|sign=2R2 U2 2R' U2 2L U2 B2 2R D2 2L' D2 2L B2 U2 2R2
 
|sign=2R2 U2 2R' U2 2L U2 B2 2R D2 2L' D2 2L B2 U2 2R2
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v8)]]]
 
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v8)]]]
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Shortest single slice quarter turn algorithms===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Shortest single slice quarter turn algorithms</span>===
 
*The current upperbound in the single slice quarter turn metric for the single dedge flip is 23.  This section contains over 100 algorithms with this quantity of moves.
 
*The current upperbound in the single slice quarter turn metric for the single dedge flip is 23.  This section contains over 100 algorithms with this quantity of moves.
 +
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
 +
The majority of algorithms in this section, like the (25,15) solutions, were found by using the {{LinkColorE|u=https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2|c=rgb(229,148,0)|t=3x3x3 Classic Setup}} in {{LinkColorE|u=http://kociemba.org/cube.htm|c=rgb(229,148,0)|t=Cube Explorer}}.  For this particular set, a search up through depth 18 was performed.
  
 
+
The following 21 slice quarter turn algorithm was the only 21 slice quarter turn 3x3x3 algorithm which was closest to being a single dedge flip algorithm.  Perhaps if the {{LinkColorE|u=https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2|c=rgb(229,148,0)|t=3x3x3 Classic Setup}} is used up to depth 21, some 21 slice quarter turn solutions may be found.
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
{{Alg6|wca=r' F l' F2 r F r' F2 D F' D l D' F D' l F2 r
| bgcolor="fbfb8b" |
 
It's worthy to note that the majority of algorithms in this section, like the (25,15) solutions, were found by using the [https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2 3x3x3 Classic Setup] in Cube Explorer.  For this particular set, a search up through depth 18 was performed.
 
 
 
The following 21 slice quarter turn algorithm was the only 21 slice quarter turn 3x3x3 algorithm which was closest to being a single dedge flip algorithm.  Perhaps if the [https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2 3x3x3 Classic Setup] is used up to depth 21, some 21 slice quarter turn solutions may be found.
 
{{Alg5|wca=r' F l' F2 r F r' F2 D F' D l D' F D' l F2 r
 
 
|sign=2R' F 2L' F2 2R F 2R' F2 D F' D 2L D' F D' 2L F2 2R
 
|sign=2R' F 2L' F2 2R F 2R' F2 D F' D 2L D' F D' 2L F2 2R
 
|length=(21,18)|name=|wide=N|author=Christopher Mowla
 
|length=(21,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=0}}
 
+
<b>Update</b><br>
<b>Update</b>
+
On March 28, 2018, Ben Whitmore found two 21 single slice quarter turn algorithms with his {{LinkColorE|u=https://www.reddit.com/r/Cubers/comments/873vzw/ksolve_a_new_fast_general_puzzle_solving_program/|c=rgb(229,148,0)|t=ksolve++ program}}.  (They also happen to be supercube safe.)
 
+
{{Alg6|wca=r' U' u r U' r U r u' r' u r U r U' r Uw' r' U2 //Safe
On March 28, 2018, Ben Whitmore found two 21 single slice quarter turn algorithms with his [https://www.reddit.com/r/Cubers/comments/873vzw/ksolve_a_new_fast_general_puzzle_solving_program/ ksolve++ program].  (They also happen to be supercube safe.)
+
|sign=2R' U' 2U 2R U' 2R U 2R 2U' 2R' 2U 2R U 2R U' 2R u' 2R' U2 //Safe
{{Alg5|wca=r' U' u r U' r U r u' r' u r U r U' r Uw' r' U2//Safe
 
|sign=2R' U' 2U 2R U' 2R U 2R 2U' 2R' 2U 2R U 2R U' 2R u' 2R' U2//Safe
 
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=r' Uw' r U' r U r u r' u' r U r U' r u U' r' U2//Safe
+
{{Alg6|wca=r' Uw' r U' r U r u r' u' r U r U' r u U' r' U2 //Safe
|sign=2R' u' 2R U' 2R U 2R 2U 2R' 2U' 2R U 2R U' 2R 2U U' 2R' U2//Safe
+
|sign=2R' u' 2R U' 2R U 2R 2U 2R' 2U' 2R U 2R U' 2R 2U U' 2R' U2 //Safe
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
 
+
{{br|b=1}}
However, unlike all of the 23 single slice quarter turn algorithms presented in this section (which can be applied to all [[big cube]] sizes), these two algorithms only work on the 4x4x4.
+
However, unlike all of the 23 single slice quarter turn algorithms presented in this section (which can be applied to all {{LinkColorI|p=big cube|c=rgb(229,148,0)|t=big cube}} sizes), these two algorithms only work on the 4x4x4.</ul>
|}
+
{{br|b=2}}
 
 
 
 
 
*Like the (25,15) solutions, these solutions have been grouped next to their transformations.  To save space, we label each group's algorithm as v1,v2,v3, and so forth.
 
*Like the (25,15) solutions, these solutions have been grouped next to their transformations.  To save space, we label each group's algorithm as v1,v2,v3, and so forth.
 
+
{{br|b=1}}
*However, unlike the (25,15) solutions, <b>this is by no means the complete set</b> of all possible <i>unique</i> (let alone all inverse, mirror, and rotation transformations of the unique solutions) 23 single slice quarter turn solutions.  (There were 36 "unique" (25,15) solutions from which all 288 algorithms were derived from.)  Perhaps in the future we will have efficient optimal solvers in the single slice quarter turn metric which we can use to do a brute force search.
+
*However, unlike the (25,15) solutions, <i>this is by no means the complete set</i> of all possible <i>unique</i> (let alone all inverse, mirror, and rotation transformations of the unique solutions) 23 single slice quarter turn solutions.  (There were 36 "unique" (25,15) solutions from which all 288 algorithms were derived from.)  Perhaps in the future we will have efficient optimal solvers in the single slice quarter turn metric which we can use to do a brute force search.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=x Rw2 U2 Rw U2 l' U2 Rw' F2 U' l' U F2 U' l U' Rw2 x'
{{Alg5|wca=x Rw2 U2 Rw U2 l' U2 Rw' F2 U' l' U F2 U' l U' Rw2 x'
 
 
|sign=x r2 U2 r U2 2L' U2 r' F2 U' 2L' U F2 U' 2L U' r2 x'
 
|sign=x r2 U2 r U2 2L' U2 r' F2 U' 2L' U F2 U' 2L U' r2 x'
 
|length=(23,16)|name=v1
 
|length=(23,16)|name=v1
Line 3,914: Line 4,139:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x Rw2 U2 Lw F2 l' F2 Lw' F2 U' l' U F2 U' l U' Rw2 x'
+
{{Alg6|wca=x Rw2 U2 Lw F2 l' F2 Lw' F2 U' l' U F2 U' l U' Rw2 x'
 
|sign=x r2 U2 l F2 2L' F2 l' F2 U' 2L' U F2 U' 2L U' r2 x'
 
|sign=x r2 U2 l F2 2L' F2 l' F2 U' 2L' U F2 U' 2L U' r2 x'
 
|length=(23,16)|name=v2
 
|length=(23,16)|name=v2
Line 3,920: Line 4,145:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x Rw2 U2 Rw U2 l' U2 Rw' F2 U l' U' F2 U l U Rw2 x'
+
{{Alg6|wca=x Rw2 U2 Rw U2 l' U2 Rw' F2 U l' U' F2 U l U Rw2 x'
 
|sign=x r2 U2 r U2 2L' U2 r' F2 U 2L' U' F2 U 2L U r2 x'
 
|sign=x r2 U2 r U2 2L' U2 r' F2 U 2L' U' F2 U 2L U r2 x'
 
|length=(23,16)|name=v1
 
|length=(23,16)|name=v1
Line 3,926: Line 4,151:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x Rw2 U2 Lw F2 l' F2 Lw' F2 U l' U' F2 U l U Rw2 x'
+
{{Alg6|wca=x Rw2 U2 Lw F2 l' F2 Lw' F2 U l' U' F2 U l U Rw2 x'
 
|sign=x r2 U2 l F2 2L' F2 l' F2 U 2L' U' F2 U 2L U r2 x'
 
|sign=x r2 U2 l F2 2L' F2 l' F2 U 2L' U' F2 U 2L U r2 x'
 
|length=(23,16)|name=v2
 
|length=(23,16)|name=v2
Line 3,932: Line 4,157:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' Rw2 U2 Lw' U2 r U2 Lw F2 U r U' F2 U r' U Rw2 x
+
{{Alg6|wca=x' Rw2 U2 Lw' U2 r U2 Lw F2 U r U' F2 U r' U Rw2 x
 
|sign=x' r2 U2 l' U2 2R U2 l F2 U 2R U' F2 U 2R' U r2 x
 
|sign=x' r2 U2 l' U2 2R U2 l F2 U 2R U' F2 U 2R' U r2 x
 
|length=(23,16)|name=cmowlaparity
 
|length=(23,16)|name=cmowlaparity
Line 3,938: Line 4,163:
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
}}
 
}}
{{Alg5|wca=x' Rw2 U2 Rw' F2 r F2 Rw F2 U r U' F2 U r' U Rw2 x
+
{{Alg6|wca=x' Rw2 U2 Rw' F2 r F2 Rw F2 U r U' F2 U r' U Rw2 x
 
|sign=x' r2 U2 r' F2 2R F2 r F2 U 2R U' F2 U 2R' U r2 x
 
|sign=x' r2 U2 r' F2 2R F2 r F2 U 2R U' F2 U 2R' U r2 x
 
|length=(23,16)|name=cmowlaparity(v2)
 
|length=(23,16)|name=cmowlaparity(v2)
Line 3,944: Line 4,169:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' Rw2 U2 Lw' U2 r U2 Lw F2 U' r U F2 U' r' U' Rw2 x
+
{{Alg6|wca=x' Rw2 U2 Lw' U2 r U2 Lw F2 U' r U F2 U' r' U' Rw2 x
 
|sign=x' r2 U2 l' U2 2R U2 l F2 U' 2R U F2 U' 2R' U' r2 x
 
|sign=x' r2 U2 l' U2 2R U2 l F2 U' 2R U F2 U' 2R' U' r2 x
 
|length=(23,16)|name=v1
 
|length=(23,16)|name=v1
Line 3,950: Line 4,175:
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
}}
 
}}
{{Alg5|wca=x' Rw2 U2 Rw' F2 r F2 Rw F2 U' r U F2 U' r' U' Rw2 x
+
{{Alg6|wca=x' Rw2 U2 Rw' F2 r F2 Rw F2 U' r U F2 U' r' U' Rw2 x
 
|sign=x' r2 U2 r' F2 2R F2 r F2 U' 2R U F2 U' 2R' U' r2 x
 
|sign=x' r2 U2 r' F2 2R F2 r F2 U' 2R U F2 U' 2R' U' r2 x
 
|length=(23,16)|name=v2
 
|length=(23,16)|name=v2
Line 3,956: Line 4,181:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw
+
{{Alg6|wca=Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw
 
|sign=r' U2 B 2R' B' U2 F2 l' B2 2R' B2 l B 2R F2 B' r
 
|sign=r' U2 B 2R' B' U2 F2 l' B2 2R' B2 l B 2R F2 B' r
 
|length=(22,17)|name=v1
 
|length=(22,17)|name=v1
Line 3,962: Line 4,187:
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-15#post-981794
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-15#post-981794
 
}}
 
}}
{{Alg5|wca=Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw
+
{{Alg6|wca=Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw
 
|sign=r' U2 B 2R' B' U2 F2 r' U2 2R' U2 r B 2R F2 B' r
 
|sign=r' U2 B 2R' B' U2 F2 r' U2 2R' U2 r B 2R F2 B' r
 
|length=(22,17)|name=v2
 
|length=(22,17)|name=v2
Line 3,968: Line 4,193:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 B Rw
+
{{Alg6|wca=Rw' U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 B Rw
 
|sign=r' U2 B' 2R' B U2 F2 l' B2 2R' B2 l B' 2R F2 B r
 
|sign=r' U2 B' 2R' B U2 F2 l' B2 2R' B2 l B' 2R F2 B r
 
|length=(22,17)|name=v1
 
|length=(22,17)|name=v1
Line 3,974: Line 4,199:
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-15#post-981794
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-15#post-981794
 
}}
 
}}
{{Alg5|wca=Rw' U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 B Rw
+
{{Alg6|wca=Rw' U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 B Rw
 
|sign=r' U2 B' 2R' B U2 F2 r' U2 2R' U2 r B' 2R F2 B r
 
|sign=r' U2 B' 2R' B U2 F2 r' U2 2R' U2 r B' 2R F2 B r
 
|length=(22,17)|name=v2
 
|length=(22,17)|name=v2
Line 3,980: Line 4,205:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' r' U B2 U' r U' r' U2 r' B2 l U2 l' U2 r2
+
{{Alg6|wca=r' U' r' U B2 U' r U' r' U2 r' B2 l U2 l' U2 r2
 
|sign=2R' U' 2R' U B2 U' 2R U' 2R' U2 2R' B2 2L U2 2L' U2 2R2
 
|sign=2R' U' 2R' U B2 U' 2R U' 2R' U2 2R' B2 2L U2 2L' U2 2R2
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U r' U' B2 U r U r' U2 r' B2 l U2 l' U2 r2
+
{{Alg6|wca=r' U r' U' B2 U r U r' U2 r' B2 l U2 l' U2 r2
 
|sign=2R' U 2R' U' B2 U 2R U 2R' U2 2R' B2 2L U2 2L' U2 2R2
 
|sign=2R' U 2R' U' B2 U 2R U 2R' U2 2R' B2 2L U2 2L' U2 2R2
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r B l B' D2 B l' B l B2 r F2 l' F2 l D2 r2
+
{{Alg6|wca=r B l B' D2 B l' B l B2 r F2 l' F2 l D2 r2
 
|sign=2R B 2L B' D2 B 2L' B 2L B2 2R F2 2L' F2 2L D2 2R2
 
|sign=2R B 2L B' D2 B 2L' B 2L B2 2R F2 2L' F2 2L D2 2R2
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 3,996: Line 4,221:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r B l B' D2 B l' B l B2 l D2 l' D2 r D2 r2
+
{{Alg6|wca=r B l B' D2 B l' B l B2 l D2 l' D2 r D2 r2
 
|sign=2R B 2L B' D2 B 2L' B 2L B2 2L D2 2L' D2 2R D2 2R2
 
|sign=2R B 2L B' D2 B 2L' B 2L B2 2L D2 2L' D2 2R D2 2R2
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,002: Line 4,227:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r B' l B D2 B' l' B' l B2 r F2 l' F2 l D2 r2
+
{{Alg6|wca=r B' l B D2 B' l' B' l B2 r F2 l' F2 l D2 r2
 
|sign=2R B' 2L B D2 B' 2L' B' 2L B2 2R F2 2L' F2 2L D2 2R2
 
|sign=2R B' 2L B D2 B' 2L' B' 2L B2 2R F2 2L' F2 2L D2 2R2
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,008: Line 4,233:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r B' l B D2 B' l' B' l B2 l D2 l' D2 r D2 r2
+
{{Alg6|wca=r B' l B D2 B' l' B' l B2 l D2 l' D2 r D2 r2
 
|sign=2R B' 2L B D2 B' 2L' B' 2L B2 2L D2 2L' D2 2R D2 2R2
 
|sign=2R B' 2L B D2 B' 2L' B' 2L B2 2L D2 2L' D2 2R D2 2R2
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,014: Line 4,239:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw D B2 D' l D B2 U2 Rw D2 l D2 Rw' D' l' U2 Rw'
+
{{Alg6|wca=Rw D B2 D' l D B2 U2 Rw D2 l D2 Rw' D' l' U2 Rw'
 
|sign=r D B2 D' 2L D B2 U2 r D2 2L D2 r' D' 2L' U2 r'
 
|sign=r D B2 D' 2L D B2 U2 r D2 2L D2 r' D' 2L' U2 r'
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,020: Line 4,245:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw D B2 D' l D B2 U2 Lw B2 l B2 Lw' D' l' U2 Rw'
+
{{Alg6|wca=Rw D B2 D' l D B2 U2 Lw B2 l B2 Lw' D' l' U2 Rw'
 
|sign=r D B2 D' 2L D B2 U2 l B2 2L B2 l' D' 2L' U2 r'
 
|sign=r D B2 D' 2L D B2 U2 l B2 2L B2 l' D' 2L' U2 r'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,026: Line 4,251:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw D' B2 D l D' B2 U2 Rw D2 l D2 Rw' D l' U2 Rw'
+
{{Alg6|wca=Rw D' B2 D l D' B2 U2 Rw D2 l D2 Rw' D l' U2 Rw'
 
|sign=r D' B2 D 2L D' B2 U2 r D2 2L D2 r' D 2L' U2 r'
 
|sign=r D' B2 D 2L D' B2 U2 r D2 2L D2 r' D 2L' U2 r'
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,032: Line 4,257:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw D' B2 D l D' B2 U2 Lw B2 l B2 Lw' D l' U2 Rw'
+
{{Alg6|wca=Rw D' B2 D l D' B2 U2 Lw B2 l B2 Lw' D l' U2 Rw'
 
|sign=r D' B2 D 2L D' B2 U2 l B2 2L B2 l' D 2L' U2 r'
 
|sign=r D' B2 D 2L D' B2 U2 l B2 2L B2 l' D 2L' U2 r'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,038: Line 4,263:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D2 B l B' D2 B l' B' Rw' B2 l B2 Rw F2 Rw
+
{{Alg6|wca=Rw' F2 D2 B l B' D2 B l' B' Rw' B2 l B2 Rw F2 Rw
 
|sign=r' F2 D2 B 2L B' D2 B 2L' B' r' B2 2L B2 r F2 r
 
|sign=r' F2 D2 B 2L B' D2 B 2L' B' r' B2 2L B2 r F2 r
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,044: Line 4,269:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D2 B l B' D2 B l' B' Lw' D2 l D2 Lw F2 Rw
+
{{Alg6|wca=Rw' F2 D2 B l B' D2 B l' B' Lw' D2 l D2 Lw F2 Rw
 
|sign=r' F2 D2 B 2L B' D2 B 2L' B' l' D2 2L D2 l F2 r
 
|sign=r' F2 D2 B 2L B' D2 B 2L' B' l' D2 2L D2 l F2 r
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,050: Line 4,275:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D2 B' l B D2 B' l' B Rw' B2 l B2 Rw F2 Rw
+
{{Alg6|wca=Rw' F2 D2 B' l B D2 B' l' B Rw' B2 l B2 Rw F2 Rw
 
|sign=r' F2 D2 B' 2L B D2 B' 2L' B r' B2 2L B2 r F2 r
 
|sign=r' F2 D2 B' 2L B D2 B' 2L' B r' B2 2L B2 r F2 r
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,056: Line 4,281:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D2 B' l B D2 B' l' B Lw' D2 l D2 Lw F2 Rw
+
{{Alg6|wca=Rw' F2 D2 B' l B D2 B' l' B Lw' D2 l D2 Lw F2 Rw
 
|sign=r' F2 D2 B' 2L B D2 B' 2L' B l' D2 2L D2 l F2 r
 
|sign=r' F2 D2 B' 2L B D2 B' 2L' B l' D2 2L D2 l F2 r
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,062: Line 4,287:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D2 l' D l D' F2 D l' D l D2 l F2 r
+
{{Alg6|wca=r2 D2 r D2 l' D l D' F2 D l' D l D2 l F2 r
 
|sign=2R2 D2 2R D2 2L' D 2L D' F2 D 2L' D 2L D2 2L F2 2R
 
|sign=2R2 D2 2R D2 2L' D 2L D' F2 D 2L' D 2L D2 2L F2 2R
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D2 l' D' l D F2 D' l' D' l D2 l F2 r
+
{{Alg6|wca=r2 D2 r D2 l' D' l D F2 D' l' D' l D2 l F2 r
 
|sign=2R2 D2 2R D2 2L' D' 2L D F2 D' 2L' D' 2L D2 2L F2 2R
 
|sign=2R2 D2 2R D2 2L' D' 2L D F2 D' 2L' D' 2L D2 2L F2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' B' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 Rw
+
{{Alg6|wca=Rw' B' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 Rw
 
|sign=r' B' U2 B 2R' B' U2 F2 l' B2 2R' B2 l B 2R F2 r
 
|sign=r' B' U2 B 2R' B' U2 F2 l' B2 2R' B2 l B 2R F2 r
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,078: Line 4,303:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' B' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 Rw
+
{{Alg6|wca=Rw' B' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 Rw
 
|sign=r' B' U2 B 2R' B' U2 F2 r' U2 2R' U2 r B 2R F2 r
 
|sign=r' B' U2 B 2R' B' U2 F2 r' U2 2R' U2 r B 2R F2 r
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,084: Line 4,309:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' B U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 Rw
+
{{Alg6|wca=Rw' B U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 Rw
 
|sign=r' B U2 B' 2R' B U2 F2 l' B2 2R' B2 l B' 2R F2 r
 
|sign=r' B U2 B' 2R' B U2 F2 l' B2 2R' B2 l B' 2R F2 r
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,090: Line 4,315:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' B U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 Rw
+
{{Alg6|wca=Rw' B U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 Rw
 
|sign=r' B U2 B' 2R' B U2 F2 r' U2 2R' U2 r B' 2R F2 r
 
|sign=r' B U2 B' 2R' B U2 F2 r' U2 2R' U2 r B' 2R F2 r
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,096: Line 4,321:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' D' r D' B2 D r' D' B2 l' D2 l' F2 l F2 l2
+
{{Alg6|wca=l' r' D' r D' B2 D r' D' B2 l' D2 l' F2 l F2 l2
 
|sign=2L' 2R' D' 2R D' B2 D 2R' D' B2 2L' D2 2L' F2 2L F2 2L2
 
|sign=2L' 2R' D' 2R D' B2 D 2R' D' B2 2L' D2 2L' F2 2L F2 2L2
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,102: Line 4,327:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r U' r U' F2 U r' U' F2 l' U2 l' B2 l B2 r2
+
{{Alg6|wca=l r U' r U' F2 U r' U' F2 l' U2 l' B2 l B2 r2
 
|sign=2L 2R U' 2R U' F2 U 2R' U' F2 2L' U2 2L' B2 2L B2 2R2
 
|sign=2L 2R U' 2R U' F2 U 2R' U' F2 2L' U2 2L' B2 2L B2 2R2
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,108: Line 4,333:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' D r D B2 D' r' D B2 l' D2 l' F2 l F2 l2
+
{{Alg6|wca=l' r' D r D B2 D' r' D B2 l' D2 l' F2 l F2 l2
 
|sign=2L' 2R' D 2R D B2 D' 2R' D B2 2L' D2 2L' F2 2L F2 2L2
 
|sign=2L' 2R' D 2R D B2 D' 2R' D B2 2L' D2 2L' F2 2L F2 2L2
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,114: Line 4,339:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r U r U F2 U' r' U F2 l' U2 l' B2 l B2 r2
+
{{Alg6|wca=l r U r U F2 U' r' U F2 l' U2 l' B2 l B2 r2
 
|sign=2L 2R U 2R U F2 U' 2R' U F2 2L' U2 2L' B2 2L B2 2R2
 
|sign=2L 2R U 2R U F2 U' 2R' U F2 2L' U2 2L' B2 2L B2 2R2
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,120: Line 4,345:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 D' r' D F2 D' r D Lw D2 r' D2 Lw' U2 Rw'
+
{{Alg6|wca=Rw U2 F2 D' r' D F2 D' r D Lw D2 r' D2 Lw' U2 Rw'
 
|sign=r U2 F2 D' 2R' D F2 D' 2R D l D2 2R' D2 l' U2 r'
 
|sign=r U2 F2 D' 2R' D F2 D' 2R D l D2 2R' D2 l' U2 r'
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,126: Line 4,351:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw'
 
|sign=r U2 F2 D' 2R' D F2 D' 2R D r F2 2R' F2 r' U2 r'
 
|sign=r U2 F2 D' 2R' D F2 D' 2R D r F2 2R' F2 r' U2 r'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,132: Line 4,357:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 D r' D' F2 D r D' Lw D2 r' D2 Lw' U2 Rw'
+
{{Alg6|wca=Rw U2 F2 D r' D' F2 D r D' Lw D2 r' D2 Lw' U2 Rw'
 
|sign=r U2 F2 D 2R' D' F2 D 2R D' l D2 2R' D2 l' U2 r'
 
|sign=r U2 F2 D 2R' D' F2 D 2R D' l D2 2R' D2 l' U2 r'
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,138: Line 4,363:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw'
 
|sign=r U2 F2 D 2R' D' F2 D 2R D' r F2 2R' F2 r' U2 r'
 
|sign=r U2 F2 D 2R' D' F2 D 2R D' r F2 2R' F2 r' U2 r'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,144: Line 4,369:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B' r B' U2 B r' B' U2 l' B2 Lw' D2 l D2 Lw r
+
{{Alg6|wca=r2 B' r B' U2 B r' B' U2 l' B2 Lw' D2 l D2 Lw r
 
|sign=2R2 B' 2R B' U2 B 2R' B' U2 2L' B2 l' D2 2L D2 l 2R
 
|sign=2R2 B' 2R B' U2 B 2R' B' U2 2L' B2 l' D2 2L D2 l 2R
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,150: Line 4,375:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 F' r F' D2 F r' F' D2 l' F2 l' U2 l U2 l' r'
+
{{Alg6|wca=l2 F' r F' D2 F r' F' D2 l' F2 l' U2 l U2 l' r'
 
|sign=2L2 F' 2R F' D2 F 2R' F' D2 2L' F2 2L' U2 2L U2 2L' 2R'
 
|sign=2L2 F' 2R F' D2 F 2R' F' D2 2L' F2 2L' U2 2L U2 2L' 2R'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,156: Line 4,381:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B r B U2 B' r' B U2 l' B2 Lw' D2 l D2 Lw r
+
{{Alg6|wca=r2 B r B U2 B' r' B U2 l' B2 Lw' D2 l D2 Lw r
 
|sign=2R2 B 2R B U2 B' 2R' B U2 2L' B2 l' D2 2L D2 l 2R
 
|sign=2R2 B 2R B U2 B' 2R' B U2 2L' B2 l' D2 2L D2 l 2R
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,162: Line 4,387:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 F r F D2 F' r' F D2 l' F2 l' U2 l U2 l' r'
+
{{Alg6|wca=l2 F r F D2 F' r' F D2 l' F2 l' U2 l U2 l' r'
 
|sign=2L2 F 2R F D2 F' 2R' F D2 2L' F2 2L' U2 2L U2 2L' 2R'
 
|sign=2L2 F 2R F D2 F' 2R' F D2 2L' F2 2L' U2 2L U2 2L' 2R'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,168: Line 4,393:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 l F' r' F U2 F' r F' r' F2 r' U2 r'
+
{{Alg6|wca=r2 U2 l' U2 l F' r' F U2 F' r F' r' F2 r' U2 r'
 
|sign=2R2 U2 2L' U2 2L F' 2R' F U2 F' 2R F' 2R' F2 2R' U2 2R'
 
|sign=2R2 U2 2L' U2 2L F' 2R' F U2 F' 2R F' 2R' F2 2R' U2 2R'
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,174: Line 4,399:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' F2 l D' r' D F2 D' r D' r' D2 l' U2 r'
+
{{Alg6|wca=r2 U2 r' F2 l D' r' D F2 D' r D' r' D2 l' U2 r'
 
|sign=2R2 U2 2R' F2 2L D' 2R' D F2 D' 2R D' 2R' D2 2L' U2 2R'
 
|sign=2R2 U2 2R' F2 2L D' 2R' D F2 D' 2R D' 2R' D2 2L' U2 2R'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,180: Line 4,405:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 l F r' F' U2 F r F r' F2 r' U2 r'
+
{{Alg6|wca=r2 U2 l' U2 l F r' F' U2 F r F r' F2 r' U2 r'
 
|sign=2R2 U2 2L' U2 2L F 2R' F' U2 F 2R F 2R' F2 2R' U2 2R'
 
|sign=2R2 U2 2L' U2 2L F 2R' F' U2 F 2R F 2R' F2 2R' U2 2R'
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,186: Line 4,411:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' F2 l D r' D' F2 D r D r' D2 l' U2 r'
+
{{Alg6|wca=r2 U2 r' F2 l D r' D' F2 D r D r' D2 l' U2 r'
 
|sign=2R2 U2 2R' F2 2L D 2R' D' F2 D 2R D 2R' D2 2L' U2 2R'
 
|sign=2R2 U2 2R' F2 2L D 2R' D' F2 D 2R D 2R' D2 2L' U2 2R'
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,192: Line 4,417:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 D2 r D b' D F2 D' b D r' B2 l r F2 r
+
{{Alg6|wca=r2 B2 D2 r D b' D F2 D' b D r' B2 l r F2 r
 
|sign=2R2 B2 D2 2R D 2B' D F2 D' 2B D 2R' B2 2L 2R F2 2R
 
|sign=2R2 B2 D2 2R D 2B' D F2 D' 2B D 2R' B2 2L 2R F2 2R
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 D2 r D' f' D' F2 D f D' r' B2 l r F2 r
+
{{Alg6|wca=r2 B2 D2 r D' f' D' F2 D f D' r' B2 l r F2 r
 
|sign=2R2 B2 D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L 2R F2 2R
 
|sign=2R2 B2 D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L 2R F2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 l' U' f U' B2 U f' U' r' B2 r l F2 r
+
{{Alg6|wca=r2 F2 U2 l' U' f U' B2 U f' U' r' B2 r l F2 r
 
|sign=2R2 F2 U2 2L' U' 2F U' B2 U 2F' U' 2R' B2 2R 2L F2 2R
 
|sign=2R2 F2 U2 2L' U' 2F U' B2 U 2F' U' 2R' B2 2R 2L F2 2R
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 l' U b U B2 U' b' U r' B2 r l F2 r
+
{{Alg6|wca=r2 F2 U2 l' U b U B2 U' b' U r' B2 r l F2 r
 
|sign=2R2 F2 U2 2L' U 2B U B2 U' 2B' U 2R' B2 2R 2L F2 2R
 
|sign=2R2 F2 U2 2L' U 2B U B2 U' 2B' U 2R' B2 2R 2L F2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D f D' B2 D f' D r D2 F2 r' B2 l r F2 r
+
{{Alg6|wca=r2 D f D' B2 D f' D r D2 F2 r' B2 l r F2 r
 
|sign=2R2 D 2F D' B2 D 2F' D 2R D2 F2 2R' B2 2L 2R F2 2R
 
|sign=2R2 D 2F D' B2 D 2F' D 2R D2 F2 2R' B2 2L 2R F2 2R
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D' b D B2 D' b' D' r D2 F2 r' B2 l r F2 r
+
{{Alg6|wca=r2 D' b D B2 D' b' D' r D2 F2 r' B2 l r F2 r
 
|sign=2R2 D' 2B D B2 D' 2B' D' 2R D2 F2 2R' B2 2L 2R F2 2R
 
|sign=2R2 D' 2B D B2 D' 2B' D' 2R D2 F2 2R' B2 2L 2R F2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U' b' U F2 U' b U' l' U2 B2 r' B2 r l F2 r
+
{{Alg6|wca=r2 U' b' U F2 U' b U' l' U2 B2 r' B2 r l F2 r
 
|sign=2R2 U' 2B' U F2 U' 2B U' 2L' U2 B2 2R' B2 2R 2L F2 2R
 
|sign=2R2 U' 2B' U F2 U' 2B U' 2L' U2 B2 2R' B2 2R 2L F2 2R
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U f' U' F2 U f U l' U2 B2 r' B2 r l F2 r
+
{{Alg6|wca=r2 U f' U' F2 U f U l' U2 B2 r' B2 r l F2 r
 
|sign=2R2 U 2F' U' F2 U 2F U 2L' U2 B2 2R' B2 2R 2L F2 2R
 
|sign=2R2 U 2F' U' F2 U 2F U 2L' U2 B2 2R' B2 2R 2L F2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D b' D F2 D' b D r' B2 l B2 r F2 r
+
{{Alg6|wca=r2 D2 r D b' D F2 D' b D r' B2 l B2 r F2 r
 
|sign=2R2 D2 2R D 2B' D F2 D' 2B D 2R' B2 2L B2 2R F2 2R
 
|sign=2R2 D2 2R D 2B' D F2 D' 2B D 2R' B2 2L B2 2R F2 2R
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,238: Line 4,463:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D b' D F2 D' b D l' D2 l D2 l F2 r
+
{{Alg6|wca=r2 D2 r D b' D F2 D' b D l' D2 l D2 l F2 r
 
|sign=2R2 D2 2R D 2B' D F2 D' 2B D 2L' D2 2L D2 2L F2 2R
 
|sign=2R2 D2 2R D 2B' D F2 D' 2B D 2L' D2 2L D2 2L F2 2R
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,244: Line 4,469:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D' f' D' F2 D f D' r' B2 l B2 r F2 r
+
{{Alg6|wca=r2 D2 r D' f' D' F2 D f D' r' B2 l B2 r F2 r
 
|sign=2R2 D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L B2 2R F2 2R
 
|sign=2R2 D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L B2 2R F2 2R
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,250: Line 4,475:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D' f' D' F2 D f D' l' D2 l D2 l F2 r
+
{{Alg6|wca=r2 D2 r D' f' D' F2 D f D' l' D2 l D2 l F2 r
 
|sign=2R2 D2 2R D' 2F' D' F2 D 2F D' 2L' D2 2L D2 2L F2 2R
 
|sign=2R2 D2 2R D' 2F' D' F2 D 2F D' 2L' D2 2L D2 2L F2 2R
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,256: Line 4,481:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' B2 l D f D' B2 D f' D r D2 r F2 r
+
{{Alg6|wca=r2 F2 r' B2 l D f D' B2 D f' D r D2 r F2 r
 
|sign=2R2 F2 2R' B2 2L D 2F D' B2 D 2F' D 2R D2 2R F2 2R
 
|sign=2R2 F2 2R' B2 2L D 2F D' B2 D 2F' D 2R D2 2R F2 2R
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,262: Line 4,487:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l' D2 l F u F' D2 F u' F r F2 l F2 r
+
{{Alg6|wca=r2 F2 l' D2 l F u F' D2 F u' F r F2 l F2 r
 
|sign=2R2 F2 2L' D2 2L F 2U F' D2 F 2U' F 2R F2 2L F2 2R
 
|sign=2R2 F2 2L' D2 2L F 2U F' D2 F 2U' F 2R F2 2L F2 2R
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,268: Line 4,493:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' B' d' B U2 B' d B' r' U2 r' U2 r'
+
{{Alg6|wca=r2 B2 r U2 r' B' d' B U2 B' d B' r' U2 r' U2 r'
 
|sign=2R2 B2 2R U2 2R' B' 2D' B U2 B' 2D B' 2R' U2 2R' U2 2R'
 
|sign=2R2 B2 2R U2 2R' B' 2D' B U2 B' 2D B' 2R' U2 2R' U2 2R'
 
|length=(23,17)|name=v3
 
|length=(23,17)|name=v3
Line 4,274: Line 4,499:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' B2 l D' b D B2 D' b' D' r D2 r F2 r
+
{{Alg6|wca=r2 F2 r' B2 l D' b D B2 D' b' D' r D2 r F2 r
 
|sign=2R2 F2 2R' B2 2L D' 2B D B2 D' 2B' D' 2R D2 2R F2 2R
 
|sign=2R2 F2 2R' B2 2L D' 2B D B2 D' 2B' D' 2R D2 2R F2 2R
 
|length=(23,17)|name=v1
 
|length=(23,17)|name=v1
Line 4,280: Line 4,505:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l' D2 l F' d F D2 F' d' F' r F2 l F2 r
+
{{Alg6|wca=r2 F2 l' D2 l F' d F D2 F' d' F' r F2 l F2 r
 
|sign=2R2 F2 2L' D2 2L F' 2D F D2 F' 2D' F' 2R F2 2L F2 2R
 
|sign=2R2 F2 2L' D2 2L F' 2D F D2 F' 2D' F' 2R F2 2L F2 2R
 
|length=(23,17)|name=v2
 
|length=(23,17)|name=v2
Line 4,286: Line 4,511:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' B u' B' U2 B u B r' U2 r' U2 r'
+
{{Alg6|wca=r2 B2 r U2 r' B u' B' U2 B u B r' U2 r' U2 r'
 
|sign=2R2 B2 2R U2 2R' B 2U' B' U2 B 2U B 2R' U2 2R' U2 2R'
 
|sign=2R2 B2 2R U2 2R' B 2U' B' U2 B 2U B 2R' U2 2R' U2 2R'
 
|length=(23,17)|name=v3
 
|length=(23,17)|name=v3
Line 4,292: Line 4,517:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 B r' U R' U r U' R U' r B U2 r U2 r' B2 Rw2
+
{{Alg6|wca=Rw2 B r' U R' U r U' R U' r B U2 r U2 r' B2 Rw2
 
|sign=r2 B 2R' U R' U 2R U' R U' 2R B U2 2R U2 2R' B2 r2
 
|sign=r2 B 2R' U R' U 2R U' R U' 2R B U2 2R U2 2R' B2 r2
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-590058
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-590058
 
}}
 
}}
{{Alg5|wca=Lw' B' r' B D2 B' r B' r' B2 r' D2 l B2 l' B2 r Lw
+
{{Alg6|wca=Lw' B' r' B D2 B' r B' r' B2 r' D2 l B2 l' B2 r Lw
 
|sign=l' B' 2R' B D2 B' 2R B' 2R' B2 2R' D2 2L B2 2L' B2 2R l
 
|sign=l' B' 2R' B D2 B' 2R B' 2R' B2 2R' D2 2L B2 2L' B2 2R l
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' B r' B' D2 B r B r' B2 r' D2 l B2 l' B2 r Lw
+
{{Alg6|wca=Lw' B r' B' D2 B r B r' B2 r' D2 l B2 l' B2 r Lw
 
|sign=l' B 2R' B' D2 B 2R B 2R' B2 2R' D2 2L B2 2L' B2 2R l
 
|sign=l' B 2R' B' D2 B 2R B 2R' B2 2R' D2 2L B2 2L' B2 2R l
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r Lw F2 l' F2 l D' r' D F2 D' r D' r' D2 r' F2 Lw'
+
{{Alg6|wca=r Lw F2 l' F2 l D' r' D F2 D' r D' r' D2 r' F2 Lw'
 
|sign=2R l F2 2L' F2 2L D' 2R' D F2 D' 2R D' 2R' D2 2R' F2 l'
 
|sign=2R l F2 2L' F2 2L D' 2R' D F2 D' 2R D' 2R' D2 2R' F2 l'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,313: Line 4,538:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F2 l' F2 r F' r' F U2 F' r F' r' F2 r' U2 Rw'
+
{{Alg6|wca=Rw l F2 l' F2 r F' r' F U2 F' r F' r' F2 r' U2 Rw'
 
|sign=r 2L F2 2L' F2 2R F' 2R' F U2 F' 2R F' 2R' F2 2R' U2 r'
 
|sign=r 2L F2 2L' F2 2R F' 2R' F U2 F' 2R F' 2R' F2 2R' U2 r'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,319: Line 4,544:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r Lw F2 r' D2 l B' r' B D2 B' r B' r' B2 l' F2 Lw'
+
{{Alg6|wca=r Lw F2 r' D2 l B' r' B D2 B' r B' r' B2 l' F2 Lw'
 
|sign=2R l F2 2R' D2 2L B' 2R' B D2 B' 2R B' 2R' B2 2L' F2 l'
 
|sign=2R l F2 2R' D2 2L B' 2R' B D2 B' 2R B' 2R' B2 2L' F2 l'
 
|length=(23,18)|name=v3
 
|length=(23,18)|name=v3
Line 4,325: Line 4,550:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r Lw F2 l' F2 l D r' D' F2 D r D r' D2 r' F2 Lw'
+
{{Alg6|wca=r Lw F2 l' F2 l D r' D' F2 D r D r' D2 r' F2 Lw'
 
|sign=2R l F2 2L' F2 2L D 2R' D' F2 D 2R D 2R' D2 2R' F2 l'
 
|sign=2R l F2 2L' F2 2L D 2R' D' F2 D 2R D 2R' D2 2R' F2 l'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,331: Line 4,556:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F2 l' F2 r F r' F' U2 F r F r' F2 r' U2 Rw'
+
{{Alg6|wca=Rw l F2 l' F2 r F r' F' U2 F r F r' F2 r' U2 Rw'
 
|sign=r 2L F2 2L' F2 2R F 2R' F' U2 F 2R F 2R' F2 2R' U2 r'
 
|sign=r 2L F2 2L' F2 2R F 2R' F' U2 F 2R F 2R' F2 2R' U2 r'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,337: Line 4,562:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r Lw F2 r' D2 l B r' B' D2 B r B r' B2 l' F2 Lw'
+
{{Alg6|wca=r Lw F2 r' D2 l B r' B' D2 B r B r' B2 l' F2 Lw'
 
|sign=2R l F2 2R' D2 2L B 2R' B' D2 B 2R B 2R' B2 2L' F2 l'
 
|sign=2R l F2 2R' D2 2L B 2R' B' D2 B 2R B 2R' B2 2L' F2 l'
 
|length=(23,18)|name=v3
 
|length=(23,18)|name=v3
Line 4,343: Line 4,568:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' r' U B2 U' r U' r' U2 l' D2 r D2 r' B2 Rw l
+
{{Alg6|wca=Rw' U' r' U B2 U' r U' r' U2 l' D2 r D2 r' B2 Rw l
 
|sign=r' U' 2R' U B2 U' 2R U' 2R' U2 2L' D2 2R D2 2R' B2 r 2L
 
|sign=r' U' 2R' U B2 U' 2R U' 2R' U2 2L' D2 2R D2 2R' B2 r 2L
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,349: Line 4,574:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' r' U B2 U' r U' r' U2 r' B2 r B2 l' B2 Rw l
+
{{Alg6|wca=Rw' U' r' U B2 U' r U' r' U2 r' B2 r B2 l' B2 Rw l
 
|sign=r' U' 2R' U B2 U' 2R U' 2R' U2 2R' B2 2R B2 2L' B2 r 2L
 
|sign=r' U' 2R' U B2 U' 2R U' 2R' U2 2R' B2 2R B2 2L' B2 r 2L
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,355: Line 4,580:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U r' U' B2 U r U r' U2 l' D2 r D2 r' B2 Rw l
+
{{Alg6|wca=Rw' U r' U' B2 U r U r' U2 l' D2 r D2 r' B2 Rw l
 
|sign=r' U 2R' U' B2 U 2R U 2R' U2 2L' D2 2R D2 2R' B2 r 2L
 
|sign=r' U 2R' U' B2 U 2R U 2R' U2 2L' D2 2R D2 2R' B2 r 2L
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,361: Line 4,586:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U r' U' B2 U r U r' U2 r' B2 r B2 l' B2 Rw l
+
{{Alg6|wca=Rw' U r' U' B2 U r U r' U2 r' B2 r B2 l' B2 Rw l
 
|sign=r' U 2R' U' B2 U 2R U 2R' U2 2R' B2 2R B2 2L' B2 r 2L
 
|sign=r' U 2R' U' B2 U 2R U 2R' U2 2R' B2 2R B2 2L' B2 r 2L
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,367: Line 4,592:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D b' D l D2 l' D' b D Rw' B2 l B2 Rw F2 Rw
+
{{Alg6|wca=Rw' F2 D b' D l D2 l' D' b D Rw' B2 l B2 Rw F2 Rw
 
|sign=r' F2 D 2B' D 2L D2 2L' D' 2B D r' B2 2L B2 r F2 r
 
|sign=r' F2 D 2B' D 2L D2 2L' D' 2B D r' B2 2L B2 r F2 r
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,373: Line 4,598:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D b' D l D2 l' D' b D Lw' D2 l D2 Lw F2 Rw
+
{{Alg6|wca=Rw' F2 D b' D l D2 l' D' b D Lw' D2 l D2 Lw F2 Rw
 
|sign=r' F2 D 2B' D 2L D2 2L' D' 2B D l' D2 2L D2 l F2 r
 
|sign=r' F2 D 2B' D 2L D2 2L' D' 2B D l' D2 2L D2 l F2 r
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,379: Line 4,604:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D' f' D' l D2 l' D f D' Rw' B2 l B2 Rw F2 Rw
+
{{Alg6|wca=Rw' F2 D' f' D' l D2 l' D f D' Rw' B2 l B2 Rw F2 Rw
 
|sign=r' F2 D' 2F' D' 2L D2 2L' D 2F D' r' B2 2L B2 r F2 r
 
|sign=r' F2 D' 2F' D' 2L D2 2L' D 2F D' r' B2 2L B2 r F2 r
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,385: Line 4,610:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' F2 D' f' D' l D2 l' D f D' Lw' D2 l D2 Lw F2 Rw
+
{{Alg6|wca=Rw' F2 D' f' D' l D2 l' D f D' Lw' D2 l D2 Lw F2 Rw
 
|sign=r' F2 D' 2F' D' 2L D2 2L' D 2F D' l' D2 2L D2 l F2 r
 
|sign=r' F2 D' 2F' D' 2L D2 2L' D 2F D' l' D2 2L D2 l F2 r
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,391: Line 4,616:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B' D2 r D b' D F2 D' b D r' B2 l B' r F2 r  
+
{{Alg6|wca=r2 B' D2 r D b' D F2 D' b D r' B2 l B' r F2 r
|sign=2R2 B' D2 2R D 2B' D F2 D' 2B D 2R' B2 2L B' 2R F2 2R  
+
|sign=2R2 B' D2 2R D 2B' D F2 D' 2B D 2R' B2 2L B' 2R F2 2R
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B D2 r D' f' D' F2 D f D' r' B2 l B r F2 r  
+
{{Alg6|wca=r2 B D2 r D' f' D' F2 D f D' r' B2 l B r F2 r
|sign=2R2 B D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L B 2R F2 2R  
+
|sign=2R2 B D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L B 2R F2 2R
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B D2 r D b' D F2 D' b D r' B2 l B r F2 r  
+
{{Alg6|wca=r2 B D2 r D b' D F2 D' b D r' B2 l B r F2 r
|sign=2R2 B D2 2R D 2B' D F2 D' 2B D 2R' B2 2L B 2R F2 2R  
+
|sign=2R2 B D2 2R D 2B' D F2 D' 2B D 2R' B2 2L B 2R F2 2R
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B' D2 r D' f' D' F2 D f D' r' B2 l B' r F2 r  
+
{{Alg6|wca=r2 B' D2 r D' f' D' F2 D f D' r' B2 l B' r F2 r
|sign=2R2 B' D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L B' 2R F2 2R  
+
|sign=2R2 B' D2 2R D' 2F' D' F2 D 2F D' 2R' B2 2L B' 2R F2 2R
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Lw' B' d' B U2 B' d B' l' B2 D2 r' D2 r l U2 Lw
+
{{Alg6|wca=r' Lw' B' d' B U2 B' d B' l' B2 D2 r' D2 r l U2 Lw
 
|sign=2R' l' B' 2D' B U2 B' 2D B' 2L' B2 D2 2R' D2 2R 2L U2 l
 
|sign=2R' l' B' 2D' B U2 B' 2D B' 2L' B2 D2 2R' D2 2R 2L U2 l
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Lw' B u' B' U2 B u B l' B2 D2 r' D2 r l U2 Lw
+
{{Alg6|wca=r' Lw' B u' B' U2 B u B l' B2 D2 r' D2 r l U2 Lw
 
|sign=2R' l' B 2U' B' U2 B 2U B 2L' B2 D2 2R' D2 2R 2L U2 l
 
|sign=2R' l' B 2U' B' U2 B 2U B 2L' B2 D2 2R' D2 2R 2L U2 l
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l D2 F2 l' F' d F' U2 F d' F' l D2 r' l' U2 Rw'
+
{{Alg6|wca=Rw l D2 F2 l' F' d F' U2 F d' F' l D2 r' l' U2 Rw'
 
|sign=r 2L D2 F2 2L' F' 2D F' U2 F 2D' F' 2L D2 2R' 2L' U2 r'
 
|sign=r 2L D2 F2 2L' F' 2D F' U2 F 2D' F' 2L D2 2R' 2L' U2 r'
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l D2 F2 l' F u F U2 F' u' F l D2 r' l' U2 Rw'
+
{{Alg6|wca=Rw l D2 F2 l' F u F U2 F' u' F l D2 r' l' U2 Rw'
 
|sign=r 2L D2 F2 2L' F 2U F U2 F' 2U' F 2L D2 2R' 2L' U2 r'
 
|sign=r 2L D2 F2 2L' F 2U F U2 F' 2U' F 2L D2 2R' 2L' U2 r'
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F' u' F D2 F' u F' l' F2 U2 l D2 r' l' U2 Rw'
+
{{Alg6|wca=Rw l F' u' F D2 F' u F' l' F2 U2 l D2 r' l' U2 Rw'
 
|sign=r 2L F' 2U' F D2 F' 2U F' 2L' F2 U2 2L D2 2R' 2L' U2 r'
 
|sign=r 2L F' 2U' F D2 F' 2U F' 2L' F2 U2 2L D2 2R' 2L' U2 r'
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F d' F' D2 F d F l' F2 U2 l D2 r' l' U2 Rw'
+
{{Alg6|wca=Rw l F d' F' D2 F d F l' F2 U2 l D2 r' l' U2 Rw'
 
|sign=r 2L F 2D' F' D2 F 2D F 2L' F2 U2 2L D2 2R' 2L' U2 r'
 
|sign=r 2L F 2D' F' D2 F 2D F 2L' F2 U2 2L D2 2R' 2L' U2 r'
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F2 l' F' d F' U2 F d' F' Lw D2 r' D2 Lw' U2 Rw'
+
{{Alg6|wca=Rw l F2 l' F' d F' U2 F d' F' Lw D2 r' D2 Lw' U2 Rw'
 
|sign=r 2L F2 2L' F' 2D F' U2 F 2D' F' l D2 2R' D2 l' U2 r'
 
|sign=r 2L F2 2L' F' 2D F' U2 F 2D' F' l D2 2R' D2 l' U2 r'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,447: Line 4,672:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F2 l' F' d F' U2 F d' F' Rw F2 r' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw l F2 l' F' d F' U2 F d' F' Rw F2 r' F2 Rw' U2 Rw'
 
|sign=r 2L F2 2L' F' 2D F' U2 F 2D' F' r F2 2R' F2 r' U2 r'
 
|sign=r 2L F2 2L' F' 2D F' U2 F 2D' F' r F2 2R' F2 r' U2 r'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,453: Line 4,678:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F2 l' F u F U2 F' u' F Lw D2 r' D2 Lw' U2 Rw'
+
{{Alg6|wca=Rw l F2 l' F u F U2 F' u' F Lw D2 r' D2 Lw' U2 Rw'
 
|sign=r 2L F2 2L' F 2U F U2 F' 2U' F l D2 2R' D2 l' U2 r'
 
|sign=r 2L F2 2L' F 2U F U2 F' 2U' F l D2 2R' D2 l' U2 r'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,459: Line 4,684:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l F2 l' F u F U2 F' u' F Rw F2 r' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw l F2 l' F u F U2 F' u' F Rw F2 r' F2 Rw' U2 Rw'
 
|sign=r 2L F2 2L' F 2U F U2 F' 2U' F r F2 2R' F2 r' U2 r'
 
|sign=r 2L F2 2L' F 2U F U2 F' 2U' F r F2 2R' F2 r' U2 r'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,465: Line 4,690:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Lw' U2 B2 l' B' u B' D2 B u' B' r' D2 r l U2 Lw
+
{{Alg6|wca=r' Lw' U2 B2 l' B' u B' D2 B u' B' r' D2 r l U2 Lw
 
|sign=2R' l' U2 B2 2L' B' 2U B' D2 B 2U' B' 2R' D2 2R 2L U2 l
 
|sign=2R' l' U2 B2 2L' B' 2U B' D2 B 2U' B' 2R' D2 2R 2L U2 l
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Lw' U2 B2 l' B d B D2 B' d' B r' D2 r l U2 Lw
+
{{Alg6|wca=r' Lw' U2 B2 l' B d B D2 B' d' B r' D2 r l U2 Lw
 
|sign=2R' l' U2 B2 2L' B 2D B D2 B' 2D' B 2R' D2 2R 2L U2 l
 
|sign=2R' l' U2 B2 2L' B 2D B D2 B' 2D' B 2R' D2 2R 2L U2 l
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l U2 r F2 r' U' b' U F2 U' b U' l' U2 r' U2 Rw'
+
{{Alg6|wca=Rw l U2 r F2 r' U' b' U F2 U' b U' l' U2 r' U2 Rw'
 
|sign=r 2L U2 2R F2 2R' U' 2B' U F2 U' 2B U' 2L' U2 2R' U2 r'
 
|sign=r 2L U2 2R F2 2R' U' 2B' U F2 U' 2B U' 2L' U2 2R' U2 r'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,481: Line 4,706:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r Lw U2 r F2 r' U' b' U F2 U' b U' r' F2 r' F2 Lw'
+
{{Alg6|wca=r Lw U2 r F2 r' U' b' U F2 U' b U' r' F2 r' F2 Lw'
 
|sign=2R l U2 2R F2 2R' U' 2B' U F2 U' 2B U' 2R' F2 2R' F2 l'
 
|sign=2R l U2 2R F2 2R' U' 2B' U F2 U' 2B U' 2R' F2 2R' F2 l'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,487: Line 4,712:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw l U2 r F2 r' U f' U' F2 U f U l' U2 r' U2 Rw'
+
{{Alg6|wca=Rw l U2 r F2 r' U f' U' F2 U f U l' U2 r' U2 Rw'
 
|sign=r 2L U2 2R F2 2R' U 2F' U' F2 U 2F U 2L' U2 2R' U2 r'
 
|sign=r 2L U2 2R F2 2R' U 2F' U' F2 U 2F U 2L' U2 2R' U2 r'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,493: Line 4,718:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r Lw U2 r F2 r' U f' U' F2 U f U r' F2 r' F2 Lw'
+
{{Alg6|wca=r Lw U2 r F2 r' U f' U' F2 U f U r' F2 r' F2 Lw'
 
|sign=2R l U2 2R F2 2R' U 2F' U' F2 U 2F U 2R' F2 2R' F2 l'
 
|sign=2R l U2 2R F2 2R' U 2F' U' F2 U 2F U 2R' F2 2R' F2 l'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,499: Line 4,724:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F' d F' r' F2 r F d' F' Lw D2 r' D2 Lw' U2 Rw'
+
{{Alg6|wca=Rw U2 F' d F' r' F2 r F d' F' Lw D2 r' D2 Lw' U2 Rw'
 
|sign=r U2 F' 2D F' 2R' F2 2R F 2D' F' l D2 2R' D2 l' U2 r'
 
|sign=r U2 F' 2D F' 2R' F2 2R F 2D' F' l D2 2R' D2 l' U2 r'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,505: Line 4,730:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F' d F' r' F2 r F d' F' Rw F2 r' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 F' d F' r' F2 r F d' F' Rw F2 r' F2 Rw' U2 Rw'
 
|sign=r U2 F' 2D F' 2R' F2 2R F 2D' F' r F2 2R' F2 r' U2 r'
 
|sign=r U2 F' 2D F' 2R' F2 2R F 2D' F' r F2 2R' F2 r' U2 r'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,511: Line 4,736:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F u F r' F2 r F' u' F Lw D2 r' D2 Lw' U2 Rw'
+
{{Alg6|wca=Rw U2 F u F r' F2 r F' u' F Lw D2 r' D2 Lw' U2 Rw'
 
|sign=r U2 F 2U F 2R' F2 2R F' 2U' F l D2 2R' D2 l' U2 r'
 
|sign=r U2 F 2U F 2R' F2 2R F' 2U' F l D2 2R' D2 l' U2 r'
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 4,517: Line 4,742:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 F u F r' F2 r F' u' F Rw F2 r' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 F u F r' F2 r F' u' F Rw F2 r' F2 Rw' U2 Rw'
 
|sign=r U2 F 2U F 2R' F2 2R F' 2U' F r F2 2R' F2 r' U2 r'
 
|sign=r U2 F 2U F 2R' F2 2R F' 2U' F r F2 2R' F2 r' U2 r'
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 4,523: Line 4,748:
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
===Shortest block quarter turn move algorithms===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Shortest block quarter turn move algorithms</span>===
*All of the algorithms in this section are [https://www.youtube.com/watch?v=GmI2UZ4fBN0&list=PL271745B9E036A65E&index=8 <u>wide turn based</u>] (they <b>require</b>--not just possess for easier execution--wide turns to create a single dedge flip).
+
*All of the algorithms in this section are {{LinkColorE|u=https://www.youtube.com/watch?v=GmI2UZ4fBN0&list=PL271745B9E036A65E&index=8|c=rgb(229,148,0)|t=<u>wide turn based</u>}} (they <i>require</i> &ndash; not just possess for easier execution &ndash; wide turns to create a single dedge flip).
 
*Most of these algorithms affect the centers of the supercube differently than the previously shown algorithms.
 
*Most of these algorithms affect the centers of the supercube differently than the previously shown algorithms.
 
+
{{br|b=1}}
 
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="fbfb8b" |
 
 
Despite that the shortest algorithm in BQTM listed is 18, it could be possible that a 17 BQTM exists, as below is a 16 BQTM algorithm which is nearly "pure".
 
Despite that the shortest algorithm in BQTM listed is 18, it could be possible that a 17 BQTM exists, as below is a 16 BQTM algorithm which is nearly "pure".
  
 
(Found in late January of 2018.)
 
(Found in late January of 2018.)
{{Alg5|wca=Rw Dw' Rw U' Rw Bw' r' Bw Rw' U R' Dw Rw' Bw' r' Bw
+
{{Alg6|wca=Rw Dw' Rw U' Rw Bw' r' Bw Rw' U R' Dw Rw' Bw' r' Bw
 
|sign=r d' r U' r b' 2R' b r' U R' d r' b' 2R' b
 
|sign=r d' r U' r b' 2R' b r' U R' d r' b' 2R' b
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
}}
+
}}</ul>
|}
+
{{br|b=1}}
 
 
  
<b>Symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Symmetrical algorithms</b></span>
{{Alg5|wca=Rw' E' Lw2 Uw' l Uw Lw2 Dw' L2 Uw' l Uw Lw' L' Dw E Rw
+
{{Alg6|wca=Rw' E' Lw2 Uw' l Uw Lw2 Dw' L2 Uw' l Uw Lw' L' Dw E Rw
 
|sign=r' e' l2 u' 2L u l2 d' L2 u' 2L u l' L' d e r
 
|sign=r' e' l2 u' 2L u l2 d' L2 u' 2L u l' L' d e r
 
|length=(20,17)|name=|wide=N|author=Christopher Mowla
 
|length=(20,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1147681
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1147681
 
}}
 
}}
{{Alg5|wca=y' Rw Uw2 x' U D r y Uw2 Rw2 Uw r Uw' Rw2 Dw r' u D' x Uw2 Rw' y
+
{{Alg6|wca=y' Rw Uw2 x' U D r y Uw2 Rw2 Uw r Uw' Rw2 Dw r' u D' x Uw2 Rw' y
 
|sign=y' r u2 x' U D 2R y u2 r2 u 2R u' r2 d 2R' 2U D' x u2 r' y
 
|sign=y' r u2 x' U D 2R y u2 r2 u 2R u' r2 d 2R' 2U D' x u2 r' y
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=Rw' 3Uw' u' Lw' r' Uw' r' Uw 3Lw r' Uw Lw' Uw' r' Uw Lw E' Rw
+
{{Alg6|wca=Rw' 3Uw' u' Lw' r' Uw' r' Uw 3Lw r' Uw Lw' Uw' r' Uw Lw E' Rw
 
|sign=r' 3u' 2U' l' 2R' u' 2R' u 3l 2R' u l' u' 2R' u l e' r
 
|sign=r' 3u' 2U' l' 2R' u' 2R' u 3l 2R' u l' u' 2R' u l e' r
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1148522
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1148522
 
}}
 
}}
{{Alg5|wca=y' Rw Uw' L Uw' y R Uw' r Uw Rw' Dw Rw2 Uw' r Uw Rw2 L' Uw Rw' y
+
{{Alg6|wca=f' U2 r U u' r' U r' Uw' r' Uw' u' r' U r' U r f
 +
|sign=2F' U2 2R U 2U' 2R' U 2R' u' 2R' u' 2U' 2R' U 2R' U 2R 2F
 +
|length=(19,18)|name=|wide=N|author=Ben Whitmore
 +
|url=
 +
}}
 +
{{Alg6|wca=y' Rw Uw' L Uw' y R Uw' r Uw Rw' Dw Rw2 Uw' r Uw Rw2 L' Uw Rw' y
 
|sign=y' r u' L u' y R u' 2R u r' d r2 u' 2R u r2 L' u r' y
 
|sign=y' r u' L u' y R u' 2R u r' d r2 u' 2R u r2 L' u r' y
 
|length=(19,18)|name=Challenger
 
|length=(19,18)|name=Challenger
Line 4,564: Line 4,792:
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1147681
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1147681
 
}}
 
}}
{{Alg5|wca=y' Rw' Uw L' Uw y' R' Uw r' Uw' Rw Dw' Rw2 Uw r' Uw' Rw2 L Uw' Rw y
+
{{Alg6|wca=y' Rw' Uw L' Uw y' R' Uw r' Uw' Rw Dw' Rw2 Uw r' Uw' Rw2 L Uw' Rw y
 
|sign=y' r' u L' u y' R' u 2R' u' r d' r2 u 2R' u' r2 L u' r y
 
|sign=y' r' u L' u y' R' u 2R' u' r d' r2 u 2R' u' r2 L u' r y
 
|length=(19,18)|name=Reverter
 
|length=(19,18)|name=Reverter
Line 4,570: Line 4,798:
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1147681
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1147681
 
}}
 
}}
{{Alg5|wca=z Dw' M D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' M' Uw x2 z'
+
{{Alg6|wca=z Dw' M D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' M' Uw x2 z'
 
|sign=z d' m D l' u' 2R' u l u' l2' b' 2R' b r' R' 2U y' m' u x2 z'
 
|sign=z d' m D l' u' 2R' u l u' l2' b' 2R' b r' R' 2U y' m' u x2 z'
 
|length=(19,18)|name=Holy Grail
 
|length=(19,18)|name=Holy Grail
Line 4,576: Line 4,804:
 
|url=http://www.youtube.com/watch?v=JOiyd3PbXZg
 
|url=http://www.youtube.com/watch?v=JOiyd3PbXZg
 
}}
 
}}
{{Alg5|wca=(Rw' E) Uw' r' Uw' Fw Uw Rw' Fw' r' Fw Rw r Uw' Fw' Uw2 (E' Rw)
+
{{Alg6|wca=(Rw' E) Uw' r' Uw' Fw Uw Rw' Fw' r' Fw Rw r Uw' Fw' Uw2 (E' Rw)
 
|sign=(r' e) u' 2R' u' f u r' f' 2R' f r 2R u' f' u2 (e' r)
 
|sign=(r' e) u' 2R' u' f u r' f' 2R' f r 2R u' f' u2 (e' r)
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
}}
 
}}
{{Alg5|wca=(Rw' E) Uw' r' Uw' r' Uw r Bw r Bw' Uw' Bw r' Bw' Uw2 (E' Rw)
+
{{Alg6|wca=(Rw' E) Uw' r' Uw' r' Uw r Bw r Bw' Uw' Bw r' Bw' Uw2 (E' Rw)
 
|sign=(r' e) u' 2R' u' 2R' u 2R b 2R b' u' b 2R' b' u2 (e' r)
 
|sign=(r' e) u' 2R' u' 2R' u 2R b 2R b' u' b 2R' b' u2 (e' r)
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E) Uw' r' Uw' r' Uw r2 Bw' Uw' Bw r' Bw' Uw Bw Uw (E' Rw)
+
{{Alg6|wca=(Rw' E) Uw' r' Uw' r' Uw r2 Bw' Uw' Bw r' Bw' Uw Bw Uw (E' Rw)
 
|sign=(r' e) u' 2R' u' 2R' u 2R2 b' u' b 2R' b' u b u (e' r)
 
|sign=(r' e) u' 2R' u' 2R' u 2R2 b' u' b 2R' b' u b u (e' r)
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw B' r) Bw' Dw Bw l' Dw' l' Dw l2 Bw' Dw' Bw l' (r' B Rw')
+
{{Alg6|wca=(Rw B' r) Bw' Dw Bw l' Dw' l' Dw l2 Bw' Dw' Bw l' (r' B Rw')
 
|sign=(r B' 2R) b' d b 2L' d' 2L' d 2L2 b' d' b 2L' (2R' B r')
 
|sign=(r B' 2R) b' d b 2L' d' 2L' d 2L2 b' d' b 2L' (2R' B r')
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Lw' u) F' Lw' b' Lw Fw Lw' Bw2 Uw' b' Uw Bw' B' Lw f' (u' Lw)
+
{{Alg6|wca=(Lw' u) F' Lw' b' Lw Fw Lw' Bw2 Uw' b' Uw Bw' B' Lw f' (u' Lw)
 
|sign=(l' 2U) F' l' 2B' l f l' b2 u' 2B' u b' B' l 2F' (2U' l)
 
|sign=(l' 2U) F' l' 2B' l f l' b2 u' 2B' u b' B' l 2F' (2U' l)
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw' Fw2 L' R' u Lw Rw Uw2 Rw d Lw' Bw2 Lw d' 3Rw Rw R Fw2 Uw
+
{{Alg6|wca=Uw' Fw2 L' R' u Lw Rw Uw2 Rw d Lw' Bw2 Lw d' 3Rw Rw R Fw2 Uw
 
|sign=u' f2 L' R' 2U l r u2 r 2D l' b2 l 2D' 3r r R f2 u
 
|sign=u' f2 L' R' 2U l r u2 r 2D l' b2 l 2D' 3r r R f2 u
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=(Rw' E) Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw (E' Rw)
+
{{Alg6|wca=(Rw' E) Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw (E' Rw)
 
|sign=(r' e) u 2B' u 2R u 2R' u' 2B u 2R' u' 2R u 2R u (e' r)
 
|sign=(r' e) u 2B' u 2R u 2R' u' 2B u 2R' u' 2R u 2R u (e' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E) Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw Rw r Fw' Uw Lw (E' Rw)
+
{{Alg6|wca=(Rw' E) Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw Rw r Fw' Uw Lw (E' Rw)
 
|sign=(r' e) u' 2R' u l' u' f r' f' 2R' f r 2R f' u l (e' r)
 
|sign=(r' e) u' 2R' u l' u' f r' f' 2R' f r 2R f' u l (e' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' U l') Uw Fw' r Fw r Fw' r' Uw' b' Uw Fw Uw' b (l U' Rw)
+
{{Alg6|wca=(Rw' U l') Uw Fw' r Fw r Fw' r' Uw' b' Uw Fw Uw' b (l U' Rw)
 
|sign=(r' U 2L') u f' 2R f 2R f' 2R' u' 2B' u f u' 2B (2L U' r)
 
|sign=(r' U 2L') u f' 2R f 2R f' 2R' u' 2B' u f u' 2B (2L U' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' U l') Uw Fw' r Fw Uw' Fw' Rw Uw r Uw' Rw' r' Fw (l U' Rw)
+
{{Alg6|wca=(Rw' U l') Uw Fw' r Fw Uw' Fw' Rw Uw r Uw' Rw' r' Fw (l U' Rw)
 
|sign=(r' U 2L') u f' 2R f u' f' r u 2R u' r' 2R' f (2L U' r)
 
|sign=(r' U 2L') u f' 2R f u' f' r u 2R u' r' 2R' f (2L U' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E) Bw r' F Lw' Fw r Fw' Lw F' Bw' Lw Bw r Bw' Lw' (E' Rw)
+
{{Alg6|wca=(Rw' E) Bw r' F Lw' Fw r Fw' Lw F' Bw' Lw Bw r Bw' Lw' (E' Rw)
 
|sign=(r' e) b 2R' F l' f 2R f' l F' b' l b 2R b' l' (e' r)
 
|sign=(r' e) b 2R' F l' f 2R f' l F' b' l b 2R b' l' (e' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E) r' F Lw' Fw r Fw' Lw F' Bw' Lw Bw r Bw' Lw' Bw (E' Rw)
+
{{Alg6|wca=(Rw' E) r' F Lw' Fw r Fw' Lw F' Bw' Lw Bw r Bw' Lw' Bw (E' Rw)
 
|sign=(r' e) 2R' F l' f 2R f' l F' b' l b 2R b' l' b (e' r)
 
|sign=(r' e) 2R' F l' f 2R f' l F' b' l b 2R b' l' b (e' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E) L Uw' Lw' r' Uw' r' Uw r' R Bw Rw' Uw' r' Uw l (E' Rw)
+
{{Alg6|wca=(Rw' E) L Uw' Lw' r' Uw' r' Uw r' R Bw Rw' Uw' r' Uw l (E' Rw)
 
|sign=(r' e) L u' l' 2R' u' 2R' u 2R' R b r' u' 2R' u 2L (e' r)
 
|sign=(r' e) L u' l' 2R' u' 2R' u 2R' R b r' u' 2R' u 2L (e' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E) Uw' r' Uw Rw' Bw' Rw Fw' Lw' f' Lw Fw f Rw' Bw Rw (E' Rw)
+
{{Alg6|wca=(Rw' E) Uw' r' Uw Rw' Bw' Rw Fw' Lw' f' Lw Fw f Rw' Bw Rw (E' Rw)
 
|sign=(r' e) u' 2R' u r' b' r f' l' 2F' l f 2F r' b r (e' r)
 
|sign=(r' e) u' 2R' u r' b' r f' l' 2F' l f 2F r' b r (e' r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' E') L Dw' Lw' l' Fw' l' Fw l' L Dw Lw' Fw' l' Fw l (E Rw)
+
{{Alg6|wca=(Rw' E') L Dw' Lw' l' Fw' l' Fw l' L Dw Lw' Fw' l' Fw l (E Rw)
 
|sign=(r' e') L d' l' 2L' f' 2L' f 2L' L d l' f' 2L' f 2L (e r)
 
|sign=(r' e') L d' l' 2L' f' 2L' f 2L' L d l' f' 2L' f 2L (e r)
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Uw U r' Uw' r Uw r Uw r' Uw2 r' Uw r Uw r Uw u r
+
{{Alg6|wca=r' Uw U r' Uw' r Uw r Uw r' Uw2 r' Uw r Uw r Uw u r
 
|sign=2R' u U 2R' u' 2R u 2R u 2R' u2 2R' u 2R u 2R u 2U 2R
 
|sign=2R' u U 2R' u' 2R u 2R u 2R' u2 2R' u 2R u 2R u 2U 2R
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Uw' u' r' Uw' r' Uw' r Uw2 r Uw' r' Uw' r' Uw r Uw' U' r
+
{{Alg6|wca=r' Uw' u' r' Uw' r' Uw' r Uw2 r Uw' r' Uw' r' Uw r Uw' U' r
 
|sign=2R' u' 2U' 2R' u' 2R' u' 2R u2 2R u' 2R' u' 2R' u 2R u' U' 2R
 
|sign=2R' u' 2U' 2R' u' 2R' u' 2R u2 2R u' 2R' u' 2R' u 2R u' U' 2R
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' F' z Rw2 B2 x' l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l u' U Rw2 D Rw z'
+
{{Alg6|wca=Dw' F' z Rw2 B2 x' l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l u' U Rw2 D Rw z'
 
|sign=d' F' z r2 B2 x' 2L' d u r2 d' 2L' d r2 d' 2L 2U' U r2 D r z'
 
|sign=d' F' z r2 B2 x' 2L' d u r2 d' 2L' d r2 d' 2L 2U' U r2 D r z'
 
|length=(24,19)|name=|wide=N|author=Christopher Mowla
 
|length=(24,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw Bw' R' r u' R' U' r U R u Rw r Bw Rw' Uw' r Uw Rw Uw'
+
{{Alg6|wca=Uw Bw' R' r u' R' U' r U R u Rw r Bw Rw' Uw' r Uw Rw Uw'
 
|sign=u b' R' 2R 2U' R' U' 2R U R 2U r 2R b r' u' 2R u r u'
 
|sign=u b' R' 2R 2U' R' U' 2R U R 2U r 2R b r' u' 2R u r u'
 
|length=(20,20)|name=|wide=N|author=Christopher Mowla
 
|length=(20,20)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw Fw' D r' Dw b Dw b' Dw' r Dw b' Dw' b Dw b Dw2 D' Fw Uw'
+
{{Alg6|wca=Uw Fw' D r' Dw b Dw b' Dw' r Dw b' Dw' b Dw b Dw2 D' Fw Uw'
 
|sign=u f' D 2R' d 2B d 2B' d' 2R d 2B' d' 2B d 2B d2 D' f u'
 
|sign=u f' D 2R' d 2B d 2B' d' 2R d 2B' d' 2B d 2B d2 D' f u'
 
|length=(21,20)|name=|wide=N|author=Christopher Mowla
 
|length=(21,20)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Fw' U' l u2 Lw Bw' Lw' u Lw Uw Bw u' Bw' Uw' Bw Lw' u l' U Fw
+
{{Alg6|wca=Fw' U' l u2 Lw Bw' Lw' u Lw Uw Bw u' Bw' Uw' Bw Lw' u l' U Fw
 
|sign=f' U' 2L 2U2 l b' l' 2U l u b 2U' b' u' b l' 2U 2L' U f
 
|sign=f' U' 2L 2U2 l b' l' 2U l u b 2U' b' u' b l' 2U 2L' U f
 
|length=(21,20)|name=|wide=N|author=Christopher Mowla
 
|length=(21,20)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw U L F' U) l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l Uw' (U' F L' U' Rw')
+
{{Alg6|wca=(Rw U L F' U) l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l Uw' (U' F L' U' Rw')
 
|sign=(r U L F' U) 2L' d u r2 d' 2L' d r2 d' 2L u' (U' F L' U' r')
 
|sign=(r U L F' U) 2L' d u r2 d' 2L' d r2 d' 2L u' (U' F L' U' r')
 
|length=(23,20)|name=|wide=N|author=Christopher Mowla
 
|length=(23,20)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.youtube.com/watch?v=XIHxGO4D2Hw&list=PL271745B9E036A65E&index=4&t=13m56s
 
|url=https://www.youtube.com/watch?v=XIHxGO4D2Hw&list=PL271745B9E036A65E&index=4&t=13m56s
 
}}
 
}}
{{Alg5|wca=Bw' R' u Rw' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' Rw u' R Bw
+
{{Alg6|wca=Bw' R' u Rw' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' Rw u' R Bw
 
|sign=b' R' 2U r' 2R' u b' u' 2R u r b 2R' b' r' b u' r 2U' R b
 
|sign=b' R' 2U r' 2R' u b' u' 2R u r b 2R' b' r' b u' r 2U' R b
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=Bw' R' u Rw' l' Dw Bw' Dw' l Dw Lw Bw l' Bw' Lw' Bw Dw' Rw u' R Bw
+
{{Alg6|wca=Bw' R' u Rw' l' Dw Bw' Dw' l Dw Lw Bw l' Bw' Lw' Bw Dw' Rw u' R Bw
 
|sign=b' R' 2U r' 2L' d b' d' 2L d l b 2L' b' l' b d' r 2U' R b
 
|sign=b' R' 2U r' 2L' d b' d' 2L d l b 2L' b' l' b d' r 2U' R b
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' Rw' Fw' r' Uw' Rw' b z Rw' u R U r' U' R' u' Rw B r Fw' Rw Uw Fw Rw x
+
{{Alg6|wca=x' Rw' Fw' r' Uw' Rw' b z Rw' u R U r' U' R' u' Rw B r Fw' Rw Uw Fw Rw x
 
|sign=x' r' f' 2R' u' r' 2B z r' 2U R U 2R' U' R' 2U' r B 2R f' r u f r x
 
|sign=x' r' f' 2R' u' r' 2B z r' 2U R U 2R' U' R' 2U' r B 2R f' r u f r x
 
|length=(22,22)|name=|wide=N|author=Christopher Mowla
 
|length=(22,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
<b>Non-symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Non-symmetrical algorithms</b></span>
{{Alg5|wca=z Rw Uw' l Uw Rw' Uw' d' L d' Rw Dw l Dw' Rw' d L' d l' Uw z'
+
{{Alg6|wca=z Rw Uw' l Uw Rw' Uw' d' L d' Rw Dw l Dw' Rw' d L' d l' Uw z'
 
|sign=z r u' 2L u r' u' 2D' L 2D' r d 2L d' r' 2D L' 2D 2L' u z'
 
|sign=z r u' 2L u r' u' 2D' L 2D' r d 2L d' r' 2D L' 2D 2L' u z'
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=http://cubesolvingprograms.freeforums.net/post/304/thread
 
|url=http://cubesolvingprograms.freeforums.net/post/304/thread
 
}}
 
}}
{{Alg5|wca=r' U r U r U' u r' E r' E' r' Uw' r U r U r' U2
+
{{Alg6|wca=r' U r U r U' u r' E r' E' r' Uw' r U r U r' U2
 
|sign=2R' U 2R U 2R U' 2U 2R' e 2R' e' 2R' u' 2R U 2R U 2R' U2
 
|sign=2R' U 2R U 2R U' 2U 2R' e 2R' e' 2R' u' 2R U 2R U 2R' U2
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U r U r Uw' r' E' r' E r' U' u r U r U r' U2
+
{{Alg6|wca=r' U r U r Uw' r' E' r' E r' U' u r U r U r' U2
 
|sign=2R' U 2R U 2R u' 2R' e' 2R' e 2R' U' 2U 2R U 2R U 2R' U2
 
|sign=2R' U 2R U 2R u' 2R' e' 2R' e 2R' U' 2U 2R U 2R U 2R' U2
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' r U' r Uw r' E r' E' r' U u' r U' r U' r' U2
+
{{Alg6|wca=r' U' r U' r Uw r' E r' E' r' U u' r U' r U' r' U2
 
|sign=2R' U' 2R U' 2R u 2R' e 2R' e' 2R' U 2U' 2R U' 2R U' 2R' U2
 
|sign=2R' U' 2R U' 2R u 2R' e 2R' e' 2R' U 2U' 2R U' 2R U' 2R' U2
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' r U' r U u' r' E' r' E r' Uw r U' r U' r' U2
+
{{Alg6|wca=r' U' r U' r U u' r' E' r' E r' Uw r U' r U' r' U2
 
|sign=2R' U' 2R U' 2R U 2U' 2R' e' 2R' e 2R' u 2R U' 2R U' 2R' U2
 
|sign=2R' U' 2R U' 2R U 2U' 2R' e' 2R' e 2R' u 2R U' 2R U' 2R' U2
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Uw Rw Bw' r F' R' r u' R' U' r' U R u r' R F Bw Rw' Uw'  
+
{{Alg6|wca=r' Uw Rw Bw' r F' R' r u' R' U' r' U R u r' R F Bw Rw' Uw'
 
|sign=2R' u r b' 2R F' R' 2R 2U' R' U' 2R' U R 2U 2R' R F b r' u'
 
|sign=2R' u r b' 2R F' R' 2R 2U' R' U' 2R' U R 2U 2R' R F b r' u'
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x2 Rw' Fw Rw' B Rw' Uw U l U' r U l' U' Uw' Rw B' R Fw' Rw Uw r Uw' x2
+
{{Alg6|wca=x2 Rw' Fw Rw' B Rw' Uw U l U' r U l' U' Uw' Rw B' R Fw' Rw Uw r Uw' x2
 
|sign=x2 r' f r' B r' u U 2L U' 2R U 2L' U' u' r B' R f' r u 2R u' x2
 
|sign=x2 r' f r' B r' u U 2L U' 2R U 2L' U' u' r B' R f' r u 2R u' x2
 
|length=(22,22)|name=|wide=N|author=Christopher Mowla
 
|length=(22,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw' U L u l Uw' r' Uw l' u' L' U' Fw r2 Uw' z
+
{{Alg6|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw' U L u l Uw' r' Uw l' u' L' U' Fw r2 Uw' z
 
|sign=z' f' u 2R' u' f u 2R' f' U L 2U 2L u' 2R' u 2L' 2U' L' U' f 2R2 u' z
 
|sign=z' f' u 2R' u' f u 2R' f' U L 2U 2L u' 2R' u 2L' 2U' L' U' f 2R2 u' z
 
|length=(23,22)|name=|wide=N|author=Christopher Mowla
 
|length=(23,22)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw' f' U L U' f r' f' U L' U' f Fw r2 Uw' z
+
{{Alg6|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw' f' U L U' f r' f' U L' U' f Fw r2 Uw' z
 
|sign=z' f' u 2R' u' f u 2R' f' 2F' U L U' 2F 2R' 2F' U L' U' 2F f 2R2 u' z
 
|sign=z' f' u 2R' u' f u 2R' f' 2F' U L U' 2F 2R' 2F' U L' U' 2F f 2R2 u' z
 
|length=(23,22)|name=|wide=N|author=Christopher Mowla
 
|length=(23,22)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw' f' L Fw R' F' r' F R Fw' L' f Fw r2 Uw' z
+
{{Alg6|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw' f' L Fw R' F' r' F R Fw' L' f Fw r2 Uw' z
 
|sign=z' f' u 2R' u' f u 2R' f' 2F' L f R' F' 2R' F R f' L' 2F f 2R2 u' z
 
|sign=z' f' u 2R' u' f u 2R' f' 2F' L f R' F' 2R' F R f' L' 2F f 2R2 u' z
 
|length=(23,22)|name=|wide=N|author=Christopher Mowla
 
|length=(23,22)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=z' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' U L U' r' U L' U' Fw Rw Uw' r2 z
+
{{Alg6|wca=z' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' U L U' r' U L' U' Fw Rw Uw' r2 z
 
|sign=z' 2F' u r' f' 2R' f r u' 2F 2R' u r' f' U L U' 2R' U L' U' f r u' 2R2 z
 
|sign=z' 2F' u r' f' 2R' f r u' 2F 2R' u r' f' U L U' 2R' U L' U' f r u' 2R2 z
 
|length=(25,24)|name=5x5x5 Alg
 
|length=(25,24)|name=5x5x5 Alg
Line 4,759: Line 4,988:
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
 
+
{{br|b=1}}
===Longer/faster algorithms===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Longer/faster algorithms</span>===
*The following list of algorithms are all unique solutions generated with the [https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2 3x3x3 Classic Setup] which use <b>2 different face turns</b>.
+
*The following list of algorithms are all unique solutions generated with the {{LinkColorE|u=https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2|c=rgb(229,148,0)|t=3x3x3 Classic Setup}} which use <i>2 different face turns</i>.
 
+
{{br|b=1}}
 
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
There is only one unique algorithm which just uses the face turn U2.  (If its inverse and mirror transformations are also considered, then there are four such algorithms.)
| bgcolor="fbfb8b" |
+
{{Alg6|wca=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r'
There is only one unique algorithm which just uses the face turn U2.  (If its inverse and mirror transformations are also considered, then there are four such algorithms.).
 
 
 
{{Alg5|wca=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r'
 
 
|sign=2R U2 2R U2 2R' U2 2R U2 2L' U2 2R U2 2R' U2 2L 2R2 U2 2R'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2L' U2 2R U2 2R' U2 2L 2R2 U2 2R'
 
|length=(27,18)|name=Alg.1|wide=Y|author=|url=
 
|length=(27,18)|name=Alg.1|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r2 l' U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
+
{{Alg6|wca=r U2 r2 l' U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
 
|sign=2R U2 2R2 2L' U2 2R U2 2R' U2 2L U2 2R' U2 2R U2 2R' U2 2R'
 
|sign=2R U2 2R2 2L' U2 2R U2 2R' U2 2L U2 2R' U2 2R U2 2R' U2 2R'
 
|length=(27,18)|name=Inverse[Alg.1(v1)]|wide=Y|author=|url=
 
|length=(27,18)|name=Inverse[Alg.1(v1)]|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l' U2 l U2 l' U2 r U2 l' U2 l U2 r' l2 U2 l
+
{{Alg6|wca=l' U2 l' U2 l U2 l' U2 r U2 l' U2 l U2 r' l2 U2 l
 
|sign=2L' U2 2L' U2 2L U2 2L' U2 2R U2 2L' U2 2L U2 2R' 2L2 U2 2L
 
|sign=2L' U2 2L' U2 2L U2 2L' U2 2R U2 2L' U2 2L U2 2R' 2L2 U2 2L
 
|length=(27,18)|name=Mirror[Alg.1(v1)]|wide=Y|author=|url=
 
|length=(27,18)|name=Mirror[Alg.1(v1)]|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l2 r U2 l' U2 l U2 r' U2 l U2 l' U2 l U2 l
+
{{Alg6|wca=l' U2 l2 r U2 l' U2 l U2 r' U2 l U2 l' U2 l U2 l
 
|sign=2L' U2 2L2 2R U2 2L' U2 2L U2 2R' U2 2L U2 2L' U2 2L U2 2L
 
|sign=2L' U2 2L2 2R U2 2L' U2 2L U2 2R' U2 2L U2 2L' U2 2L U2 2L
 
|length=(27,18)|name=Inverse[Mirror[Alg.1(v1)]]|wide=Y|author=|url=
 
|length=(27,18)|name=Inverse[Mirror[Alg.1(v1)]]|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
 
 
It is common speedcubing practice to execute the inner slice turns of (l r2) as (M r').  Similar adjustments (such as (l' r) to (M')) can be done to several algorithms on this page.
 
It is common speedcubing practice to execute the inner slice turns of (l r2) as (M r').  Similar adjustments (such as (l' r) to (M')) can be done to several algorithms on this page.
{{Alg5|wca=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 (M r') U2 r'
+
{{br|b=-0.25}}
 +
{{Alg6|wca=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 (M r') U2 r'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2L' U2 2R U2 2R' U2 (m 2R') U2 2R'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2L' U2 2R U2 2R' U2 (m 2R') U2 2R'
 
|length=(26,18)|name=Alg.1 (v2)|wide=N|author=|url=
 
|length=(26,18)|name=Alg.1 (v2)|wide=N|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
However, the majority of algorithms on this page are presented <i>without</i> this "simplification" to show the "full nxnxn direct translation version" of the algorithm and also to show a version whose inner slice turns can be converted to wide turns to still preserve the first 3 layers (F3L).</ul>
However, the majority of algorithms on this page are presented <b>without</b> this "simplification" to show the "full nxnxn direct translation version" of the algorithm and also to show a version whose inner slice turns can be converted to wide turns to still preserve the first 3 layers (F3L).
+
{{br|b=1}}
|}
 
 
 
  
 
*Algorithms with moves such as (Lw Rw') or (Lw' Rw) reduce to the cube rotations x' and x, respectively, when all slice turns are substituted with wide turns.
 
*Algorithms with moves such as (Lw Rw') or (Lw' Rw) reduce to the cube rotations x' and x, respectively, when all slice turns are substituted with wide turns.
 
+
{{br|b=1}}
 
*All solutions ending in B2 may be conjugated with B2 to create a handful more of "unique" algorithms.
 
*All solutions ending in B2 may be conjugated with B2 to create a handful more of "unique" algorithms.
 
+
{{br|b=1}}
*All other algorithms can be modified by inverses, mirrors, cube rotations, or a combination of any of these to create every possible algorithm which uses 2 faces which are generated from the [https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2 3x3x3 Classic Setup].  (Clearly this was done for the 15 BHTM solutions.)
+
*All other algorithms can be modified by inverses, mirrors, cube rotations, or a combination of any of these to create every possible algorithm which uses 2 faces which are generated from the {{LinkColorE|u=https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2|c=rgb(229,148,0)|t=3x3x3 Classic Setup}}.  (Clearly this was done for the 15 BHTM solutions.)
 
+
{{br|b=1}}
 
*Even though it is very likely that algorithms related by transformations are listed next to each other, no official sorting by transformations was done.
 
*Even though it is very likely that algorithms related by transformations are listed next to each other, no official sorting by transformations was done.
 +
{{br|b=1}}
 
*Since these algorithms use either U and F faces or U and B faces, all algorithms which affect one or the other have been grouped together for convenience of personal preference.
 
*Since these algorithms use either U and F faces or U and B faces, all algorithms which affect one or the other have been grouped together for convenience of personal preference.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=r' U2 r U2 l F2 l' r' F2 r' U2 r' U2 F2 r2 F2
{{Alg5|wca=r' U2 r U2 l F2 l' r' F2 r' U2 r' U2 F2 r2 F2
+
|sign=2R' U2 2R U2 2L F2 2L' 2R' F2 2R' U2 2R' U2 F2 2R2 F2
|sign=2R' U2 2R U2 2L F2 2L' 2R' F2 2R' U2 2R' U2 F2 2R2 F2
 
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 l' U2 l r U2 r U2 r' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 l' U2 l r U2 r U2 r' U2 F2 r2 F2
 
|sign=2R' U2 2R U2 2L' U2 2L 2R U2 2R U2 2R' U2 F2 2R2 F2
 
|sign=2R' U2 2R U2 2L' U2 2L 2R U2 2R U2 2R' U2 F2 2R2 F2
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 l' F2 l r F2 r F2 l' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 l F2 l' F2 l r F2 r F2 l' U2 F2 r2 F2
 
|sign=2R' U2 2L F2 2L' F2 2L 2R F2 2R F2 2L' U2 F2 2R2 F2
 
|sign=2R' U2 2L F2 2L' F2 2L 2R F2 2R F2 2L' U2 F2 2R2 F2
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 r' U2 l B2 l2 B2 U2 r B2 l' B2 l' r' B2
+
{{Alg6|wca=r B2 r' U2 l B2 l2 B2 U2 r B2 l' B2 l' r' B2
 
|sign=2R B2 2R' U2 2L B2 2L2 B2 U2 2R B2 2L' B2 2L' 2R' B2
 
|sign=2R B2 2R' U2 2L B2 2L2 B2 U2 2R B2 2L' B2 2L' 2R' B2
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' r' B2 r' B2 l U2 B2 r2 B2 r U2 l' B2 l B2
+
{{Alg6|wca=l' r' B2 r' B2 l U2 B2 r2 B2 r U2 l' B2 l B2
 
|sign=2L' 2R' B2 2R' B2 2L U2 B2 2R2 B2 2R U2 2L' B2 2L B2
 
|sign=2L' 2R' B2 2R' B2 2L U2 B2 2R2 B2 2R U2 2L' B2 2L B2
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r' U2 r U2 r U2 r2 F2 l r2 F2 l' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 r U2 r2 F2 l r2 F2 l' U2 F2 r2 F2
 
|sign=2R' U2 2R U2 2R U2 2R2 F2 2L 2R2 F2 2L' U2 F2 2R2 F2
 
|sign=2R' U2 2R U2 2R U2 2R2 F2 2L 2R2 F2 2L' U2 F2 2R2 F2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 r F2 l2 U2 l r2 U2 r' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 l F2 r F2 l2 U2 l r2 U2 r' U2 F2 r2 F2
 
|sign=2R' U2 2L F2 2R F2 2L2 U2 2L 2R2 U2 2R' U2 F2 2R2 F2
 
|sign=2R' U2 2L F2 2R F2 2L2 U2 2L 2R2 U2 2R' U2 F2 2R2 F2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r' U2 r' U2 r2 U2 r U2 r2 B2 r U2 r U2 r2 B2
+
{{Alg6|wca=r' U2 r' U2 r2 U2 r U2 r2 B2 r U2 r U2 r2 B2
 
|sign=2R' U2 2R' U2 2R2 U2 2R U2 2R2 B2 2R U2 2R U2 2R2 B2
 
|sign=2R' U2 2R' U2 2R2 U2 2R U2 2R2 B2 2R U2 2R U2 2R2 B2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l' B2 r2 B2 l U2 r2 B2 r U2 r U2 r2 B2
+
{{Alg6|wca=r' U2 l' B2 r2 B2 l U2 r2 B2 r U2 r U2 r2 B2
 
|sign=2R' U2 2L' B2 2R2 B2 2L U2 2R2 B2 2R U2 2R U2 2R2 B2
 
|sign=2R' U2 2L' B2 2R2 B2 2L U2 2R2 B2 2R U2 2R U2 2R2 B2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r U2 r U2 r' U2 l F2 l' F2 r F2 r' F2 r' U2 r'
+
{{Alg6|wca=r U2 r U2 r' U2 l F2 l' F2 r F2 r' F2 r' U2 r'
 
|sign=2R U2 2R U2 2R' U2 2L F2 2L' F2 2R F2 2R' F2 2R' U2 2R'
 
|sign=2R U2 2R U2 2R' U2 2L F2 2L' F2 2R F2 2R' F2 2R' U2 2R'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r'
+
{{Alg6|wca=r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2L' U2 2L F2 2R' F2 2R' U2 2R'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2L' U2 2L F2 2R' F2 2R' U2 2R'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l F2 l' U2 r U2 r' F2 r F2 r' F2 r' U2 r'
+
{{Alg6|wca=r U2 l F2 l' U2 r U2 r' F2 r F2 r' F2 r' U2 r'
 
|sign=2R U2 2L F2 2L' U2 2R U2 2R' F2 2R F2 2R' F2 2R' U2 2R'
 
|sign=2R U2 2L F2 2L' U2 2R U2 2R' F2 2R F2 2R' F2 2R' U2 2R'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l F2 r' F2 r F2 l' F2 r F2 r' F2 r' U2 r'
+
{{Alg6|wca=r U2 l F2 r' F2 r F2 l' F2 r F2 r' F2 r' U2 r'
 
|sign=2R U2 2L F2 2R' F2 2R F2 2L' F2 2R F2 2R' F2 2R' U2 2R'
 
|sign=2R U2 2L F2 2R' F2 2R F2 2L' F2 2R F2 2R' F2 2R' U2 2R'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 r U2 r' F2 r F2 l' F2 l F2 l U2 l
+
{{Alg6|wca=r' F2 l' F2 r U2 r' F2 r F2 l' F2 l F2 l U2 l
 
|sign=2R' F2 2L' F2 2R U2 2R' F2 2R F2 2L' F2 2L F2 2L U2 2L
 
|sign=2R' F2 2L' F2 2R U2 2R' F2 2R F2 2L' F2 2L F2 2L U2 2L
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 r U2 l' U2 r U2 r' F2 l F2 l U2 l
+
{{Alg6|wca=r' F2 l' F2 r U2 l' U2 r U2 r' F2 l F2 l U2 l
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2R U2 2R' F2 2L F2 2L U2 2L
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2R U2 2R' F2 2L F2 2L U2 2L
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l' r'
+
{{Alg6|wca=l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l' r'
 
|sign=2L 2R U2 F2 2L' F2 2R F2 2R' F2 U2 2R' U2 2L U2 2L' 2R'
 
|sign=2L 2R U2 F2 2L' F2 2R F2 2R' F2 U2 2R' U2 2L U2 2L' 2R'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l r U2 r F2 r' F2 U2 r' U2 l F2 l' F2 U2 l' r'
+
{{Alg6|wca=l r U2 r F2 r' F2 U2 r' U2 l F2 l' F2 U2 l' r'
 
|sign=2L 2R U2 2R F2 2R' F2 U2 2R' U2 2L F2 2L' F2 U2 2L' 2R'
 
|sign=2L 2R U2 2R F2 2R' F2 U2 2R' U2 2L F2 2L' F2 U2 2L' 2R'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r' U2 r' U2 l F2 r' U2 r' U2 r2 F2 r' U2 l' U2 r2
+
{{Alg6|wca=r' U2 r' U2 l F2 r' U2 r' U2 r2 F2 r' U2 l' U2 r2
 
|sign=2R' U2 2R' U2 2L F2 2R' U2 2R' U2 2R2 F2 2R' U2 2L' U2 2R2
 
|sign=2R' U2 2R' U2 2L F2 2R' U2 2R' U2 2R2 F2 2R' U2 2L' U2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' F2 l r F2 l' r2 U2 r' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 r' F2 l r F2 l' r2 U2 r' U2 F2 r2 F2
 
|sign=2R' U2 2R U2 2R' F2 2L 2R F2 2L' 2R2 U2 2R' U2 F2 2R2 F2
 
|sign=2R' U2 2R U2 2R' F2 2L 2R F2 2L' 2R2 U2 2R' U2 F2 2R2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r U2 l' r' U2 l r2 U2 r' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 r U2 l' r' U2 l r2 U2 r' U2 F2 r2 F2
 
|sign=2R' U2 2R U2 2R U2 2L' 2R' U2 2L 2R2 U2 2R' U2 F2 2R2 F2
 
|sign=2R' U2 2R U2 2R U2 2L' 2R' U2 2L 2R2 U2 2R' U2 F2 2R2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 l' F2 r2 U2 l F2 r' F2 l' r F2 r2 F2
+
{{Alg6|wca=r' U2 l F2 l' F2 r2 U2 l F2 r' F2 l' r F2 r2 F2
 
|sign=2R' U2 2L F2 2L' F2 2R2 U2 2L F2 2R' F2 2L' 2R F2 2R2 F2
 
|sign=2R' U2 2L F2 2L' F2 2R2 U2 2L F2 2R' F2 2L' 2R F2 2R2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 r F2 l' r' F2 l r2 F2 l' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 l F2 r F2 l' r' F2 l r2 F2 l' U2 F2 r2 F2
 
|sign=2R' U2 2L F2 2R F2 2L' 2R' F2 2L 2R2 F2 2L' U2 F2 2R2 F2
 
|sign=2R' U2 2L F2 2R F2 2L' 2R' F2 2L 2R2 F2 2L' U2 F2 2R2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 l2 r U2 l r U2 l F2 l' U2 F2 r2 F2
+
{{Alg6|wca=r' U2 l F2 l2 r U2 l r U2 l F2 l' U2 F2 r2 F2
 
|sign=2R' U2 2L F2 2L2 2R U2 2L 2R U2 2L F2 2L' U2 F2 2R2 F2
 
|sign=2R' U2 2L F2 2L2 2R U2 2L 2R U2 2L F2 2L' U2 F2 2R2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 r2 U2 l' r
+
{{Alg6|wca=r' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 r2 U2 l' r
 
|sign=2R' U2 2L F2 2R' U2 2R2 U2 F2 2R' F2 2R F2 2R2 U2 2L' 2R
 
|sign=2R' U2 2L F2 2R' U2 2R2 U2 F2 2R' F2 2R F2 2R2 U2 2L' 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 l F2 U2 r2 U2 r F2 l' U2 l U2 l' r
+
{{Alg6|wca=r2 U2 r' U2 l F2 U2 r2 U2 r F2 l' U2 l U2 l' r
 
|sign=2R2 U2 2R' U2 2L F2 U2 2R2 U2 2R F2 2L' U2 2L U2 2L' 2R
 
|sign=2R2 U2 2R' U2 2L F2 U2 2R2 U2 2R F2 2L' U2 2L U2 2L' 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' F2 r F2 l' U2 l F2 r' U2 r' U2 r2 F2 r
+
{{Alg6|wca=r2 U2 r' F2 r F2 l' U2 l F2 r' U2 r' U2 r2 F2 r
 
|sign=2R2 U2 2R' F2 2R F2 2L' U2 2L F2 2R' U2 2R' U2 2R2 F2 2R
 
|sign=2R2 U2 2R' F2 2R F2 2L' U2 2L F2 2R' U2 2R' U2 2R2 F2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 l F2 r' F2 r F2 r' U2 r' U2 r2 F2 r
+
{{Alg6|wca=r2 U2 l' U2 l F2 r' F2 r F2 r' U2 r' U2 r2 F2 r
 
|sign=2R2 U2 2L' U2 2L F2 2R' F2 2R F2 2R' U2 2R' U2 2R2 F2 2R
 
|sign=2R2 U2 2L' U2 2L F2 2R' F2 2R F2 2R' U2 2R' U2 2R2 F2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 r U2 r' U2 l F2 r' U2 r' U2 r2 F2 r
+
{{Alg6|wca=r2 U2 l' U2 r U2 r' U2 l F2 r' U2 r' U2 r2 F2 r
 
|sign=2R2 U2 2L' U2 2R U2 2R' U2 2L F2 2R' U2 2R' U2 2R2 F2 2R
 
|sign=2R2 U2 2L' U2 2R U2 2R' U2 2L F2 2R' U2 2R' U2 2R2 F2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r F2 l2 r U2 F2 l' F2 l F2 r' F2 U2 l r
+
{{Alg6|wca=r2 F2 r F2 l2 r U2 F2 l' F2 l F2 r' F2 U2 l r
 
|sign=2R2 F2 2R F2 2L2 2R U2 F2 2L' F2 2L F2 2R' F2 U2 2L 2R
 
|sign=2R2 F2 2R F2 2L2 2R U2 F2 2L' F2 2L F2 2R' F2 U2 2L 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' U2 l F2 l' U2 r U2 r' F2 r' U2 r2 F2 r
+
{{Alg6|wca=r2 F2 r' U2 l F2 l' U2 r U2 r' F2 r' U2 r2 F2 r
 
|sign=2R2 F2 2R' U2 2L F2 2L' U2 2R U2 2R' F2 2R' U2 2R2 F2 2R
 
|sign=2R2 F2 2R' U2 2L F2 2L' U2 2R U2 2R' F2 2R' U2 2R2 F2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' U2 l F2 r' F2 r F2 l' F2 r' U2 r2 F2 r
+
{{Alg6|wca=r2 F2 r' U2 l F2 r' F2 r F2 l' F2 r' U2 r2 F2 r
 
|sign=2R2 F2 2R' U2 2L F2 2R' F2 2R F2 2L' F2 2R' U2 2R2 F2 2R
 
|sign=2R2 F2 2R' U2 2L F2 2R' F2 2R F2 2L' F2 2R' U2 2R2 F2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' U2 r U2 r' U2 l F2 l' F2 r' U2 r2 F2 r
+
{{Alg6|wca=r2 F2 r' U2 r U2 r' U2 l F2 l' F2 r' U2 r2 F2 r
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2L F2 2L' F2 2R' U2 2R2 F2 2R
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2L F2 2L' F2 2R' U2 2R2 F2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' U2 r U2 r' U2 r U2 l' U2 r U2 l2 F2 l'
+
{{Alg6|wca=r2 F2 r' U2 r U2 r' U2 r U2 l' U2 r U2 l2 F2 l'
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2R U2 2L' U2 2R U2 2L2 F2 2L'
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2R U2 2L' U2 2R U2 2L2 F2 2L'
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l r2 F2 r F2 r F2 l' r' F2 r' U2 r' U2 F2 r2 F2
+
{{Alg6|wca=l r2 F2 r F2 r F2 l' r' F2 r' U2 r' U2 F2 r2 F2
 
|sign=2L 2R2 F2 2R F2 2R F2 2L' 2R' F2 2R' U2 2R' U2 F2 2R2 F2
 
|sign=2L 2R2 F2 2R F2 2R F2 2L' 2R' F2 2R' U2 2R' U2 F2 2R2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2 U2 l r'
+
{{Alg6|wca=r B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2 U2 l r'
 
|sign=2R B2 2R' U2 2R U2 2L2 B2 2L' B2 2L B2 U2 2L2 U2 2L 2R'
 
|sign=2R B2 2R' U2 2R U2 2L2 B2 2L' B2 2L B2 U2 2L2 U2 2L 2R'
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2 U2 l r'
+
{{Alg6|wca=r B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2 U2 l r'
 
|sign=2R B2 2L' B2 2R B2 2R2 U2 2L' U2 2R B2 U2 2L2 U2 2L 2R'
 
|sign=2R B2 2L' B2 2R B2 2R2 U2 2L' U2 2R B2 U2 2L2 U2 2L 2R'
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' B2 r2 B2 U2 r' U2 l' r2 B2 l r B2
+
{{Alg6|wca=r' U2 r U2 r' B2 r2 B2 U2 r' U2 l' r2 B2 l r B2
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2R' U2 2L' 2R2 B2 2L 2R B2
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2R' U2 2L' 2R2 B2 2L 2R B2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l2 U2 l' r
+
{{Alg6|wca=r' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l2 U2 l' r
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2L' B2 2R B2 2L2 U2 2L' 2R
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2L' B2 2R B2 2L2 U2 2L' 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r B2 r U2 r2 B2 r B2 r U2 l' B2 l U2 r
+
{{Alg6|wca=r2 U2 r B2 r U2 r2 B2 r B2 r U2 l' B2 l U2 r
 
|sign=2R2 U2 2R B2 2R U2 2R2 B2 2R B2 2R U2 2L' B2 2L U2 2R
 
|sign=2R2 U2 2R B2 2R U2 2R2 B2 2R B2 2R U2 2L' B2 2L U2 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 l U2 l' r
+
{{Alg6|wca=r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 l U2 l' r
 
|sign=2R2 U2 2R' U2 2R U2 B2 2R2 B2 2R U2 2R' U2 2L U2 2L' 2R
 
|sign=2R2 U2 2R' U2 2R U2 B2 2R2 B2 2R U2 2R' U2 2L U2 2L' 2R
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 r' B2 r2 U2 r' U2 l' r' B2 r B2 l B2
+
{{Alg6|wca=r2 U2 r' U2 r' B2 r2 U2 r' U2 l' r' B2 r B2 l B2
 
|sign=2R2 U2 2R' U2 2R' B2 2R2 U2 2R' U2 2L' 2R' B2 2R B2 2L B2
 
|sign=2R2 U2 2R' U2 2R' B2 2R2 U2 2R' U2 2L' 2R' B2 2R B2 2L B2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 r' B2 l' r' B2 r' B2 r2 B2 r B2 l B2
+
{{Alg6|wca=r2 U2 r' U2 r' B2 l' r' B2 r' B2 r2 B2 r B2 l B2
 
|sign=2R2 U2 2R' U2 2R' B2 2L' 2R' B2 2R' B2 2R2 B2 2R B2 2L B2
 
|sign=2R2 U2 2R' U2 2R' B2 2L' 2R' B2 2R' B2 2R2 B2 2R B2 2L B2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 r U2 r' U2 r U2 r' B2 r' B2 r2 U2 l
+
{{Alg6|wca=r2 U2 l' U2 r U2 r' U2 r U2 r' B2 r' B2 r2 U2 l
 
|sign=2R2 U2 2L' U2 2R U2 2R' U2 2R U2 2R' B2 2R' B2 2R2 U2 2L
 
|sign=2R2 U2 2L' U2 2R U2 2R' U2 2R U2 2R' B2 2R' B2 2R2 U2 2L
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' B2 r B2 l r' B2 r2 B2 r U2 l' B2 l B2
+
{{Alg6|wca=r2 U2 l' B2 r B2 l r' B2 r2 B2 r U2 l' B2 l B2
 
|sign=2R2 U2 2L' B2 2R B2 2L 2R' B2 2R2 B2 2R U2 2L' B2 2L B2
 
|sign=2R2 U2 2L' B2 2R B2 2L 2R' B2 2R2 B2 2R U2 2L' B2 2L B2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 U2 l' U2 r U2 r' U2 B2 l r2 U2 l U2 l' r'
+
{{Alg6|wca=r2 B2 U2 l' U2 r U2 r' U2 B2 l r2 U2 l U2 l' r'
 
|sign=2R2 B2 U2 2L' U2 2R U2 2R' U2 B2 2L 2R2 U2 2L U2 2L' 2R'
 
|sign=2R2 B2 U2 2L' U2 2R U2 2R' U2 B2 2L 2R2 U2 2L U2 2L' 2R'
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 U2 l' U2 r U2 r' U2 l r' U2 r' U2 r B2 r2
+
{{Alg6|wca=r2 B2 U2 l' U2 r U2 r' U2 l r' U2 r' U2 r B2 r2
 
|sign=2R2 B2 U2 2L' U2 2R U2 2R' U2 2L 2R' U2 2R' U2 2R B2 2R2
 
|sign=2R2 B2 U2 2L' U2 2R U2 2R' U2 2L 2R' U2 2R' U2 2R B2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 l' B2 l r' B2 r' B2 r B2 r' U2 B2 r2
+
{{Alg6|wca=r2 B2 r U2 l' B2 l r' B2 r' B2 r B2 r' U2 B2 r2
 
|sign=2R2 B2 2R U2 2L' B2 2L 2R' B2 2R' B2 2R B2 2R' U2 B2 2R2
 
|sign=2R2 B2 2R U2 2L' B2 2L 2R' B2 2R' B2 2R B2 2R' U2 B2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' B2 l' B2 l U2 l' B2 l U2 r2 U2 r'
+
{{Alg6|wca=r2 B2 r U2 r' B2 l' B2 l U2 l' B2 l U2 r2 U2 r'
 
|sign=2R2 B2 2R U2 2R' B2 2L' B2 2L U2 2L' B2 2L U2 2R2 U2 2R'
 
|sign=2R2 B2 2R U2 2R' B2 2L' B2 2L U2 2L' B2 2L U2 2R2 U2 2R'
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 B2 r' B2 r B2 l' B2 l r' B2 r2
+
{{Alg6|wca=r2 B2 r U2 r' U2 B2 r' B2 r B2 l' B2 l r' B2 r2
 
|sign=2R2 B2 2R U2 2R' U2 B2 2R' B2 2R B2 2L' B2 2L 2R' B2 2R2
 
|sign=2R2 B2 2R U2 2R' U2 B2 2R' B2 2R B2 2L' B2 2L 2R' B2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 l r' U2 l' B2 r B2 r' U2 B2 r2
+
{{Alg6|wca=r2 B2 r U2 r' U2 l r' U2 l' B2 r B2 r' U2 B2 r2
 
|sign=2R2 B2 2R U2 2R' U2 2L 2R' U2 2L' B2 2R B2 2R' U2 B2 2R2
 
|sign=2R2 B2 2R U2 2R' U2 2L 2R' U2 2L' B2 2R B2 2R' U2 B2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 l r' U2 r' U2 r U2 l' U2 B2 r2
+
{{Alg6|wca=r2 B2 r U2 r' U2 l r' U2 r' U2 r U2 l' U2 B2 r2
 
|sign=2R2 B2 2R U2 2R' U2 2L 2R' U2 2R' U2 2R U2 2L' U2 B2 2R2
 
|sign=2R2 B2 2R U2 2R' U2 2L 2R' U2 2R' U2 2R U2 2L' U2 B2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l' r B2 l' B2 l U2 r' U2 B2 r' B2 l B2 r2
+
{{Alg6|wca=r2 B2 l' r B2 l' B2 l U2 r' U2 B2 r' B2 l B2 r2
 
|sign=2R2 B2 2L' 2R B2 2L' B2 2L U2 2R' U2 B2 2R' B2 2L B2 2R2
 
|sign=2R2 B2 2L' 2R B2 2L' B2 2L U2 2R' U2 B2 2R' B2 2L B2 2R2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r U r U' F2 U r' U' l F2 l' F2 U2 r' U2 r2 F2 r
+
{{Alg6|wca=r U r U' F2 U r' U' l F2 l' F2 U2 r' U2 r2 F2 r
 
|sign=2R U 2R U' F2 U 2R' U' 2L F2 2L' F2 U2 2R' U2 2R2 F2 2R
 
|sign=2R U 2R U' F2 U 2R' U' 2L F2 2L' F2 U2 2R' U2 2R2 F2 2R
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l U2 r' U2 r F2 r F r' F U2 F' r F l' r2
+
{{Alg6|wca=r2 U2 l U2 r' U2 r F2 r F r' F U2 F' r F l' r2
 
|sign=2R2 U2 2L U2 2R' U2 2R F2 2R F 2R' F U2 F' 2R F 2L' 2R2
 
|sign=2R2 U2 2L U2 2R' U2 2R F2 2R F 2R' F U2 F' 2R F 2L' 2R2
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r F2 l2 r U2 r' F2 U' l' U F2 U' l U' l r
+
{{Alg6|wca=r2 F2 r F2 l2 r U2 r' F2 U' l' U F2 U' l U' l r
 
|sign=2R2 F2 2R F2 2L2 2R U2 2R' F2 U' 2L' U F2 U' 2L U' 2L 2R
 
|sign=2R2 F2 2R F2 2L2 2R U2 2R' F2 U' 2L' U F2 U' 2L U' 2L 2R
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 l F2 l' U' l' U F2 U' l U F2 l2 F2 r
+
{{Alg6|wca=r' F2 l' F2 l F2 l' U' l' U F2 U' l U F2 l2 F2 r
 
|sign=2R' F2 2L' F2 2L F2 2L' U' 2L' U F2 U' 2L U F2 2L2 F2 2R
 
|sign=2R' F2 2L' F2 2L F2 2L' U' 2L' U F2 U' 2L U F2 2L2 F2 2R
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r U2 r U2 r' U2 r B r B' U2 B r' B' U2 r2 U2 r'
+
{{Alg6|wca=r U2 r U2 r' U2 r B r B' U2 B r' B' U2 r2 U2 r'
 
|sign=2R U2 2R U2 2R' U2 2R B 2R B' U2 B 2R' B' U2 2R2 U2 2R'
 
|sign=2R U2 2R U2 2R' U2 2R B 2R B' U2 B 2R' B' U2 2R2 U2 2R'
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' B2 l r2
+
{{Alg6|wca=r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' B2 l r2
 
|sign=2R2 U2 2L' U2 2R U' 2R' U B2 U' 2R U' 2R' U2 2R' B2 2L 2R2
 
|sign=2R2 U2 2L' U2 2R U' 2R' U B2 U' 2R U' 2R' U2 2R' B2 2L 2R2
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 B r' B' l U2 l' U2 l' B' l B' r2
+
{{Alg6|wca=r2 B2 r U2 r' U2 B r' B' l U2 l' U2 l' B' l B' r2
 
|sign=2R2 B2 2R U2 2R' U2 B 2R' B' 2L U2 2L' U2 2L' B' 2L B' 2R2
 
|sign=2R2 B2 2R U2 2R' U2 B 2R' B' 2L U2 2L' U2 2L' B' 2L B' 2R2
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 B r' B' r B2 l' B2 r' B' l B' r2
+
{{Alg6|wca=r2 B2 r U2 r' U2 B r' B' r B2 l' B2 r' B' l B' r2
 
|sign=2R2 B2 2R U2 2R' U2 B 2R' B' 2R B2 2L' B2 2R' B' 2L B' 2R2
 
|sign=2R2 B2 2R U2 2R' U2 B 2R' B' 2R B2 2L' B2 2R' B' 2L B' 2R2
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B' r B' U2 B r' B' U2 l' B2 l r2 U2 l U2 l' r'
+
{{Alg6|wca=r2 B' r B' U2 B r' B' U2 l' B2 l r2 U2 l U2 l' r'
 
|sign=2R2 B' 2R B' U2 B 2R' B' U2 2L' B2 2L 2R2 U2 2L U2 2L' 2R'
 
|sign=2R2 B' 2R B' U2 B 2R' B' U2 2L' B2 2L 2R2 U2 2L U2 2L' 2R'
 
|length=(25,18)|name=|wide=Y|author=|url=
 
|length=(25,18)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=(r2 U2)2 (r U2)2 r' U2 B2 U' r' U B2 U' r U'
+
{{Alg6|wca=(r2 U2)2 (r U2)2 r' U2 B2 U' r' U B2 U' r U'
 
|sign=(2R2 U2)2 (2R U2)2 2R' U2 B2 U' 2R' U B2 U' 2R U'
 
|sign=(2R2 U2)2 (2R U2)2 2R' U2 B2 U' 2R' U B2 U' 2R U'
 
|length=(27,18)|name=|wide=N|author=Christopher Mowla
 
|length=(27,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-with-only-two-algs.28003/page-2#post-545348
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-with-only-two-algs.28003/page-2#post-545348
 
}}
 
}}
{{Alg5|wca=(r2 U2)2 (r U2)2 r' U2 B2 U r' U' B2 U r U
+
{{Alg6|wca=(r2 U2)2 (r U2)2 r' U2 B2 U r' U' B2 U r U
 
|sign=(2R2 U2)2 (2R U2)2 2R' U2 B2 U 2R' U' B2 U 2R U
 
|sign=(2R2 U2)2 (2R U2)2 2R' U2 B2 U 2R' U' B2 U 2R U
 
|length=(27,18)|name=|wide=N|author=Christopher Mowla
 
|length=(27,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r U2 r2 U2 r' U2 l F2 l' U2 l U2 r F2 r' U2 l' r'
+
{{Alg6|wca=r U2 r2 U2 r' U2 l F2 l' U2 l U2 r F2 r' U2 l' r'
 
|sign=2R U2 2R2 U2 2R' U2 2L F2 2L' U2 2L U2 2R F2 2R' U2 2L' 2R'
 
|sign=2R U2 2R2 U2 2R' U2 2L F2 2L' U2 2L U2 2R F2 2R' U2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 l r2 F2 l'
+
{{Alg6|wca=r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 l r2 F2 l'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2R' F2 2R F2 2R' F2 2L 2R2 F2 2L'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2R' F2 2R F2 2R' F2 2L 2R2 F2 2L'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 r' U2 r U2 r' F2 r F2 l' U2 l r2 U2 r'
+
{{Alg6|wca=r U2 r U2 r' U2 r U2 r' F2 r F2 l' U2 l r2 U2 r'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2R' F2 2R F2 2L' U2 2L 2R2 U2 2R'
 
|sign=2R U2 2R U2 2R' U2 2R U2 2R' F2 2R F2 2L' U2 2L 2R2 U2 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l F2 r' F2 l' r2 U2 l' U2 l F2 r' F2 r' U2 r'
+
{{Alg6|wca=r U2 l F2 r' F2 l' r2 U2 l' U2 l F2 r' F2 r' U2 r'
 
|sign=2R U2 2L F2 2R' F2 2L' 2R2 U2 2L' U2 2L F2 2R' F2 2R' U2 2R'
 
|sign=2R U2 2L F2 2R' F2 2L' 2R2 U2 2L' U2 2L F2 2R' F2 2R' U2 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l F2 l' U2 r U2 l' U2 r U2 l r2 F2 r' U2 r'
+
{{Alg6|wca=r U2 l F2 l' U2 r U2 l' U2 r U2 l r2 F2 r' U2 r'
 
|sign=2R U2 2L F2 2L' U2 2R U2 2L' U2 2R U2 2L 2R2 F2 2R' U2 2R'
 
|sign=2R U2 2L F2 2L' U2 2R U2 2L' U2 2R U2 2L 2R2 F2 2R' U2 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 l' r' U2 l r'
+
{{Alg6|wca=r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 l' r' U2 l r'
 
|sign=2R' U2 2R U2 2R U2 2R2 F2 2R' U2 2R' U2 F2 2L' 2R' U2 2L 2R'
 
|sign=2R' U2 2R U2 2R U2 2R2 F2 2R' U2 2R' U2 F2 2L' 2R' U2 2L 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' F2 r2 U2 r U2 r' U2 l' r U2 l r F2
+
{{Alg6|wca=r' U2 r U2 r' F2 r2 U2 r U2 r' U2 l' r U2 l r F2
 
|sign=2R' U2 2R U2 2R' F2 2R2 U2 2R U2 2R' U2 2L' 2R U2 2L 2R F2
 
|sign=2R' U2 2R U2 2R' F2 2R2 U2 2R U2 2R' U2 2L' 2R U2 2L 2R F2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' F2 l r F2 r F2 r' F2 l' r F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 r' F2 l r F2 r F2 r' F2 l' r F2 r2 F2
 
|sign=2R' U2 2R U2 2R' F2 2L 2R F2 2R F2 2R' F2 2L' 2R F2 2R2 F2
 
|sign=2R' U2 2R U2 2R' F2 2L 2R F2 2R F2 2R' F2 2L' 2R F2 2R2 F2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 l' U2 l r U2 l F2 r' F2 l' r F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 l' U2 l r U2 l F2 r' F2 l' r F2 r2 F2
 
|sign=2R' U2 2R U2 2L' U2 2L 2R U2 2L F2 2R' F2 2L' 2R F2 2R2 F2
 
|sign=2R' U2 2R U2 2L' U2 2L 2R U2 2L F2 2R' F2 2L' 2R F2 2R2 F2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 r' U2 r2 U2 F2 l' U2 r U2 l r U2 l' r
+
{{Alg6|wca=r' U2 l F2 r' U2 r2 U2 F2 l' U2 r U2 l r U2 l' r
 
|sign=2R' U2 2L F2 2R' U2 2R2 U2 F2 2L' U2 2R U2 2L 2R U2 2L' 2R
 
|sign=2R' U2 2L F2 2R' U2 2R2 U2 F2 2L' U2 2R U2 2L 2R U2 2L' 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l F2 l' F2 r2 U2 l F2 l' U2 l' r U2 l r F2
+
{{Alg6|wca=r' U2 l F2 l' F2 r2 U2 l F2 l' U2 l' r U2 l r F2
 
|sign=2R' U2 2L F2 2L' F2 2R2 U2 2L F2 2L' U2 2L' 2R U2 2L 2R F2
 
|sign=2R' U2 2L F2 2L' F2 2R2 U2 2L F2 2L' U2 2L' 2R U2 2L 2R F2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 r2 U2 r U2 r F2 r' F2 r F2 r' F2 l F2 l' r'
+
{{Alg6|wca=r' F2 r2 U2 r U2 r F2 r' F2 r F2 r' F2 l F2 l' r'
 
|sign=2R' F2 2R2 U2 2R U2 2R F2 2R' F2 2R F2 2R' F2 2L F2 2L' 2R'
 
|sign=2R' F2 2R2 U2 2R U2 2R F2 2R' F2 2R F2 2R' F2 2L F2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 r U2 l' U2 r U2 l' U2 l U2 l2 r' U2 l
+
{{Alg6|wca=r' F2 l' F2 r U2 l' U2 r U2 l' U2 l U2 l2 r' U2 l
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2R U2 2L' U2 2L U2 2L2 2R' U2 2L
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2R U2 2L' U2 2L U2 2L2 2R' U2 2L
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 r U2 l' U2 l F2 l' F2 r U2 l2 r' U2 l
+
{{Alg6|wca=r' F2 l' F2 r U2 l' U2 l F2 l' F2 r U2 l2 r' U2 l
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2L F2 2L' F2 2R U2 2L2 2R' U2 2L
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2L F2 2L' F2 2R U2 2L2 2R' U2 2L
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 r U2 l' U2 l F2 l' F2 l F2 l2 r' F2 r
+
{{Alg6|wca=r' F2 l' F2 r U2 l' U2 l F2 l' F2 l F2 l2 r' F2 r
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2L F2 2L' F2 2L F2 2L2 2R' F2 2R
 
|sign=2R' F2 2L' F2 2R U2 2L' U2 2L F2 2L' F2 2L F2 2L2 2R' F2 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 l F2 l' F2 r F2 l' F2 r U2 l2 r' U2 l
+
{{Alg6|wca=r' F2 l' F2 l F2 l' F2 r F2 l' F2 r U2 l2 r' U2 l
 
|sign=2R' F2 2L' F2 2L F2 2L' F2 2R F2 2L' F2 2R U2 2L2 2R' U2 2L
 
|sign=2R' F2 2L' F2 2L F2 2L' F2 2R F2 2L' F2 2R U2 2L2 2R' U2 2L
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 l F2 l' F2 r F2 l' F2 l F2 l2 r' F2 r
+
{{Alg6|wca=r' F2 l' F2 l F2 l' F2 r F2 l' F2 l F2 l2 r' F2 r
 
|sign=2R' F2 2L' F2 2L F2 2L' F2 2R F2 2L' F2 2L F2 2L2 2R' F2 2R
 
|sign=2R' F2 2L' F2 2L F2 2L' F2 2R F2 2L' F2 2L F2 2L2 2R' F2 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l' F2 l F2 l' F2 l' r2 U2 r' F2 l F2 l U2 l
+
{{Alg6|wca=r' F2 l' F2 l F2 l' F2 l' r2 U2 r' F2 l F2 l U2 l
 
|sign=2R' F2 2L' F2 2L F2 2L' F2 2L' 2R2 U2 2R' F2 2L F2 2L U2 2L
 
|sign=2R' F2 2L' F2 2L F2 2L' F2 2L' 2R2 U2 2R' F2 2L F2 2L U2 2L
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l2 F2 r U2 r' F2 r U2 r' U2 l' F2 l U2 l r
+
{{Alg6|wca=r' F2 l2 F2 r U2 r' F2 r U2 r' U2 l' F2 l U2 l r
 
|sign=2R' F2 2L2 F2 2R U2 2R' F2 2R U2 2R' U2 2L' F2 2L U2 2L 2R
 
|sign=2R' F2 2L2 F2 2R U2 2R' F2 2R U2 2R' U2 2L' F2 2L U2 2L 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r' U2 l' r' U2 l
+
{{Alg6|wca=r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r' U2 l' r' U2 l
 
|sign=2R2 U2 2R' F2 2R F2 2R' F2 2R F2 2R' U2 2R' U2 2L' 2R' U2 2L
 
|sign=2R2 U2 2R' F2 2R F2 2R' F2 2R F2 2R' U2 2R' U2 2L' 2R' U2 2L
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r F2 l r F2 l'
+
{{Alg6|wca=r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r F2 l r F2 l'
 
|sign=2R2 U2 2R' F2 2R F2 2R' F2 2R F2 2R' U2 2R F2 2L 2R F2 2L'
 
|sign=2R2 U2 2R' F2 2R F2 2R' F2 2R F2 2R' U2 2R F2 2L 2R F2 2L'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 l' U2 l F' r' F U2 F' r F r2 U2 r2 F2 r
+
{{Alg6|wca=r2 F2 U2 l' U2 l F' r' F U2 F' r F r2 U2 r2 F2 r
 
|sign=2R2 F2 U2 2L' U2 2L F' 2R' F U2 F' 2R F 2R2 U2 2R2 F2 2R
 
|sign=2R2 F2 U2 2L' U2 2L F' 2R' F U2 F' 2R F 2R2 U2 2R2 F2 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l
+
{{Alg6|wca=r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2R U2 2R' F2 2R' U2 2L' 2R' U2 2L
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2R U2 2R' F2 2R' U2 2L' 2R' U2 2L
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r F2 l r F2 l'
+
{{Alg6|wca=r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r F2 l r F2 l'
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2R U2 2R' F2 2R F2 2L 2R F2 2L'
 
|sign=2R2 F2 2R' U2 2R U2 2R' U2 2R U2 2R' F2 2R F2 2L 2R F2 2L'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 l' r F2 l' U2 l U2 l' U2 F2 l' F2 l U2 l r
+
{{Alg6|wca=r2 F2 l' r F2 l' U2 l U2 l' U2 F2 l' F2 l U2 l r
 
|sign=2R2 F2 2L' 2R F2 2L' U2 2L U2 2L' U2 F2 2L' F2 2L U2 2L 2R
 
|sign=2R2 F2 2L' 2R F2 2L' U2 2L U2 2L' U2 F2 2L' F2 2L U2 2L 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l r' U2 l' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 l' r'
+
{{Alg6|wca=l r' U2 l' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 l' r'
 
|sign=2L 2R' U2 2L' U2 2L F2 2R' U2 2R2 U2 F2 2R' F2 2R F2 2L' 2R'
 
|sign=2L 2R' U2 2L' U2 2L F2 2R' U2 2R2 U2 F2 2R' F2 2R F2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r U2 r U2 l' B2 r B2 r' U2 r U2 r' U2 l r2 U2 r'
+
{{Alg6|wca=r U2 r U2 l' B2 r B2 r' U2 r U2 r' U2 l r2 U2 r'
 
|sign=2R U2 2R U2 2L' B2 2R B2 2R' U2 2R U2 2R' U2 2L 2R2 U2 2R'
 
|sign=2R U2 2R U2 2L' B2 2R B2 2R' U2 2R U2 2R' U2 2L 2R2 U2 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 l' B2 r B2 l' B2 l U2 r' U2 r' B2 l r2
+
{{Alg6|wca=r U2 r U2 l' B2 r B2 l' B2 l U2 r' U2 r' B2 l r2
 
|sign=2R U2 2R U2 2L' B2 2R B2 2L' B2 2L U2 2R' U2 2R' B2 2L 2R2
 
|sign=2R U2 2R U2 2L' B2 2R B2 2L' B2 2L U2 2R' U2 2R' B2 2L 2R2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' B2 l r2
+
{{Alg6|wca=r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' B2 l r2
 
|sign=2R U2 2R U2 2L' B2 2L U2 2L' U2 2R U2 2R' U2 2R' B2 2L 2R2
 
|sign=2R U2 2R U2 2L' B2 2L U2 2L' U2 2R U2 2R' U2 2R' B2 2L 2R2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 l' B2 l' U2 l U2 l' U2 r B2 r' B2 l' r'
+
{{Alg6|wca=r U2 l2 B2 l' B2 l' U2 l U2 l' U2 r B2 r' B2 l' r'
 
|sign=2R U2 2L2 B2 2L' B2 2L' U2 2L U2 2L' U2 2R B2 2R' B2 2L' 2R'
 
|sign=2R U2 2L2 B2 2L' B2 2L' U2 2L U2 2L' U2 2R B2 2R' B2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 l' B2 l' U2 r B2 l' B2 l B2 r' B2 l' r'
+
{{Alg6|wca=r U2 l2 B2 l' B2 l' U2 r B2 l' B2 l B2 r' B2 l' r'
 
|sign=2R U2 2L2 B2 2L' B2 2L' U2 2R B2 2L' B2 2L B2 2R' B2 2L' 2R'
 
|sign=2R U2 2L2 B2 2L' B2 2L' U2 2R B2 2L' B2 2L B2 2R' B2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 l' B2 l' U2 r B2 r' U2 l U2 l' B2 l' r'
+
{{Alg6|wca=r U2 l2 B2 l' B2 l' U2 r B2 r' U2 l U2 l' B2 l' r'
 
|sign=2R U2 2L2 B2 2L' B2 2L' U2 2R B2 2R' U2 2L U2 2L' B2 2L' 2R'
 
|sign=2R U2 2L2 B2 2L' B2 2L' U2 2R B2 2R' U2 2L U2 2L' B2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 l' U2 l' B2 l B2 r' U2 r B2 l' U2 l' r'
+
{{Alg6|wca=r U2 l2 B2 l' U2 l' B2 l B2 r' U2 r B2 l' U2 l' r'
 
|sign=2R U2 2L2 B2 2L' U2 2L' B2 2L B2 2R' U2 2R B2 2L' U2 2L' 2R'
 
|sign=2R U2 2L2 B2 2L' U2 2L' B2 2L B2 2R' U2 2R B2 2L' U2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 l' U2 r' U2 l U2 l' U2 r B2 l' U2 l' r'
+
{{Alg6|wca=r U2 l2 B2 l' U2 r' U2 l U2 l' U2 r B2 l' U2 l' r'
 
|sign=2R U2 2L2 B2 2L' U2 2R' U2 2L U2 2L' U2 2R B2 2L' U2 2L' 2R'
 
|sign=2R U2 2L2 B2 2L' U2 2R' U2 2L U2 2L' U2 2R B2 2L' U2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 l' U2 r' U2 r B2 l' B2 l B2 l' U2 l' r'
+
{{Alg6|wca=r U2 l2 B2 l' U2 r' U2 r B2 l' B2 l B2 l' U2 l' r'
 
|sign=2R U2 2L2 B2 2L' U2 2R' U2 2R B2 2L' B2 2L B2 2L' U2 2L' 2R'
 
|sign=2R U2 2L2 B2 2L' U2 2R' U2 2R B2 2L' B2 2L B2 2L' U2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l2 B2 r' B2 l B2 r' B2 r B2 r' B2 r U2 l r
+
{{Alg6|wca=r U2 l2 B2 r' B2 l B2 r' B2 r B2 r' B2 r U2 l r
 
|sign=2R U2 2L2 B2 2R' B2 2L B2 2R' B2 2R B2 2R' B2 2R U2 2L 2R
 
|sign=2R U2 2L2 B2 2R' B2 2L B2 2R' B2 2R B2 2R' B2 2R U2 2L 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r B2 r' U2 r U2 l' r' U2 l' U2 r B2 U2 l2 U2 l r'
+
{{Alg6|wca=r B2 r' U2 r U2 l' r' U2 l' U2 r B2 U2 l2 U2 l r'
 
|sign=2R B2 2R' U2 2R U2 2L' 2R' U2 2L' U2 2R B2 U2 2L2 U2 2L 2R'
 
|sign=2R B2 2R' U2 2R U2 2L' 2R' U2 2L' U2 2R B2 U2 2L2 U2 2L 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r B2 r' U2 l B2 l2 B2 U2 r B2 r' U2 l' r' U2 l' r
+
{{Alg6|wca=r B2 r' U2 l B2 l2 B2 U2 r B2 r' U2 l' r' U2 l' r
 
|sign=2R B2 2R' U2 2L B2 2L2 B2 U2 2R B2 2R' U2 2L' 2R' U2 2L' 2R
 
|sign=2R B2 2R' U2 2L B2 2L2 B2 U2 2R B2 2R' U2 2L' 2R' U2 2L' 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r B2 l B2 r' U2 l B2 l B2 l2 U2 l B2 r B2 l' r'
+
{{Alg6|wca=r B2 l B2 r' U2 l B2 l B2 l2 U2 l B2 r B2 l' r'
 
|sign=2R B2 2L B2 2R' U2 2L B2 2L B2 2L2 U2 2L B2 2R B2 2L' 2R'
 
|sign=2R B2 2L B2 2R' U2 2L B2 2L B2 2L2 U2 2L B2 2R B2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r B2 l' B2 r B2 l' r' B2 l' B2 l B2 U2 l2 U2 l r'
+
{{Alg6|wca=r B2 l' B2 r B2 l' r' B2 l' B2 l B2 U2 l2 U2 l r'
 
|sign=2R B2 2L' B2 2R B2 2L' 2R' B2 2L' B2 2L B2 U2 2L2 U2 2L 2R'
 
|sign=2R B2 2L' B2 2R B2 2L' 2R' B2 2L' B2 2L B2 U2 2L2 U2 2L 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r B2 l' B2 r' U2 l r U2 l B2 l B2 U2 l2 U2 l r'
+
{{Alg6|wca=r B2 l' B2 r' U2 l r U2 l B2 l B2 U2 l2 U2 l r'
 
|sign=2R B2 2L' B2 2R' U2 2L 2R U2 2L B2 2L B2 U2 2L2 U2 2L 2R'
 
|sign=2R B2 2L' B2 2R' U2 2L 2R U2 2L B2 2L B2 U2 2L2 U2 2L 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' B2 l r U2 l' r U2 r' U2 r U2 r2 B2
+
{{Alg6|wca=r' U2 r U2 r' B2 l r U2 l' r U2 r' U2 r U2 r2 B2
 
|sign=2R' U2 2R U2 2R' B2 2L 2R U2 2L' 2R U2 2R' U2 2R U2 2R2 B2
 
|sign=2R' U2 2R U2 2R' B2 2L 2R U2 2L' 2R U2 2R' U2 2R U2 2R2 B2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' B2 r2 B2 l' r B2 r' B2 r B2 l r B2
+
{{Alg6|wca=r' U2 r U2 r' B2 r2 B2 l' r B2 r' B2 r B2 l r B2
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 2L' 2R B2 2R' B2 2R B2 2L 2R B2
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 2L' 2R B2 2R' B2 2R B2 2L 2R B2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 l' r' B2 l r
+
{{Alg6|wca=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 l' r' B2 l r
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2R' U2 2R' B2 2L' 2R' B2 2L 2R
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2R' U2 2R' B2 2L' 2R' B2 2L 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 l' r
+
{{Alg6|wca=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 l' r
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 2L 2R U2 2L' 2R
 
|sign=2R' U2 2R U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 2L 2R U2 2L' 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r' U2 l' r' B2 r B2 l r B2 r U2 r U2 r2 B2
+
{{Alg6|wca=r' U2 r' U2 l' r' B2 r B2 l r B2 r U2 r U2 r2 B2
 
|sign=2R' U2 2R' U2 2L' 2R' B2 2R B2 2L 2R B2 2R U2 2R U2 2R2 B2
 
|sign=2R' U2 2R' U2 2L' 2R' B2 2R B2 2L 2R B2 2R U2 2R U2 2R2 B2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l r
+
{{Alg6|wca=r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l r
 
|sign=2R' U2 2R' U2 2R U2 2R' B2 2R' B2 2R2 U2 2R' B2 2L' B2 2L 2R
 
|sign=2R' U2 2R' U2 2R U2 2R' B2 2R' B2 2R2 U2 2R' B2 2L' B2 2L 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 l r'
+
{{Alg6|wca=r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 l r'
 
|sign=2R' U2 2R U2 2R U2 2L' 2R' U2 2R' B2 2R' B2 U2 2R2 U2 2L 2R'
 
|sign=2R' U2 2R U2 2R U2 2L' 2R' U2 2R' B2 2R' B2 U2 2R2 U2 2L 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l r' U2 l' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l r
+
{{Alg6|wca=l r' U2 l' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l r
 
|sign=2L 2R' U2 2L' U2 2R U2 2R' B2 2R2 B2 U2 2L' B2 2R B2 2L 2R
 
|sign=2L 2R' U2 2L' U2 2R U2 2R' B2 2R2 B2 U2 2L' B2 2R B2 2L 2R
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' B2 l U2 l r' U2 l' r' B2 r U2 l' B2 l B2
+
{{Alg6|wca=r2 U2 l' B2 l U2 l r' U2 l' r' B2 r U2 l' B2 l B2
 
|sign=2R2 U2 2L' B2 2L U2 2L 2R' U2 2L' 2R' B2 2R U2 2L' B2 2L B2
 
|sign=2R2 U2 2L' B2 2L U2 2L 2R' U2 2L' 2R' B2 2R U2 2L' B2 2L B2
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r U2 r' U2 B2 r' B2 r B2 r' U2 l r' U2 l' r'
+
{{Alg6|wca=r2 B2 r U2 r' U2 B2 r' B2 r B2 r' U2 l r' U2 l' r'
 
|sign=2R2 B2 2R U2 2R' U2 B2 2R' B2 2R B2 2R' U2 2L 2R' U2 2L' 2R'
 
|sign=2R2 B2 2R U2 2R' U2 B2 2R' B2 2R B2 2R' U2 2L 2R' U2 2L' 2R'
 
|length=(27,18)|name=|wide=Y|author=|url=
 
|length=(27,18)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw U2 Rw2 U L U r U' L' U2 L U r' U' L' U Rw' U2 r U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw2 U L U r U' L' U2 L U r' U' L' U Rw' U2 r U2 Rw' U2 Rw'
 
|sign=r U2 r2 U L U 2R U' L' U2 L U 2R' U' L' U r' U2 2R U2 r' U2 r'
 
|sign=r U2 r2 U L U 2R U' L' U2 L U 2R' U' L' U r' U2 2R U2 r' U2 r'
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/page-2#post-971016
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-useful-rw-r-u-parity-algorithms-for-4x4x4.45513/page-2#post-971016
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw2 U L' U r U' L U2 L' U r' U' L U Rw' U2 r U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw2 U L' U r U' L U2 L' U r' U' L U Rw' U2 r U2 Rw' U2 Rw'
 
|sign=r U2 r2 U L' U 2R U' L U2 L' U 2R' U' L U r' U2 2R U2 r' U2 r'
 
|sign=r U2 r2 U L' U 2R U' L U2 L' U 2R' U' L U r' U2 2R U2 r' U2 r'
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">2-Gen and "Semi 2-gen" algorithms</span>===
 
 
===2-Gen and "Semi 2-gen" algorithms===
 
 
*<u>2 Gen</u> (short for "2 generator") algorithms are algorithms which only use two different types of turns, such as r and U or Rw and U.
 
*<u>2 Gen</u> (short for "2 generator") algorithms are algorithms which only use two different types of turns, such as r and U or Rw and U.
*Several 2-gen algorithms in this section were found using Kåre Krig's "[[Ksolve]]" program or Ben Whitmore's [https://www.reddit.com/r/Cubers/comments/873vzw/ksolve_a_new_fast_general_puzzle_solving_program/ ksolve++ program]. They are move optimal.
+
*There are <i>five types</i> (move sets) of 2-gen parity algorithms which can exist on the 4x4x4.
 +
*Several 2-gen algorithms in this section were found using Kåre Krig's {{LinkColorI|p=Ksolve|c=rgb(229,148,0)|t=Ksolve}} program or Ben Whitmore's {{LinkColorE|u=https://www.reddit.com/r/Cubers/comments/873vzw/ksolve_a_new_fast_general_puzzle_solving_program/|c=rgb(229,148,0)|t=ksolve++ program}}.
 +
*Although all 2-gen algorithms in this section are move optimal in their respective move sets (with the exception of the algorithms in the move set <Rw, 3Uw>, whose optimal solution is unknown but of which Tom Rokicki established {{LinkColorE|u=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1301372|c=rgb(229,148,0)|t=a lowerbound of 50}} and {{LinkColorE|u=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1302197|c=rgb(229,148,0)|t=an upperbound of 87}} half turn moves in 2018), here is a {{LinkColorE|u=https://www.youtube.com/watch?v=Igb2zrmXV3M&list=PLo3YvnW-NFSrcq_E7bvy_RxOM16laESP9|c=rgb(229,148,0)|t=video tutorial}} by Christopher Mowla which shows how to create longer (but more humanly comprehensible) algorithms for all five types of 2-gen 4x4x4 single dedge flip algorithms by hand which are about double the length of optimal solutions in their respective move sets (on average).
 +
**The two exceptions to this general length trend (of being double move optimal in length) are algorithms for 'Type 3' (which Christopher later found {{LinkColorE|u=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1301743|c=rgb(229,148,0)|t=an algorithm}} for which is about double the move optimal length, after he uploaded the video series) and algorithms for 'Type 5'.
 +
***No humanly comprehensible algorithms close to optimal in length for the 'Type 5' 2-gen move set have been found; however, there are <i>short repeated sequences</i> which achieve a single dedge flip on the 4x4x4 in this move set at the end of the following list of algorithms.
 +
**All five types of 2-gen cases have been named according to which of the five types they are labelled as in this video series.
 +
{{br|b=1}}
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>2-Gen</b></span>
<b>2-Gen</b>
+
{{Alg6|wca=r U2 r' U2 r U2 r U r U r U2 r2 U2 r U2 r U r' U' r2 U2
{{Alg5|wca=r U2 r' U2 r U2 r U r U r U2 r2 U2 r U2 r U r' U' r2 U2
 
 
|sign=2R U2 2R' U2 2R U2 2R U 2R U 2R U2 2R2 U2 2R U2 2R U 2R' U' 2R2 U2
 
|sign=2R U2 2R' U2 2R U2 2R U 2R U 2R U2 2R2 U2 2R U2 2R U 2R' U' 2R2 U2
|length=(31,22)|name=|wide=N|author=Lucas Garron
+
|length=(31,22)|name=Type 1|wide=N|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
}}
 
}}
{{Alg5|wca=r U2 r' U2 r U2 r U' r U' r U2 r2 U2 r U2 r U' r' U r2 U2
+
{{Alg6|wca=r U2 r' U2 r U2 r U' r U' r U2 r2 U2 r U2 r U' r' U r2 U2
 
|sign=2R U2 2R' U2 2R U2 2R U' 2R U' 2R U2 2R2 U2 2R U2 2R U' 2R' U 2R2 U2
 
|sign=2R U2 2R' U2 2R U2 2R U' 2R U' 2R U2 2R2 U2 2R U2 2R U' 2R' U 2R2 U2
|length=(31,22)|name=|wide=N|author=Lucas Garron
+
|length=(31,22)|name=Type 1|wide=N|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
}}
 
}}
{{Alg5|wca=r2 U r' U' r U2 r U2 r2 U2 r U' r U' r U2 r U2 r' U2 r U2
+
{{Alg6|wca=r2 U r' U' r U2 r U2 r2 U2 r U' r U' r U2 r U2 r' U2 r U2
 
|sign=2R2 U 2R' U' 2R U2 2R U2 2R2 U2 2R U' 2R U' 2R U2 2R U2 2R' U2 2R U2
 
|sign=2R2 U 2R' U' 2R U2 2R U2 2R2 U2 2R U' 2R U' 2R U2 2R U2 2R' U2 2R U2
|length=(31,22)|name=|wide=N|author=Lucas Garron
+
|length=(31,22)|name=Type 1|wide=N|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
}}
 
}}
{{Alg5|wca=r2 U' r' U r U2 r U2 r2 U2 r U r U r U2 r U2 r' U2 r U2
+
{{Alg6|wca=r2 U' r' U r U2 r U2 r2 U2 r U r U r U2 r U2 r' U2 r U2
 
|sign=2R2 U' 2R' U 2R U2 2R U2 2R2 U2 2R U 2R U 2R U2 2R U2 2R' U2 2R U2
 
|sign=2R2 U' 2R' U 2R U2 2R U2 2R2 U2 2R U 2R U 2R U2 2R U2 2R' U2 2R U2
|length=(31,22)|name=|wide=N|author=Lucas Garron
+
|length=(31,22)|name=Type 1|wide=N|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
}}
 
}}
{{Alg5|wca=y' Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U' Rw U Rw' U' Rw U2 Rw' U2 y
+
{{Alg6|wca=y' Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U' Rw U Rw' U' Rw U2 Rw' U2 y
 
|sign=y' r' U' r U' r U r2 U' r2 U2 r U2 r' U2 r U2 r U' r U r' U' r U2 r' U2 y
 
|sign=y' r' U' r U' r U r2 U' r2 U2 r U2 r' U2 r U2 r U' r U r' U' r U2 r' U2 y
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
+
|length=(34,26)|name=Type 4|wide=Y|author=Bruce Norskog
 
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
 
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
 
}}
 
}}
{{Alg5|wca=y' Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U Rw U Rw' U' Rw U2 Rw' U2 y
+
{{Alg6|wca=y' Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U Rw U Rw' U' Rw U2 Rw' U2 y
 
|sign=y' r' U' r U' r U' r2 U2 r2 U' r U2 r' U2 r U2 r U r U r' U' r U2 r' U2 y
 
|sign=y' r' U' r U' r U' r2 U2 r2 U' r U2 r' U2 r U2 r U r U r' U' r U2 r' U2 y
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
+
|length=(34,26)|name=Type 4|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y Rw' U2 Rw U' Rw' U Rw U Rw U2 Rw U2 Rw' U2 Rw U' Rw2 U2 Rw2 U' Rw U' Rw U' Rw' U2 y'
+
{{Alg6|wca=y Rw' U2 Rw U' Rw' U Rw U Rw U2 Rw U2 Rw' U2 Rw U' Rw2 U2 Rw2 U' Rw U' Rw U' Rw' U2 y'
 
|sign=y r' U2 r U' r' U r U r U2 r U2 r' U2 r U' r2 U2 r2 U' r U' r U' r' U2 y'
 
|sign=y r' U2 r U' r' U r U r U2 r U2 r' U2 r U' r2 U2 r2 U' r U' r U' r' U2 y'
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
+
|length=(34,26)|name=Type 4|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y Rw' U2 Rw U' Rw' U Rw U' Rw U2 Rw U2 Rw' U2 Rw U2 Rw2 U' Rw2 U Rw U' Rw U' Rw' U2 y'
+
{{Alg6|wca=y Rw' U2 Rw U' Rw' U Rw U' Rw U2 Rw U2 Rw' U2 Rw U2 Rw2 U' Rw2 U Rw U' Rw U' Rw' U2 y'
 
|sign=y r' U2 r U' r' U r U' r U2 r U2 r' U2 r U2 r2 U' r2 U r U' r U' r' U2 y'
 
|sign=y r' U2 r U' r' U r U' r U2 r U2 r' U2 r U2 r2 U' r2 U r U' r U' r' U2 y'
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
+
|length=(34,26)|name=Type 4|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=
+
{{Alg6|wca=
 
r2 Uw2 r' Uw r Uw2 r Uw r Uw r Uw' r' Uw' r Uw r Uw r' Uw2 r2 Uw2 r' Uw' r Uw2 r2
 
r2 Uw2 r' Uw r Uw2 r Uw r Uw r Uw' r' Uw' r Uw r Uw r' Uw2 r2 Uw2 r' Uw' r Uw2 r2
 
|sign=2R2 u2 2R' u 2R u2 2R u 2R u 2R u' 2R' u' 2R u 2R u 2R' u2 2R2 u2 2R' u' 2R u2 2R2
 
|sign=2R2 u2 2R' u 2R u2 2R u 2R u 2R u' 2R' u' 2R u 2R u 2R' u2 2R2 u2 2R' u' 2R u2 2R2
|length=(35,27)|name=|wide=Y|author=Ben Whitmore
+
|length=(35,27)|name=Type 3|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_u_/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_u_/index.html
 
}}
 
}}
{{Alg5|wca=r 3Uw r2 3Uw2 r2 3Uw2 r 3Uw' r 3Uw r 3Uw r' 3Uw' r' 3Uw' r' 3Uw r' 3Uw2 r2 3Uw2 r2 3Uw' r 3Uw2 r2 3Uw2 r2
+
{{Alg6|wca=r 3Uw r2 3Uw2 r2 3Uw2 r 3Uw' r 3Uw r 3Uw r' 3Uw' r' 3Uw' r' 3Uw r' 3Uw2 r2 3Uw2 r2 3Uw' r 3Uw2 r2 3Uw2 r2
 
|sign=2R 3u 2R2 3u2 2R2 3u2 2R 3u' 2R 3u 2R 3u 2R' 3u' 2R' 3u' 2R' 3u 2R' 3u2 2R2 3u2 2R2 3u' 2R 3u2 2R2 3u2 2R2
 
|sign=2R 3u 2R2 3u2 2R2 3u2 2R 3u' 2R 3u 2R 3u 2R' 3u' 2R' 3u' 2R' 3u 2R' 3u2 2R2 3u2 2R2 3u' 2R 3u2 2R2 3u2 2R2
|length=(40,29)|name=|wide=N|author=Ben Whitmore
+
|length=(40,29)|name=Type 2|wide=N|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_3u/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_3u/index.html
 
}}
 
}}
{{Alg5|wca=r2 3Uw r 3Uw2 r 3Uw2 r' 3Uw r 3Uw r' 3Uw2 r 3Uw2 r2 3Uw2 r' 3Uw2 r' 3Uw' r' 3Uw' r 3Uw2 r2 3Uw2 r' 3Uw' r2
+
{{Alg6|wca=r2 3Uw r 3Uw2 r 3Uw2 r' 3Uw r 3Uw r' 3Uw2 r 3Uw2 r2 3Uw2 r' 3Uw2 r' 3Uw' r' 3Uw' r 3Uw2 r2 3Uw2 r' 3Uw' r2
 
|sign=2R2 3u 2R 3u2 2R 3u2 2R' 3u 2R 3u 2R' 3u2 2R 3u2 2R2 3u2 2R' 3u2 2R' 3u' 2R' 3u' 2R 3u2 2R2 3u2 2R' 3u' 2R2
 
|sign=2R2 3u 2R 3u2 2R 3u2 2R' 3u 2R 3u 2R' 3u2 2R 3u2 2R2 3u2 2R' 3u2 2R' 3u' 2R' 3u' 2R 3u2 2R2 3u2 2R' 3u' 2R2
|length=(40,29)|name=5x5x5 Alg|wide=N|author=Ben Whitmore
+
|length=(40,29)|name=Type 2 (5x5x5 Alg)|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/873vzw/ksolve_a_new_fast_general_puzzle_solving_program/dwds4sy/
 
|url=https://www.reddit.com/r/Cubers/comments/873vzw/ksolve_a_new_fast_general_puzzle_solving_program/dwds4sy/
 
}}
 
}}
{{Alg5|wca=y Rw U Rw2 U' Rw U' Rw' U Rw U' Rw2 U2 Rw' U2 Rw U2 Rw' U Rw2 U' Rw U Rw' U' Rw U2 Rw U2 Rw2 U Rw' U' Rw' y'
+
{{Alg6|wca=y Rw U Rw2 U' Rw U' Rw' U Rw U' Rw2 U2 Rw' U2 Rw U2 Rw' U Rw2 U' Rw U Rw' U' Rw U2 Rw U2 Rw2 U Rw' U' Rw' y'
 
|sign=y r U r2 U' r U' r' U r U' r2 U2 r' U2 r U2 r' U r2 U' r U r' U' r U2 r U2 r2 U r' U' r' y'
 
|sign=y r U r2 U' r U' r' U r U' r2 U2 r' U2 r U2 r' U r2 U' r U r' U' r U2 r U2 r2 U r' U' r' y'
|length=(42,33)|name=5x5x5 Alg
+
|length=(42,33)|name=Type 4 (5x5x5 Alg)
 
|wide=Y|author=Ben Whitmore
 
|wide=Y|author=Ben Whitmore
 
|url=
 
|url=
 
}}
 
}}
 +
{{Alg6|wca=(Rw' 3Uw Rw 3Uw' Rw' 3Uw' Rw 3Uw Rw 3Uw' Rw' 3Uw Rw 3Uw Rw2 3Uw' Rw 3Uw Rw 3Uw Rw' 3Uw Rw 3Uw2 Rw 3Uw Rw 3Uw2 Rw' 3Uw Rw)3
 +
|sign=(r' 3u r 3u' r' 3u' r 3u r 3u' r' 3u r 3u r2 3u' r 3u r 3u r' 3u r 3u2 r 3u r 3u2 r' 3u r)3
 +
|length=(98,87)|name=Type 5|wide=Y|author=Tom Rokicki
 +
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1302197
 +
}}
 +
{{Alg6|wca=(3Uw Rw' 3Uw2 Rw2 3Uw2 Rw 3Uw' Rw 3Uw2 Rw 3Uw2 Rw' 3Uw2 Rw' 3Uw' Rw' 3Uw2 Rw 3Uw Rw' 3Uw2 Rw 3Uw' Rw2 3Uw2 Rw' 3Uw Rw2 3Uw Rw2 3Uw' Rw2 3Uw Rw2)3
 +
|sign=
 +
(3u r' 3u2 r2 3u2 r 3u' r 3u2 r 3u2 r' 3u2 r' 3u' r' 3u2 r 3u r' 3u2 r 3u' r2 3u2 r' 3u r2 3u r2 3u' r2 3u r2)3
 +
|length=(144,102)|name=Type 5|wide=Y|author=xyzzy
 +
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-3#post-1301191
 +
}}
 +
{{Alg6|wca=z' (3Uw' Rw2 3Uw2 Rw2 3Uw2 Rw 3Uw2 Rw' 3Uw2 Rw)15 z
 +
|sign=z' (3u' r2 3u2 r2 3u2 r 3u2 r' 3u2 r)15 z
 +
|length=(240,150)|name=Type 5|wide=Y|author=Christopher Mowla
 +
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1301785
 +
}}
 +
{{Alg6|wca=(3Uw2 Rw 3Uw Rw 3Uw2 Rw' 3Uw' Rw 3Uw Rw)315
 +
|sign=(3u2 r 3u r 3u2 r' 3u' r 3u r)315
 +
|length=(3780,3150)|name=Type 5|wide=Y|author=Tom Rokicki
 +
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1301747
 +
}}
 +
{{Alg6|wca=z (3Uw' Rw2 3Uw Rw 3Uw' Rw' 3Uw2 Rw)585 z'
 +
|sign=z (3u' r2 3u r 3u' r' 3u2 r)585 z'
 +
|length=(5850,4680)|name=Type 5|wide=Y|author=Christopher Mowla
 +
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-4#post-1301785
 +
}}
 +
{{br|b=1}}
  
<b>Semi 2-Gen</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Semi 2-Gen</b></span>
{{Alg5|wca=Rw U2 Rw U Rw U2 Rw U2 Rw' U2 Rw' U r' U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U Rw U2 Rw U2 Rw' U2 Rw' U r' U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw' U2 Rw'
 
|sign=r U2 r U r U2 r U2 r' U2 r' U 2R' U' r U2 r U2 r' U2 r' U 2R2 U2 r' U2 r'
 
|sign=r U2 r U r U2 r U2 r' U2 r' U 2R' U' r U2 r U2 r' U2 r' U 2R2 U2 r' U2 r'
 
|length=(37,27)|name=|wide=N|author=Christopher Mowla
 
|length=(37,27)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-497777
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-497777
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U' Rw U2 Rw U2 Rw' U2 Rw' U' r' U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U' Rw U2 Rw U2 Rw' U2 Rw' U' r' U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw' U2 Rw'
 
|sign=r U2 r U' r U2 r U2 r' U2 r' U' 2R' U r U2 r U2 r' U2 r' U' 2R2 U2 r' U2 r'
 
|sign=r U2 r U' r U2 r U2 r' U2 r' U' 2R' U r U2 r U2 r' U2 r' U' 2R2 U2 r' U2 r'
 
|length=(37,27)|name=|wide=N|author=Christopher Mowla
 
|length=(37,27)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
===4x4x4 supercube safe algorithms===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">4x4x4 supercube safe algorithms</span>===
 
*All of the algorithms in this section "prove" that one can just switch two 4x4x4 supercube wing edges without affecting its centers.
 
*All of the algorithms in this section "prove" that one can just switch two 4x4x4 supercube wing edges without affecting its centers.
 
+
{{br|b=1}}
 
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
This is not true for the nxnxn supercube in general, but there is a {{LinkColorE|u=https://www.speedsolving.com/forum/threads/theory-about-big-cube-parity.49062/#post-1010936|c=rgb(229,148,0)|t=mathematically quantifiable minimum number}} of center pieces which must be switched along with two wing edges, for example, of the 5x5x5 and larger nxnxn supercubes.
| bgcolor="fbfb8b" |
+
</ul>
This is not true for the nxnxn supercube, in general; but there is a [https://www.speedsolving.com/forum/threads/theory-about-big-cube-parity.49062/#post-1010936 mathematically quantifiable minimum number] of center pieces which must be switched along with two wing edges, for example, of the 5x5x5 and larger nxnxn supercubes.
+
{{br|b=1}}
|}
+
{{super4|wca=r' U' u r U' r U r u' r' u r U r U' r Uw' r' U2 //Safe
 
+
|sign=2R' U' 2U 2R U' 2R U 2R 2U' 2R' 2U 2R U 2R U' 2R u' 2R' U2
 
 
{{Alg5|wca=r' U' u r U' r U r u' r' u r U r U' r Uw' r' U2//Safe
 
|sign=2R' U' 2U 2R U' 2R U 2R 2U' 2R' 2U 2R U 2R U' 2R u' 2R' U2//Safe
 
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=r' Uw' r U' r U r u r' u' r U r U' r u U' r' U2//Safe
+
{{super4|wca=r' Uw' r U' r U r u r' u' r U r U' r u U' r' U2 //Safe
|sign=2R' u' 2R U' 2R U 2R 2U 2R' 2U' 2R U 2R U' 2R 2U U' 2R' U2//Safe
+
|sign=2R' u' 2R U' 2R U 2R 2U 2R' 2U' 2R U 2R U' 2R 2U U' 2R' U2
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=r' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U r//Safe
+
{{super4|wca=r' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U r //Safe
|sign=2R' U2 2R' U' 2R U 2R U 2R' D' 2F2 2R 2F2 2R' D U2 2R' U 2R U 2R U 2R//Safe
+
|sign=2R' U2 2R' U' 2R U 2R U 2R' D' 2F2 2R 2F2 2R' D U2 2R' U 2R U 2R U 2R
 
|length=(27,23)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
|length=(27,23)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
}}
 
}}
{{Alg5|wca=Rw2 U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw2 x'//Safe
+
{{super4|wca=Rw2 U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw2 x' //Safe
|sign=r2 U2 2R' U2 2R' U' 2L 2R 2U2 2L' 2R' U 2L 2R 2U2 x U2 2L' U2 2R U2 2R' U2 r2 x'//Safe
+
|sign=r2 U2 2R' U2 2R' U' 2L 2R 2U2 2L' 2R' U 2L 2R 2U2 x U2 2L' U2 2R U2 2R' U2 r2 x'
 
|length=(33,23)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(33,23)|name=|wide=N|author=Per Kristen Fredlund
 
|url=https://www.speedsolving.com/forum/threads/big-cubes-parity.4044/page-2#post-51209
 
|url=https://www.speedsolving.com/forum/threads/big-cubes-parity.4044/page-2#post-51209
 
}}
 
}}
{{Alg5|wca=r2 U (r2 U2)2 (r' U)2 r' (U2 r2)2 U' r U' (r U2)3 r U' r U2 r2//Safe
+
{{super4|wca=r2 U (r2 U2)2 (r' U)2 r' (U2 r2)2 U' r U' (r U2)3 r U' r U2 r2 //Safe
|sign=2R2 U (2R2 U2)2 (2R' U)2 2R' (U2 2R2)2 U' 2R U' (2R U2)3 2R U' 2R U2 2R2//Safe
+
|sign=2R2 U 2R2 U2 2R2 U2 2R' U 2R' U 2R' U2 2R2 U2 2R2 U' 2R U' 2R U2 2R U2 2R U2 2R U' 2R U2 2R2
 
|length=(42,29)|name=|wide=N|author=Ben Whitmore
 
|length=(42,29)|name=|wide=N|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_U/index.html
 
}}
 
}}
{{Alg5|wca=(Rw' U')(U' r2 U Rw (r2 u r2 u') U' r' U Rw')3 (U Rw)//Safe
+
{{super4|wca=(Rw' U')(U' r2 U Rw (r2 u r2 u') U' r' U Rw')3 (U Rw) //Safe
|sign=(r' U')(U' 2R2 U r (2R2 2U 2R2 2U') U' 2R' U r')3 (U r)//Safe
+
|sign=r' U2 2R2 U r 2R2 2U 2R2 u' 2R' U r' U' 2R2 U r 2R2 2U 2R2 u' 2R' U r' U' 2R2 U r 2R2 2U 2R2 u' 2R' U r' U r
 
|length=(43,36)|name=|wide=N|author=Christopher Mowla
 
|length=(43,36)|name=|wide=N|author=Christopher Mowla
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374338#p374338
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374338#p374338
 
}}
 
}}
 +
{{br|b=1}}
  
==Three dedge flips==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Three dedge flips</span>==
===In the last layer===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">In the last layer</span>===
 
[[Image:Ollpo3flip.png|110px|]]
 
[[Image:Ollpo3flip.png|110px|]]
{{Alg5|wca=u2 f' U f2 Lw2 U2 f U2 B2 Lw2 f2 U f u2 Lw2 B2 Lw2
+
{{Alg6|wca=u2 f' U f2 Lw2 U2 f U2 B2 Lw2 f2 U f u2 Lw2 B2 Lw2
 
|sign=2U2 2F' U 2F2 l2 U2 2F U2 B2 l2 2F2 U 2F 2U2 l2 B2 l2
 
|sign=2U2 2F' U 2F2 l2 U2 2F U2 B2 l2 2F2 U 2F 2U2 l2 B2 l2
 
|length=(29,17)|name=|wide=N|author=Clément Gallet
 
|length=(29,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 b' U' (L2 f2)2 U b U f' U2 (f M2)2 U R2
+
{{Alg6|wca=R2 b' U' (L2 f2)2 U b U f' U2 (f M2)2 U R2
 
|sign=R2 2B' U' (L2 2F2)2 U 2B U 2F' U2 (2F m2)2 U R2
 
|sign=R2 2B' U' (L2 2F2)2 U 2B U 2F' U2 (2F m2)2 U R2
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D' R2
+
{{Alg6|wca=R2 D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D' R2
 
|sign=R2 D' 2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D' R2
 
|sign=R2 D' 2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D' R2
 
|length=(29,18)|name=|wide=N|author=Walter Randelshofer
 
|length=(29,18)|name=|wide=N|author=Walter Randelshofer
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350729#p350729
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350729#p350729
 
}}
 
}}
{{Alg5|wca=y M U r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2 U' M' y'
+
{{Alg6|wca=y M U r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2 U' M' y'
 
|sign=y m U 2R B2 2L' D2 2L' B2 2R2 B2 U2 2L' D2 2L U2 2L2 B2 U' m' y'
 
|sign=y m U 2R B2 2L' D2 2L' B2 2R2 B2 U2 2L' D2 2L U2 2L2 B2 U' m' y'
 
|length=(29,19)|name=|wide=N|author=|url=
 
|length=(29,19)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=y M U r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2 U' M' y'
+
{{Alg6|wca=y M U r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2 U' M' y'
 
|sign=y m U 2R2 D2 2R' U2 2R D2 B2 2L2 B2 2R U2 2R B2 2L' B2 U' m' y'
 
|sign=y m U 2R2 D2 2R' U2 2R D2 B2 2L2 B2 2R U2 2R B2 2L' B2 U' m' y'
 
|length=(29,19)|name=|wide=N|author=|url=
 
|length=(29,19)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=M2' U' x' r2 U2 M r' U2 r F2 U2 r2 U2 M' r x U2 r U2 r' U' M2'
+
{{Alg6|wca=M2' U' x' r2 U2 M r' U2 r F2 U2 r2 U2 M' r x U2 r U2 r' U' M2'
 
|sign=m2' U' x' 2R2 U2 m 2R' U2 2R F2 U2 2R2 U2 m' 2R x U2 2R U2 2R' U' m2'
 
|sign=m2' U' x' 2R2 U2 m 2R' U2 2R F2 U2 2R2 U2 m' 2R x U2 2R U2 2R' U' m2'
 
|length=(31,20)|name=|wide=N|author=|url=
 
|length=(31,20)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=y M U l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r' U' M' y'
+
{{Alg6|wca=y M U l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r' U' M' y'
 
|sign=y m U 2L 2R F2 2L B 2U' B D2 B' 2U B 2R' D2 B2 2L2 F2 2R' U' m' y'
 
|sign=y m U 2L 2R F2 2L B 2U' B D2 B' 2U B 2R' D2 B2 2L2 F2 2R' U' m' y'
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M U l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r' U' M' y'
+
{{Alg6|wca=y M U l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r' U' M' y'
 
|sign=y m U 2L 2R F2 2L B' 2D' B' D2 B 2D B' 2R' D2 B2 2L2 F2 2R' U' m' y'
 
|sign=y m U 2L 2R F2 2L B' 2D' B' D2 B 2D B' 2R' D2 B2 2L2 F2 2R' U' m' y'
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M U r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2 U' M' y'
+
{{Alg6|wca=y M U r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2 U' M' y'
 
|sign=y m U 2R' D2 2L' 2R' B2 D2 2L' B 2U B' D2 B 2U' B 2L D2 2R2 U' m' y'
 
|sign=y m U 2R' D2 2L' 2R' B2 D2 2L' B 2U B' D2 B 2U' B 2L D2 2R2 U' m' y'
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M U r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2 U' M' y'
+
{{Alg6|wca=y M U r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2 U' M' y'
 
|sign=y m U 2R' D2 2L' 2R' B2 D2 2L' B' 2D B D2 B' 2D' B' 2L D2 2R2 U' m' y'
 
|sign=y m U 2R' D2 2L' 2R' B2 D2 2L' B' 2D B D2 B' 2D' B' 2L D2 2R2 U' m' y'
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M U l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r U' M' y'
+
{{Alg6|wca=y M U l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r U' M' y'
 
|sign=y m U 2L' 2R' U2 2L' D' 2F D' B2 D 2F' D' 2R B2 D2 2L2 U2 2R U' m' y'
 
|sign=y m U 2L' 2R' U2 2L' D' 2F D' B2 D 2F' D' 2R B2 D2 2L2 U2 2R U' m' y'
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M U l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r U' M' y'
+
{{Alg6|wca=y M U l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r U' M' y'
 
|sign=y m U 2L' 2R' U2 2L' D 2B D B2 D' 2B' D 2R B2 D2 2L2 U2 2R U' m' y'
 
|sign=y m U 2L' 2R' U2 2L' D 2B D B2 D' 2B' D 2R B2 D2 2L2 U2 2R U' m' y'
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|length=(27,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U Rw U2 Rw U2 Rw U Rw' U2 r' U2 Rw' U Rw U2 Rw U2 Rw U Rw
+
{{Alg6|wca=Rw U Rw U2 Rw U2 Rw U Rw' U2 r' U2 Rw' U Rw U2 Rw U2 Rw U Rw
 
|sign=r U r U2 r U2 r U r' U2 2R' U2 r' U r U2 r U2 r U r
 
|sign=r U r U2 r U2 r U r' U2 2R' U2 r' U r U2 r U2 r U r
 
|length=(27,21)|name=v1
 
|length=(27,21)|name=v1
Line 5,477: Line 5,729:
 
|url=http://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/
 
|url=http://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/
 
}}
 
}}
{{Alg5|wca=Rw' U' Rw' U2 Rw' U2 Rw' U' Rw U2 r U2 Rw U' Rw' U2 Rw' U2 Rw' U' Rw'
+
{{Alg6|wca=Rw' U' Rw' U2 Rw' U2 Rw' U' Rw U2 r U2 Rw U' Rw' U2 Rw' U2 Rw' U' Rw'
 
|sign=r' U' r' U2 r' U2 r' U' r U2 2R U2 r U' r' U2 r' U2 r' U' r'
 
|sign=r' U' r' U2 r' U2 r' U' r U2 2R U2 r U' r' U2 r' U2 r' U' r'
 
|length=(27,21)|name=v2
 
|length=(27,21)|name=v2
Line 5,483: Line 5,735:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw2 F2 Lw' U' L U Lw U2 Lw' U' L' U' l' U2 Lw' F2 l F2 Lw' U2 Lw' l' F2 Uw2
+
{{Alg6|wca=Rw U' R' U' r U' R U' r2 U R' U r' U R U r U2 r' U2 Rw' r'
 +
|sign=r U' R' U' 2R U' R U' 2R2 U R' U 2R' U R U 2R U2 2R' U2 r' 2R'
 +
|length=(25,22)|name=|wide=N|author=Ben Whitmore
 +
|url=
 +
}}
 +
{{Alg6|wca=Uw2 F2 Lw' U' L U Lw U2 Lw' U' L' U' l' U2 Lw' F2 l F2 Lw' U2 Lw' l' F2 Uw2
 
|sign=u2 F2 l' U' L U l U2 l' U' L' U' 2L' U2 l' F2 2L F2 l' U2 l' 2L' F2 u2
 
|sign=u2 F2 l' U' L U l U2 l' U' L' U' 2L' U2 l' F2 2L F2 l' U2 l' 2L' F2 u2
 
|length=(33,24)|name=|wide=N|author=Christopher Mowla
 
|length=(33,24)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw2 B2 Lw U L' U' Lw' U2 Lw U L U l U2 Lw B2 l' B2 Lw U2 Lw l B2 Uw2
+
{{Alg6|wca=Uw2 B2 Lw U L' U' Lw' U2 Lw U L U l U2 Lw B2 l' B2 Lw U2 Lw l B2 Uw2
 
|sign=u2 B2 l U L' U' l' U2 l U L U 2L U2 l B2 2L' B2 l U2 l 2L B2 u2
 
|sign=u2 B2 l U L' U' l' U2 l U L U 2L U2 l B2 2L' B2 l U2 l 2L B2 u2
 
|length=(33,24)|name=|wide=N|author=Christopher Mowla
 
|length=(33,24)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R2 f' U2 b L2 b' L2 f2 U2 f U2 f' U2 L2 b2 U' S2 L2 S L2 U L2 S' R2
+
{{Alg6|wca=R2 f' U2 b L2 b' L2 f2 U2 f U2 f' U2 L2 b2 U' S2 L2 S L2 U L2 S' R2
 
|sign=R2 2F' U2 2B L2 2B' L2 2F2 U2 2F U2 2F' U2 L2 2B2 U' s2 L2 s L2 U L2 s' R2
 
|sign=R2 2F' U2 2B L2 2B' L2 2F2 U2 2F U2 2F' U2 L2 2B2 U' s2 L2 s L2 U L2 s' R2
 
|length=(39,24)|name=|wide=N|author=André Boulouard
 
|length=(39,24)|name=|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M2' U' l U2 r' F2 r D2 F2 r F2 r' Dw2 l r U' l' r' d2 l r U l M F2 l U' M2'//Safe
+
{{Alg6|wca=M2' U' l U2 r' F2 r D2 F2 r F2 r' Dw2 l r U' l' r' d2 l r U l M F2 l U' M2' //Safe
|sign=m2' U' 2L U2 2R' F2 2R D2 F2 2R F2 2R' d2 2L 2R U' 2L' 2R' 2D2 2L 2R U 2L m F2 2L U' m2'//Safe
+
|sign=m2' U' 2L U2 2R' F2 2R D2 F2 2R F2 2R' d2 2L 2R U' 2L' 2R' 2D2 2L 2R U 2L m F2 2L U' m2' //Safe
 
|length=(38,28)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(38,28)|name=|wide=N|author=Per Kristen Fredlund
 
|url=https://www.speedsolving.com/forum/threads/big-cubes-parity.4044/page-2#post-51209
 
|url=https://www.speedsolving.com/forum/threads/big-cubes-parity.4044/page-2#post-51209
 
}}
 
}}
{{Alg5|wca=M2' U' r' U2 l F2 l' D2 F2 l' F2 l Dw2 l' r' U l r d2 l' r' U' r' M F2 r' U' M2'//Safe
+
{{Alg6|wca=M2' U' r' U2 l F2 l' D2 F2 l' F2 l Dw2 l' r' U l r d2 l' r' U' r' M F2 r' U' M2' //Safe
|sign=m2' U' 2R' U2 2L F2 2L' D2 F2 2L' F2 2L d2 2L' 2R' U 2L 2R 2D2 2L' 2R' U' 2R' m F2 2R' U' m2'//Safe
+
|sign=m2' U' 2R' U2 2L F2 2L' D2 F2 2L' F2 2L d2 2L' 2R' U 2L 2R 2D2 2L' 2R' U' 2R' m F2 2R' U' m2' //Safe
 
|length=(38,28)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(38,28)|name=|wide=N|author=Per Kristen Fredlund
 
|url=https://www.speedsolving.com/forum/threads/big-cubes-parity.4044/page-2#post-51209
 
|url=https://www.speedsolving.com/forum/threads/big-cubes-parity.4044/page-2#post-51209
 
}}
 
}}
{{Alg5|wca=L R U2 L' R' U' L R U2 L2 x' U B2 r2 U2 r D2 r' U2 x' U2 l2 U2 r' B2 r' U2 x l U' M' U'//Safe
+
{{Alg6|wca=L R U2 L' R' U' L R U2 L2 x' U B2 r2 U2 r D2 r' U2 x' U2 l2 U2 r' B2 r' U2 x l U' M' U' //Safe
|sign=L R U2 L' R' U' L R U2 L2 x' U B2 2R2 U2 2R D2 2R' U2 x' U2 2L2 U2 2R' B2 2R' U2 x 2L U' m' U'//Safe
+
|sign=L R U2 L' R' U' L R U2 L2 x' U B2 2R2 U2 2R D2 2R' U2 x' U2 2L2 U2 2R' B2 2R' U2 x 2L U' m' U' //Safe
 
|length=(42,29)|name=|wide=N|author=François Courtès
 
|length=(42,29)|name=|wide=N|author=François Courtès
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y Rw U Rw2 U2 Rw2 U Rw' U Rw2 U Rw2 U2 Rw U' Rw' U' Rw U' Rw U' Rw U' Rw' U2 Rw' U2 Rw U2 Rw2 U2 Rw' y'
+
{{Alg6|wca=y Rw U Rw2 U2 Rw2 U Rw' U Rw2 U Rw2 U2 Rw U' Rw' U' Rw U' Rw U' Rw U' Rw' U2 Rw' U2 Rw U2 Rw2 U2 Rw' y'
 
|sign=y r U r2 U2 r2 U r' U r2 U r2 U2 r U' r' U' r U' r U' r U' r' U2 r' U2 r U2 r2 U2 r' y'
 
|sign=y r U r2 U2 r2 U r' U r2 U r2 U2 r U' r' U' r U' r U' r U' r' U2 r' U2 r U2 r2 U2 r' y'
 
|length=(42,31)|name=|wide=Y|author=Ben Whitmore
 
|length=(42,31)|name=|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
}}
 
}}
{{Alg5|wca=y2 3Uw' r2 3Uw2 r 3Uw' r' 3Uw2 r2 3Uw2 r' 3Uw2 r 3Uw2 r' 3Uw2 r2 3Uw2 r2 3Uw2 r2 3Uw2 r 3Uw2 r' 3Uw2 r2 3Uw2 r 3Uw' r' 3Uw2 r2 3Uw y2
+
{{Alg6|wca=y2 3Uw' r2 3Uw2 r 3Uw' r' 3Uw2 r2 3Uw2 r' 3Uw2 r 3Uw2 r' 3Uw2 r2 3Uw2 r2 3Uw2 r2 3Uw2 r 3Uw2 r' 3Uw2 r2 3Uw2 r 3Uw' r' 3Uw2 r2 3Uw y2
 
|sign=y2 3u' 2R2 3u2 2R 3u' 2R' 3u2 2R2 3u2 2R' 3u2 2R 3u2 2R' 3u2 2R2 3u2 2R2 3u2 2R2 3u2 2R 3u2 2R' 3u2 2R2 3u2 2R 3u' 2R' 3u2 2R2 3u y2
 
|sign=y2 3u' 2R2 3u2 2R 3u' 2R' 3u2 2R2 3u2 2R' 3u2 2R 3u2 2R' 3u2 2R2 3u2 2R2 3u2 2R2 3u2 2R 3u2 2R' 3u2 2R2 3u2 2R 3u' 2R' 3u2 2R2 3u y2
 
|length=(53,33)|name=|wide=N|author=Ben Whitmore
 
|length=(53,33)|name=|wide=N|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_3u/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_3u/index.html
 
}}
 
}}
 
+
{{br|b=1}}
===In the M layer===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">In the M layer</span>===
 
[[Image:3SingleParityDedgeFlipInM.png|110px|]]
 
[[Image:3SingleParityDedgeFlipInM.png|110px|]]
{{Alg5|wca=r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2
+
{{Alg6|wca=r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2
 
|sign=2R B2 2L' D2 2L' B2 2R2 B2 U2 2L' D2 2L U2 2L2 B2
 
|sign=2R B2 2L' D2 2L' B2 2R2 B2 U2 2L' D2 2L U2 2L2 B2
 
|length=(25,15)|name=|wide=N|author=|Alg.1
 
|length=(25,15)|name=|wide=N|author=|Alg.1
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2
+
{{Alg6|wca=l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2
 
|sign=2L' B2 2R D2 2R B2 2L2 B2 U2 2R D2 2R' U2 2R2 B2
 
|sign=2L' B2 2R D2 2R B2 2L2 B2 U2 2R D2 2R' U2 2R2 B2
 
|length=(25,15)|name=|wide=N|author=|Mirror[Alg.1]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Alg.1]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=B2 l2 U2 l' D2 l U2 B2 r2 B2 l D2 l B2 r'
+
{{Alg6|wca=B2 l2 U2 l' D2 l U2 B2 r2 B2 l D2 l B2 r'
 
|sign=B2 2L2 U2 2L' D2 2L U2 B2 2R2 B2 2L D2 2L B2 2R'
 
|sign=B2 2L2 U2 2L' D2 2L U2 B2 2R2 B2 2L D2 2L B2 2R'
 
|length=(25,15)|name=|wide=N|author=|Inverse[Alg.1]
 
|length=(25,15)|name=|wide=N|author=|Inverse[Alg.1]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D2
+
{{Alg6|wca=l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D2
 
|sign=2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D2
 
|sign=2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D2
 
|length=(25,15)|name=|wide=N|author=|Rotation[Alg.1]
 
|length=(25,15)|name=|wide=N|author=|Rotation[Alg.1]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=B2 r2 U2 r D2 r' U2 B2 l2 B2 r' D2 r' B2 l
+
{{Alg6|wca=B2 r2 U2 r D2 r' U2 B2 l2 B2 r' D2 r' B2 l
 
|sign=B2 2R2 U2 2R D2 2R' U2 B2 2L2 B2 2R' D2 2R' B2 2L
 
|sign=B2 2R2 U2 2R D2 2R' U2 B2 2L2 B2 2R' D2 2R' B2 2L
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Alg.1]]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Alg.1]]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l B2 l D2 r2 D2 F2 l B2 l' F2 l2 D2
+
{{Alg6|wca=r' D2 l B2 l D2 r2 D2 F2 l B2 l' F2 l2 D2
 
|sign=2R' D2 2L B2 2L D2 2R2 D2 F2 2L B2 2L' F2 2L2 D2
 
|sign=2R' D2 2L B2 2L D2 2R2 D2 F2 2L B2 2L' F2 2L2 D2
 
|length=(25,15)|name=|wide=N|author=|Mirror[Rotation[Alg.1]]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Rotation[Alg.1]]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=D2 r2 F2 r' B2 r F2 D2 l2 D2 r B2 r D2 l'
+
{{Alg6|wca=D2 r2 F2 r' B2 r F2 D2 l2 D2 r B2 r D2 l'
 
|sign=D2 2R2 F2 2R' B2 2R F2 D2 2L2 D2 2R B2 2R D2 2L'
 
|sign=D2 2R2 F2 2R' B2 2R F2 D2 2L2 D2 2R B2 2R D2 2L'
 
|length=(25,15)|name=|wide=N|author=|Inverse[Rotation[Alg.1]]
 
|length=(25,15)|name=|wide=N|author=|Inverse[Rotation[Alg.1]]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=D2 l2 F2 l B2 l' F2 D2 r2 D2 l' B2 l' D2 r
+
{{Alg6|wca=D2 l2 F2 l B2 l' F2 D2 r2 D2 l' B2 l' D2 r
 
|sign=D2 2L2 F2 2L B2 2L' F2 D2 2R2 D2 2L' B2 2L' D2 2R
 
|sign=D2 2L2 F2 2L B2 2L' F2 D2 2R2 D2 2L' B2 2L' D2 2R
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Rotation[Alg.1]]]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Rotation[Alg.1]]]
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2
+
{{Alg6|wca=r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2
 
|sign=2R2 D2 2R' U2 2R D2 B2 2L2 B2 2R U2 2R B2 2L' B2
 
|sign=2R2 D2 2R' U2 2R D2 B2 2L2 B2 2R U2 2R B2 2L' B2
 
|length=(25,15)|name=|wide=N|author=|Alg.2
 
|length=(25,15)|name=|wide=N|author=|Alg.2
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l U2 l' D2 B2 r2 B2 l' U2 l' B2 r B2
+
{{Alg6|wca=l2 D2 l U2 l' D2 B2 r2 B2 l' U2 l' B2 r B2
 
|sign=2L2 D2 2L U2 2L' D2 B2 2R2 B2 2L' U2 2L' B2 2R B2
 
|sign=2L2 D2 2L U2 2L' D2 B2 2R2 B2 2L' U2 2L' B2 2R B2
 
|length=(25,15)|name=|wide=N|author=|Mirror[Alg.2]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Alg.2]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=B2 l B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 r2
+
{{Alg6|wca=B2 l B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 r2
 
|sign=B2 2L B2 2R' U2 2R' B2 2L2 B2 D2 2R' U2 2R D2 2R2
 
|sign=B2 2L B2 2R' U2 2R' B2 2L2 B2 D2 2R' U2 2R D2 2R2
 
|length=(25,15)|name=|wide=N|author=|Inverse[Alg.2]
 
|length=(25,15)|name=|wide=N|author=|Inverse[Alg.2]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 l' F2 l B2 D2 r2 D2 l F2 l D2 r' D2
+
{{Alg6|wca=l2 B2 l' F2 l B2 D2 r2 D2 l F2 l D2 r' D2
 
|sign=2L2 B2 2L' F2 2L B2 D2 2R2 D2 2L F2 2L D2 2R' D2
 
|sign=2L2 B2 2L' F2 2L B2 D2 2R2 D2 2L F2 2L D2 2R' D2
 
|length=(25,15)|name=|wide=N|author=|Rotation[Alg.2]
 
|length=(25,15)|name=|wide=N|author=|Rotation[Alg.2]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=B2 r' B2 l U2 l B2 r2 B2 D2 l U2 l' D2 l2
+
{{Alg6|wca=B2 r' B2 l U2 l B2 r2 B2 D2 l U2 l' D2 l2
 
|sign=B2 2R' B2 2L U2 2L B2 2R2 B2 D2 2L U2 2L' D2 2L2
 
|sign=B2 2R' B2 2L U2 2L B2 2R2 B2 D2 2L U2 2L' D2 2L2
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Alg.2]]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Alg.2]]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r F2 r' B2 D2 l2 D2 r' F2 r' D2 l D2
+
{{Alg6|wca=r2 B2 r F2 r' B2 D2 l2 D2 r' F2 r' D2 l D2
 
|sign=2R2 B2 2R F2 2R' B2 D2 2L2 D2 2R' F2 2R' D2 2L D2
 
|sign=2R2 B2 2R F2 2R' B2 D2 2L2 D2 2R' F2 2R' D2 2L D2
 
|length=(25,15)|name=|wide=N|author=|Mirror[Rotation[Alg.2]]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Rotation[Alg.2]]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=D2 r D2 l' F2 l' D2 r2 D2 B2 l' F2 l B2 l2
+
{{Alg6|wca=D2 r D2 l' F2 l' D2 r2 D2 B2 l' F2 l B2 l2
 
|sign=D2 2R D2 2L' F2 2L' D2 2R2 D2 B2 2L' F2 2L B2 2L2
 
|sign=D2 2R D2 2L' F2 2L' D2 2R2 D2 B2 2L' F2 2L B2 2L2
 
|length=(25,15)|name=|wide=N|author=|Inverse[Rotation[Alg.2]]
 
|length=(25,15)|name=|wide=N|author=|Inverse[Rotation[Alg.2]]
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=D2 l' D2 r F2 r D2 l2 D2 B2 r F2 r' B2 r2
+
{{Alg6|wca=D2 l' D2 r F2 r D2 l2 D2 B2 r F2 r' B2 r2
 
|sign=D2 2L' D2 2R F2 2R D2 2L2 D2 B2 2R F2 2R' B2 2R2
 
|sign=D2 2L' D2 2R F2 2R D2 2L2 D2 B2 2R F2 2R' B2 2R2
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Rotation[Alg.2]]]
 
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Rotation[Alg.2]]]
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r'
+
{{Alg6|wca=l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r'
 
|sign=2L 2R F2 2L B 2U' B D2 B' 2U B 2R' D2 B2 2L2 F2 2R'
 
|sign=2L 2R F2 2L B 2U' B D2 B' 2U B 2R' D2 B2 2L2 F2 2R'
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r'
+
{{Alg6|wca=l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r'
 
|sign=2L 2R F2 2L B' 2D' B' D2 B 2D B' 2R' D2 B2 2L2 F2 2R'
 
|sign=2L 2R F2 2L B' 2D' B' D2 B 2D B' 2R' D2 B2 2L2 F2 2R'
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2
+
{{Alg6|wca=r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2
 
|sign=2R' D2 2L' 2R' B2 D2 2L' B 2U B' D2 B 2U' B 2L D2 2R2
 
|sign=2R' D2 2L' 2R' B2 D2 2L' B 2U B' D2 B 2U' B 2L D2 2R2
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2
+
{{Alg6|wca=r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2
 
|sign=2R' D2 2L' 2R' B2 D2 2L' B' 2D B D2 B' 2D' B' 2L D2 2R2
 
|sign=2R' D2 2L' 2R' B2 D2 2L' B' 2D B D2 B' 2D' B' 2L D2 2R2
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r
+
{{Alg6|wca=l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r
 
|sign=2L' 2R' U2 2L' D' 2F D' B2 D 2F' D' 2R B2 D2 2L2 U2 2R
 
|sign=2L' 2R' U2 2L' D' 2F D' B2 D 2F' D' 2R B2 D2 2L2 U2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r
+
{{Alg6|wca=l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r
 
|sign=2L' 2R' U2 2L' D 2B D B2 D' 2B' D 2R B2 D2 2L2 U2 2R
 
|sign=2L' 2R' U2 2L' D 2B D B2 D' 2B' D 2R B2 D2 2L2 U2 2R
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2
+
{{Alg6|wca=r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2
 
|sign=2R F2 2R2 F2 U2 D 2L D' F2 D 2L' D' 2R F2 2R' U2 2R2
 
|sign=2R F2 2R2 F2 U2 D 2L D' F2 D 2L' D' 2R F2 2R' U2 2R2
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2
+
{{Alg6|wca=r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2
 
|sign=2R F2 2R2 F2 U2 D' 2L D F2 D' 2L' D 2R F2 2R' U2 2R2
 
|sign=2R F2 2R2 F2 U2 D' 2L D F2 D' 2L' D 2R F2 2R' U2 2R2
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2
+
{{Alg6|wca=r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2
 
|sign=2R F2 2R2 F2 U2 D' 2L D F2 D' 2L' D 2R F2 2R' U2 2R2
 
|sign=2R F2 2R2 F2 U2 D' 2L D F2 D' 2L' D 2R F2 2R' U2 2R2
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2
+
{{Alg6|wca=r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2
 
|sign=2R F2 2R2 F2 U2 D 2L D' F2 D 2L' D' 2R F2 2R' U2 2R2
 
|sign=2R F2 2R2 F2 U2 D 2L D' F2 D 2L' D' 2R F2 2R' U2 2R2
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l2 D2 F2 l' D b D' F2 D b' D M l D2 r2
+
{{Alg6|wca=r' D2 l2 D2 F2 l' D b D' F2 D b' D M l D2 r2
 
|sign=2R' D2 2L2 D2 F2 2L' D 2B D' F2 D 2B' D m 2L D2 2R2
 
|sign=2R' D2 2L2 D2 F2 2L' D 2B D' F2 D 2B' D m 2L D2 2R2
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' D2 l2 D2 F2 l' D' f D F2 D' f' D' M l D2 r2
+
{{Alg6|wca=r' D2 l2 D2 F2 l' D' f D F2 D' f' D' M l D2 r2
 
|sign=2R' D2 2L2 D2 F2 2L' D' 2F D F2 D' 2F' D' m 2L D2 2R2
 
|sign=2R' D2 2L2 D2 F2 2L' D' 2F D F2 D' 2F' D' m 2L D2 2R2
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|length=(24,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 M' r U2 r' B2 U2 r2 U2 M r' B2 r' B2 r B2
+
{{Alg6|wca=r2 U2 M' r U2 r' B2 U2 r2 U2 M r' B2 r' B2 r B2
 
|sign=2R2 U2 m' 2R U2 2R' B2 U2 2R2 U2 m 2R' B2 2R' B2 2R B2
 
|sign=2R2 U2 m' 2R U2 2R' B2 U2 2R2 U2 m 2R' B2 2R' B2 2R B2
 
|length=(27,17)|name=|wide=N|author=|url=
 
|length=(27,17)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 r U2 r U2 F2 r2 U2 F2 r' U2 r U2 F2 r U2
+
{{Alg6|wca=r2 F2 r U2 r U2 F2 r2 U2 F2 r' U2 r U2 F2 r U2
 
|sign=2R2 F2 2R U2 2R U2 F2 2R2 U2 F2 2R' U2 2R U2 F2 2R U2
 
|sign=2R2 F2 2R U2 2R U2 F2 2R2 U2 F2 2R' U2 2R U2 F2 2R U2
 
|length=(29,17)|name=|wide=N|author=|url=
 
|length=(29,17)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 F2 r U2 F2 r U2 r2 U2 F2 r U2 r F2 r' U2
+
{{Alg6|wca=r2 U2 F2 r U2 F2 r U2 r2 U2 F2 r U2 r F2 r' U2
 
|sign=2R2 U2 F2 2R U2 F2 2R U2 2R2 U2 F2 2R U2 2R F2 2R' U2
 
|sign=2R2 U2 F2 2R U2 F2 2R U2 2R2 U2 F2 2R U2 2R F2 2R' U2
 
|length=(29,17)|name=|wide=N|author=|url=
 
|length=(29,17)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(Rw' U' F' R' F R2 U' Lw' E' R2 E) r' (E' R2 E Lw U R2 F' R F U Rw) (r U2 r' U2) (U2 r2 U2 r2 U2 r2 U2)  
+
{{Alg6|wca=(Rw' U' F' R' F R2 U' Lw' E' R2 E) r' (E' R2 E Lw U R2 F' R F U Rw) (r U2 r' U2) (U2 r2 U2 r2 U2 r2 U2)
|sign=(r' U' F' R' F R2 U' l' e' R2 e) 2R' (e' R2 e l U R2 F' R F U r) (2R U2 2R' U2) (U2 2R2 U2 2R2 U2 2R2 U2)  
+
|sign=(r' U' F' R' F R2 U' l' e' R2 e) 2R' (e' R2 e l U R2 F' R F U r) (2R U2 2R' U2) (U2 2R2 U2 2R2 U2 2R2 U2)
 
|length=(41,31)|name=|wide=N|author=Christopher Mowla
 
|length=(41,31)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw) (D' U' F2 U D) (r' F2 r F2) (F2 r2 F2 r2 F2 r2 F2) (D' U' F2 U D)  
+
{{Alg6|wca=(Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw) (D' U' F2 U D) (r' F2 r F2) (F2 r2 F2 r2 F2 r2 F2) (D' U' F2 U D)
|sign=(r' U' F' R' F R2 U') 2R (U R2 F' R F U r) (D' U' F2 U D) (2R' F2 2R F2) (F2 2R2 F2 2R2 F2 2R2 F2) (D' U' F2 U D)  
+
|sign=(r' U' F' R' F R2 U') 2R (U R2 F' R F U r) (D' U' F2 U D) (2R' F2 2R F2) (F2 2R2 F2 2R2 F2 2R2 F2) (D' U' F2 U D)
 
|length=(43,33)|name=|wide=N|author=Christopher Mowla
 
|length=(43,33)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">In miscellaneous portions of the cube</span>===
===In miscellaneous portions of the cube===
 
 
*There are many possible 3 dedge flip cases outside of the confinement of a single layer (e.g., the last layer) and the M layer.  All algorithms are labeled/named according to which dedges they flip.
 
*There are many possible 3 dedge flip cases outside of the confinement of a single layer (e.g., the last layer) and the M layer.  All algorithms are labeled/named according to which dedges they flip.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=F2 D L' (b L2 f' D2 f' L2 b2 L2 U2 f' D2 f U2 f2 L2) L D' F2
{{Alg5|wca=F2 D L' (b L2 f' D2 f' L2 b2 L2 U2 f' D2 f U2 f2 L2) L D' F2
 
 
|sign=F2 D L' (2B L2 2F' D2 2F' L2 2B2 L2 U2 2F' D2 2F U2 2F2 L2) L D' F2
 
|sign=F2 D L' (2B L2 2F' D2 2F' L2 2B2 L2 U2 2F' D2 2F U2 2F2 L2) L D' F2
 
|length=(31,20)|name=(ur)(rf)(fu)|wide=N|author=Walter Randelshofer
 
|length=(31,20)|name=(ur)(rf)(fu)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U L' u2 L2 F2 d F2 d' F2 d2 L2 u L2 u' F2 u L' U L E L2 E2 L U2  
+
{{Alg6|wca=U L' u2 L2 F2 d F2 d' F2 d2 L2 u L2 u' F2 u L' U L E L2 E2 L U2
 
|sign=U L' 2U2 L2 F2 2D F2 2D' F2 2D2 L2 2U L2 2U' F2 2U L' U L e L2 e2 L U2
 
|sign=U L' 2U2 L2 F2 2D F2 2D' F2 2D2 L2 2U L2 2U' F2 2U L' U L e L2 e2 L U2
 
|length=(36,24)|name=(ur)(rf)(fu)|wide=N|author=André Boulouard
 
|length=(36,24)|name=(ur)(rf)(fu)|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Rw U R U Rw U2 Rw' U' R' U' Rw' R' U R U Rw U2 Rw' U' R' U' Rw U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U2 Rw U R U Rw U2 Rw' U' R' U' Rw' R' U R U Rw U2 Rw' U' R' U' Rw U2 Rw' U2 Rw'
 
|sign=r U2 r U2 r U R U r U2 r' U' R' U' r' R' U R U r U2 r' U' R' U' r U2 r' U2 r'
 
|sign=r U2 r U2 r U R U r U2 r' U' R' U' r' R' U R U r U2 r' U' R' U' r U2 r' U2 r'
 
|length=(36,30)|name=(ur)(rf)(fu)|wide=Y|author=Christopher Mowla
 
|length=(36,30)|name=(ur)(rf)(fu)|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=F (D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D') F'
+
{{Alg6|wca=F (D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D') F'
 
|sign=F (D' 2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D') F'
 
|sign=F (D' 2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D') F'
 
|length=(27,18)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
 
|length=(27,18)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R F (l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2) F' R'
+
{{Alg6|wca=R F (l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2) F' R'
 
|sign=R F (2L' B2 2R D2 2R B2 2L2 B2 U2 2R D2 2R' U2 2R2 B2) F' R'
 
|sign=R F (2L' B2 2R D2 2R B2 2L2 B2 U2 2R D2 2R' U2 2R2 B2) F' R'
 
|length=(27,19)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
 
|length=(27,19)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=E' Rw' B2 l U2 l' U2 r2 B2 r B2 r' B2 U2 r2 U2 E' R2 F2 E R' E R F2 R'
+
{{Alg6|wca=E' Rw' B2 l U2 l' U2 r2 B2 r B2 r' B2 U2 r2 U2 E' R2 F2 E R' E R F2 R'
 
|sign=e' r' B2 2L U2 2L' U2 2R2 B2 2R B2 2R' B2 U2 2R2 U2 e' R2 F2 e R' e R F2 R'
 
|sign=e' r' B2 2L U2 2L' U2 2R2 B2 2R B2 2R' B2 U2 2R2 U2 e' R2 F2 e R' e R F2 R'
 
|length=(37,24)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
 
|length=(37,24)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=F2 (D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D') F2
+
{{Alg6|wca=F2 (D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D') F2
 
|sign=F2 (D' 2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D') F2
 
|sign=F2 (D' 2L D2 2R' B2 2R' D2 2L2 D2 F2 2R' B2 2R F2 2R2 D') F2
 
|length=(29,18)|name=(ub)(rd)(fd)|wide=N|author=Walter Randelshofer
 
|length=(29,18)|name=(ub)(rd)(fd)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw)(D' F2 D)(r' F2 r F2)(F2 r2 F2 r2 F2 r2 F2)(D' F2 D)
+
{{Alg6|wca=(Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw)(D' F2 D)(r' F2 r F2)(F2 r2 F2 r2 F2 r2 F2)(D' F2 D)
 
|sign=(r' U' F' R' F R2 U') 2R (U R2 F' R F U r)(D' F2 D)(2R' F2 2R F2)(F2 2R2 F2 2R2 F2 2R2 F2)(D' F2 D)
 
|sign=(r' U' F' R' F R2 U') 2R (U R2 F' R F U r)(D' F2 D)(2R' F2 2R F2)(F2 2R2 F2 2R2 F2 2R2 F2)(D' F2 D)
 
|length=(39,29)|name=(ub)(rd)(fd)|wide=N|author=Christopher Mowla
 
|length=(39,29)|name=(ub)(rd)(fd)|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
==Five dedge flips==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Five dedge flips</span>==
 
*There are many possible 5 dedge flip cases.  All algorithms are labeled/named according to which dedges they flip.
 
*There are many possible 5 dedge flip cases.  All algorithms are labeled/named according to which dedges they flip.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=R2 U R2 f D2 f' R2 f R2 b2 D2 b' D2 b D2 R2 f2 U' S2 R2 S'
{{Alg5|wca=R2 U R2 f D2 f' R2 f R2 b2 D2 b' D2 b D2 R2 f2 U' S2 R2 S'
 
 
|sign=R2 U R2 2F D2 2F' R2 2F R2 2B2 D2 2B' D2 2B D2 R2 2F2 U' s2 R2 s'
 
|sign=R2 U R2 2F D2 2F' R2 2F R2 2B2 D2 2B' D2 2B D2 R2 2F2 U' s2 R2 s'
 
|length=(34,21)|name=(ur)(uf)(ul)(ub)(dr)|wide=N|author=Walter Randelshofer
 
|length=(34,21)|name=(ur)(uf)(ul)(ub)(dr)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=L2 S' R2 U R2 f D2 f' R2 f R2 b2 D2 b' D2 b D2 R2 f2 U' S2 M2 x2
+
{{Alg6|wca=L2 S' R2 U R2 f D2 f' R2 f R2 b2 D2 b' D2 b D2 R2 f2 U' S2 M2 x2
 
|sign=L2 s' R2 U R2 2F D2 2F' R2 2F R2 2B2 D2 2B' D2 2B D2 R2 2F2 U' s2 m2 x2
 
|sign=L2 s' R2 U R2 2F D2 2F' R2 2F R2 2B2 D2 2B' D2 2B D2 R2 2F2 U' s2 m2 x2
 
|length=(36,22)|name=(ur)(uf)(ul)(ub)(dr)|wide=N|author=André Boulouard
 
|length=(36,22)|name=(ur)(uf)(ul)(ub)(dr)|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U Rw2 U Rw' U' Rw U' Rw' U' Rw U' Rw U Rw' U Rw' U' Rw U2 Rw2 U2 Rw U Rw' U2 Rw U' Rw2 U Rw2 U2 Rw U2 Rw' U' Rw2 U' Rw2 U Rw'
+
{{Alg6|wca=Rw U Rw2 U Rw' U' Rw U' Rw' U' Rw U' Rw U Rw' U Rw' U' Rw U2 Rw2 U2 Rw U Rw' U2 Rw U' Rw2 U Rw2 U2 Rw U2 Rw' U' Rw2 U' Rw2 U Rw'
 
|sign=r U r2 U r' U' r U' r' U' r U' r U r' U r' U' r U2 r2 U2 r U r' U2 r U' r2 U r2 U2 r U2 r' U' r2 U' r2 U r'
 
|sign=r U r2 U r' U' r U' r' U' r U' r U r' U r' U' r U2 r2 U2 r U r' U2 r U' r2 U r2 U2 r U2 r' U' r2 U' r2 U r'
 
|length=(52,41)|name=(ur)(uf)(ul)(ub)(dr)|wide=Y|author=Ben Whitmore
 
|length=(52,41)|name=(ur)(uf)(ul)(ub)(dr)|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw U Rw U' Rw2 U2 Rw' U' Rw U Rw U Rw U Rw' U2 Rw' U2 Rw U2 Rw U' Rw' U' Rw2 U Rw' U Rw' U Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw2 U2 Rw
+
{{Alg6|wca=Rw U Rw U' Rw2 U2 Rw' U' Rw U Rw U Rw U Rw' U2 Rw' U2 Rw U2 Rw U' Rw' U' Rw2 U Rw' U Rw' U Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw2 U2 Rw
|sign=r U r U' r2 U2 r' U' r U r U r U r' U2 r' U2 r U2 r U' r' U' r2 U r' U r' U r2 U2 r' U2 r U2 r' U2 r2 U2 r  
+
|sign=r U r U' r2 U2 r' U' r U r U r U r' U2 r' U2 r U2 r U' r' U' r2 U r' U r' U r2 U2 r' U2 r U2 r' U2 r2 U2 r
 
|length=(54,41)|name=(ur)(uf)(ul)(ub)(fr)|wide=Y|author=Ben Whitmore
 
|length=(54,41)|name=(ur)(uf)(ul)(ub)(fr)|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
}}
 
}}
 
+
{{br|b=1}}
==Seven dedge flips==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Seven dedge flips</span>==
 
*There are many possible 7 dedge flip cases.  All algorithms are labeled/named according to which dedges they flip.
 
*There are many possible 7 dedge flip cases.  All algorithms are labeled/named according to which dedges they flip.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=D' M' F2 L2 F2 U' D' r' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 Rw2 B2 U'
{{Alg5|wca=D' M' F2 L2 F2 U' D' r' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 Rw2 B2 U'
 
 
|sign=D' m' F2 L2 F2 U' D' 2R' B2 2L U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 r2 B2 U'
 
|sign=D' m' F2 L2 F2 U' D' 2R' B2 2L U2 2R' B2 2R2 B2 U2 2R' U2 2R U2 r2 B2 U'
 
|length=(36,23)|name=(uf)(ul)(ub)(dr)(df)(dl)(db)|wide=N|author=André Boulouard
 
|length=(36,23)|name=(uf)(ul)(ub)(dr)(df)(dl)(db)|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=u R2 d' F2 d' R2 u2 R2 B2 d' F2 d B2 d2 L2 B2 M' B2 D M2 F2 M F2 D' x2
+
{{Alg6|wca=u R2 d' F2 d' R2 u2 R2 B2 d' F2 d B2 d2 L2 B2 M' B2 D M2 F2 M F2 D' x2
 
|sign=2U R2 2D' F2 2D' R2 2U2 R2 B2 2D' F2 2D B2 2D2 L2 B2 m' B2 D m2 F2 m F2 D' x2
 
|sign=2U R2 2D' F2 2D' R2 2U2 R2 B2 2D' F2 2D B2 2D2 L2 B2 m' B2 D m2 F2 m F2 D' x2
 
|length=(39,24)|name=(ur)(uf)(ul)(ub)(fl)(lb)(br)|wide=N|author=Walter Randelshofer
 
|length=(39,24)|name=(ur)(uf)(ul)(ub)(fl)(lb)(br)|wide=N|author=Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Nine dedge flips</span>==
==Nine dedge flips==
 
 
*There are several possible 9 dedge flip cases.  All algorithms are labeled/named according to which dedges they flip.
 
*There are several possible 9 dedge flip cases.  All algorithms are labeled/named according to which dedges they flip.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=D' S L2 B2 d2 F2 d F2 d' F2 L2 d2 L2 d' F2 u L2 Uw' D' S' R2 F2 R2 U'
{{Alg5|wca=D' S L2 B2 d2 F2 d F2 d' F2 L2 d2 L2 d' F2 u L2 Uw' D' S' R2 F2 R2 U'
 
 
|sign=D' s L2 B2 2D2 F2 2D F2 2D' F2 L2 2D2 L2 2D' F2 2U L2 Uw' D' s' R2 F2 R2 U'
 
|sign=D' s L2 B2 2D2 F2 2D F2 2D' F2 L2 2D2 L2 2D' F2 2U L2 Uw' D' s' R2 F2 R2 U'
 
|length=(38,24)|name=(ur)(uf)(ul)(ub)(rf)(dr)(df)(dl)(db)|wide=N|author=André Boulouard
 
|length=(38,24)|name=(ur)(uf)(ul)(ub)(rf)(dr)(df)(dl)(db)|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Eleven dedge flips</span>==
==Eleven dedge flips==
 
 
[[Image:11_Flip.png|110px|]]
 
[[Image:11_Flip.png|110px|]]
 
*There is only one case of the 11 dedge flip (when applying symmetry).  All algorithms listed solve/generate the case shown in the image above.
 
*There is only one case of the 11 dedge flip (when applying symmetry).  All algorithms listed solve/generate the case shown in the image above.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=Rw2 F2 l U2 x' l U2 l2 x' U2 r' U2 l D2 F2 l U2 L R E M S x
{{Alg5|wca=Rw2 F2 l U2 x' l U2 l2 x' U2 r' U2 l D2 F2 l U2 L R E M S x
 
 
|sign=r2 F2 2L U2 x' 2L U2 2L2 x' U2 2R' U2 2L D2 F2 2L U2 L R e m s x
 
|sign=r2 F2 2L U2 x' 2L U2 2L2 x' U2 2R' U2 2L D2 F2 2L U2 L R e m s x
 
|length=(30,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
 
|length=(30,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r D2 x U2 l D2 r' D2 l2 F2 l U2 l x' U2 r2 F2 R2 E L' R U' D y x R2
+
{{Alg6|wca=r D2 x U2 l D2 r' D2 l2 F2 l U2 l x' U2 r2 F2 R2 E L' R U' D y x R2
 
|sign=2R D2 x U2 2L D2 2R' D2 2L2 F2 2L U2 2L x' U2 2R2 F2 R2 e L' R U' D y x R2
 
|sign=2R D2 x U2 2L D2 2R' D2 2L2 F2 2L U2 2L x' U2 2R2 F2 R2 e L' R U' D y x R2
 
|length=(31,20)|name=|wide=N|author=Herbert Kociemba
 
|length=(31,20)|name=|wide=N|author=Herbert Kociemba
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1116598
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1116598
 
}}
 
}}
{{Alg5|wca=Lw2 F2 M r' F2 r' U2 r2 B2 r D2 l' B2 D2 r' F2 L2 E' M S' x2
+
{{Alg6|wca=Lw2 F2 M r' F2 r' U2 r2 B2 r D2 l' B2 D2 r' F2 L2 E' M S' x2
 
|sign=l2 F2 m 2R' F2 2R' U2 2R2 B2 2R D2 2L' B2 D2 2R' F2 L2 e' m s' x2
 
|sign=l2 F2 m 2R' F2 2R' U2 2R2 B2 2R D2 2L' B2 D2 2R' F2 L2 e' m s' x2
 
|length=(31,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
 
|length=(31,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 F2 l U2 r' x' U2 l2 F2 r D2 M l x U2 B2 r F2 R2 E M S x2
+
{{Alg6|wca=Rw2 F2 l U2 r' x' U2 l2 F2 r D2 M l x U2 B2 r F2 R2 E M S x2
 
|sign=r2 F2 2L U2 2R' x' U2 2L2 F2 2R D2 m 2L x U2 B2 2R F2 R2 e m s x2
 
|sign=r2 F2 2L U2 2R' x' U2 2L2 F2 2R D2 m 2L x U2 B2 2R F2 R2 e m s x2
 
|length=(31,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
 
|length=(31,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l B2 U2 r D2 l' D2 r2 B2 r U2 r F2 l2 U2 L2 S' M' E' 3Rw2  
+
{{Alg6|wca=l B2 U2 r D2 l' D2 r2 B2 r U2 r F2 l2 U2 L2 S' M' E' 3Rw2
|sign=2L B2 U2 2R D2 2L' D2 2R2 B2 2R U2 2R F2 2L2 U2 L2 s' m' e' 3r2  
+
|sign=2L B2 U2 2R D2 2L' D2 2R2 B2 2R U2 2R F2 2L2 U2 L2 s' m' e' 3r2
 
|length=(32,20)|name=|wide=N|author=Herbert Kociemba &Walter Randelshofer
 
|length=(32,20)|name=|wide=N|author=Herbert Kociemba &Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r D2 F2 l B2 r' B2 l2 D2 l F2 l U2 r2 F2 R2 E M S 3Lw2
+
{{Alg6|wca=r D2 F2 l B2 r' B2 l2 D2 l F2 l U2 r2 F2 R2 E M S 3Lw2
 
|sign=2R D2 F2 2L B2 2R' B2 2L2 D2 2L F2 2L U2 2R2 F2 R2 e m s 3l2
 
|sign=2R D2 F2 2L B2 2R' B2 2L2 D2 2L F2 2L U2 2R2 F2 R2 e m s 3l2
 
|length=(32,20)|name=|wide=N|author=Herbert Kociemba &Walter Randelshofer
 
|length=(32,20)|name=|wide=N|author=Herbert Kociemba &Walter Randelshofer
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 Rw2 S' U2 B2 M' U2 R2 E' F2 U2 x2
+
{{Alg6|wca=r B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 Rw2 S' U2 B2 M' U2 R2 E' F2 U2 x2
 
|sign=2R B2 2R' U2 2R' B2 2L2 B2 D2 2R' U2 2R D2 r2 s' U2 B2 m' U2 R2 e' F2 U2 x2
 
|sign=2R B2 2R' U2 2R' B2 2L2 B2 D2 2R' U2 2R D2 r2 s' U2 B2 m' U2 R2 e' F2 U2 x2
 
|length=(38,23)|name=|wide=N|author=Christopher Mowla
 
|length=(38,23)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1116454
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1116454
 
}}
 
}}
{{Alg5|wca=r B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 Rw2 S' U2 B2 M' D2 L2 E' B2 D2 x2
+
{{Alg6|wca=r B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 Rw2 S' U2 B2 M' D2 L2 E' B2 D2 x2
 
|sign=2R B2 2R' U2 2R' B2 2L2 B2 D2 2R' U2 2R D2 r2 s' U2 B2 m' D2 L2 e' B2 D2 x2
 
|sign=2R B2 2R' U2 2R' B2 2L2 B2 D2 2R' U2 2R D2 r2 s' U2 B2 m' D2 L2 e' B2 D2 x2
 
|length=(38,23)|name=|wide=N|author=Christopher Mowla
 
|length=(38,23)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1116454
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1116454
 
}}
 
}}
{{Alg5|wca=y x2 r U' F2 U l F2 r U2 r U' B2 U r D2 L' R' B2 L2 B' R2 B D2 B E F M y2 x
+
{{Alg6|wca=y x2 r U' F2 U l F2 r U2 r U' B2 U r D2 L' R' B2 L2 B' R2 B D2 B E F M y2 x
 
|sign=y x2 2R U' F2 U 2L F2 2R U2 2R U' B2 U 2R D2 L' R' B2 L2 B' R2 B D2 B e F m y2 x
 
|sign=y x2 2R U' F2 U 2L F2 2R U2 2R U' B2 U 2R D2 L' R' B2 L2 B' R2 B D2 B e F m y2 x
 
|length=(35,26)|name=|wide=N|author=Christopher Mowla
 
|length=(35,26)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1115975
 
|url=https://www.speedsolving.com/forum/threads/4x4x4-superflip-of-11-out-of-12-edges.55024/#post-1115975
 
}}
 
}}
{{Alg5|wca=R' D2 R' E2 S' Rw' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 Rw2 S' R S2 E' L' B2 R' S2 z2
+
{{Alg6|wca=R' D2 R' E2 S' Rw' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 Rw2 S' R S2 E' L' B2 R' S2 z2
 
|sign=R' D2 R' e2 s' r' U2 2L F2 2R' U2 2R2 U2 F2 2R' F2 2R F2 r2 s' R s2 e' L' B2 R' s2 z2
 
|sign=R' D2 R' e2 s' r' U2 2L F2 2R' U2 2R2 U2 F2 2R' F2 2R F2 r2 s' R s2 e' L' B2 R' s2 z2
 
|length=(40,27)|name=|wide=N|author=André Boulouard
 
|length=(40,27)|name=|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=D2 L' S2 R' B2 L' E S2 R S' Rw2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 Rw' S' E2 R' z2
+
{{Alg6|wca=D2 L' S2 R' B2 L' E S2 R S' Rw2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 Rw' S' E2 R' z2
 
|sign=D2 L' s2 R' B2 L' e s2 R s' r2 F2 2R F2 2R' F2 D2 2R2 D2 2R' F2 2L D2 r' s' e2 R' z2
 
|sign=D2 L' s2 R' B2 L' e s2 R s' r2 F2 2R F2 2R' F2 D2 2R2 D2 2R' F2 2L D2 r' s' e2 R' z2
 
|length=(41,27)|name=|wide=N|author=André Boulouard
 
|length=(41,27)|name=|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M D2 F2 Rw2 F2 r' F2 r F2 U2 r2 U2 r F2 l' U2 l F' E F' U2 F E' B' D' U' S L2 x y'
+
{{Alg6|wca=M D2 F2 Rw2 F2 r' F2 r F2 U2 r2 U2 r F2 l' U2 l F' E F' U2 F E' B' D' U' S L2 x y'
 
|sign=m D2 F2 r2 F2 2R' F2 2R F2 U2 2R2 U2 2R F2 2L' U2 2L F' e F' U2 F e' B' D' U' s L2 x y'
 
|sign=m D2 F2 r2 F2 2R' F2 2R F2 U2 2R2 U2 2R F2 2L' U2 2L F' e F' U2 F e' B' D' U' s L2 x y'
 
|length=(41,28)|name=|wide=N|author=André Boulouard
 
|length=(41,28)|name=|wide=N|author=André Boulouard
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=M S r U2 r F2 r' D2 r E2 r U' f2 Rw2 U f2 U' Rw2 f2 D' B2 R2 B2 L2 D2 Fw2 U2 Fw2 y
+
{{Alg6|wca=M S r U2 r F2 r' D2 r E2 r U' f2 Rw2 U f2 U' Rw2 f2 D' B2 R2 B2 L2 D2 Fw2 U2 Fw2 y
 
|sign=m s 2R U2 2R F2 2R' D2 2R e2 2R U' 2F2 r2 U 2F2 U' r2 2F2 D' B2 R2 B2 L2 D2 f2 U2 f2 y
 
|sign=m s 2R U2 2R F2 2R' D2 2R e2 2R U' 2F2 r2 U 2F2 U' r2 2F2 D' B2 R2 B2 L2 D2 f2 U2 f2 y
 
|length=(45,28)|name=|wide=N|author=Bruce Norskog
 
|length=(45,28)|name=|wide=N|author=Bruce Norskog
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-10#post-872653
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-10#post-872653
 
}}
 
}}
{{Alg5|wca=y d E M R D R' Bw f M d' M' Fw b M' F Uw M' R' S L F' U R D' R' E S2 R F' z'
+
{{Alg6|wca=y d E M R D R' Bw f M d' M' Fw b M' F Uw M' R' S L F' U R D' R' E S2 R F' z'
 
|sign=y 2D e m R D R' b 2F m 2D' m' f 2B m' F u m' R' s L F' U R D' R' e s2 R F' z'
 
|sign=y 2D e m R D R' b 2F m 2D' m' f 2B m' F u m' R' s L F' U R D' R' e s2 R F' z'
 
|length=(30,29)|name=|wide=N|author=Bruce Norskog &Christopher Mowla
 
|length=(30,29)|name=|wide=N|author=Bruce Norskog &Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-10#post-872801
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-10#post-872801
 
}}
 
}}
 
+
{{br|b=1}}
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">Double Parity Cases Only Affecting Dedges</span>=
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">In the last layer</span>==
=Double Parity Cases Only Affecting Dedges=
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Opposite double parity</span>===
==In the last layer==
 
===Opposite double parity===
 
 
[[Image:DblParity.png|110px|]]
 
[[Image:DblParity.png|110px|]]
 
*Note: Since this is a <u>4-cycle</u> case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a <u>4-cycle</u> case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=r B2 r' U2 r U2 r' F2 Rw D2 l D2 Rw' (S2) z2
{{Alg5|wca=r B2 r' U2 r U2 r' F2 Rw D2 l D2 Rw' (S2) z2
 
 
|sign=2R B2 2R' U2 2R U2 2R' F2 r D2 2L D2 r' (s2) z2
 
|sign=2R B2 2R' U2 2R U2 2R' F2 r D2 2L D2 r' (s2) z2
 
|length=(21,14)|name=Alg.1|wide=Y|author=
 
|length=(21,14)|name=Alg.1|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 l' U2 l F2 Lw' D2 r' D2 Lw (S2) z2
+
{{Alg6|wca=l' B2 l U2 l' U2 l F2 Lw' D2 r' D2 Lw (S2) z2
 
|sign=2L' B2 2L U2 2L' U2 2L F2 l' D2 2R' D2 l (s2) z2
 
|sign=2L' B2 2L U2 2L' U2 2L F2 l' D2 2R' D2 l (s2) z2
 
|length=(21,14)|name=Mirror[Alg.1]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.1]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l U2 l' U2 l F2 Rw' B2 r' B2 Rw (S2) z2
+
{{Alg6|wca=l' B2 l U2 l' U2 l F2 Rw' B2 r' B2 Rw (S2) z2
 
|sign=2L' B2 2L U2 2L' U2 2L F2 r' B2 2R' B2 r (s2) z2
 
|sign=2L' B2 2L U2 2L' U2 2L F2 r' B2 2R' B2 r (s2) z2
 
|length=(21,14)|name=Alg.2|wide=Y|author=
 
|length=(21,14)|name=Alg.2|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r B2 r' U2 r U2 r' F2 Lw B2 l B2 Lw' (S2) z2
+
{{Alg6|wca=r B2 r' U2 r U2 r' F2 Lw B2 l B2 Lw' (S2) z2
 
|sign=2R B2 2R' U2 2R U2 2R' F2 l B2 2L B2 l' (s2) z2
 
|sign=2R B2 2R' U2 2R U2 2R' F2 l B2 2L B2 l' (s2) z2
 
|length=(21,14)|name=Mirror[Alg.2]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.2]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(S2) Lw' U2 r U2 Lw B2 l' D2 l D2 l' F2 l z2
+
{{Alg6|wca=(S2) Lw' U2 r U2 Lw B2 l' D2 l D2 l' F2 l z2
 
|sign=(s2) l' U2 2R U2 l B2 2L' D2 2L D2 2L' F2 2L z2
 
|sign=(s2) l' U2 2R U2 l B2 2L' D2 2L D2 2L' F2 2L z2
 
|length=(21,14)|name=Alg.3|wide=Y|author=
 
|length=(21,14)|name=Alg.3|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(S2) Rw U2 l' U2 Rw' B2 r D2 r' D2 r F2 r' z2
+
{{Alg6|wca=(S2) Rw U2 l' U2 Rw' B2 r D2 r' D2 r F2 r' z2
 
|sign=(s2) r U2 2L' U2 r' B2 2R D2 2R' D2 2R F2 2R' z2
 
|sign=(s2) r U2 2L' U2 r' B2 2R D2 2R' D2 2R F2 2R' z2
 
|length=(21,14)|name=Mirror[Alg.3]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.3]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(S2) Rw' F2 r F2 Rw B2 l' D2 l D2 l' F2 l z2
+
{{Alg6|wca=(S2) Rw' F2 r F2 Rw B2 l' D2 l D2 l' F2 l z2
 
|sign=(s2) r' F2 2R F2 r B2 2L' D2 2L D2 2L' F2 2L z2
 
|sign=(s2) r' F2 2R F2 r B2 2L' D2 2L D2 2L' F2 2L z2
 
|length=(21,14)|name=Alg.4|wide=Y|author=
 
|length=(21,14)|name=Alg.4|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(S2) Lw F2 l' F2 Lw' B2 r D2 r' D2 r F2 r' z2
+
{{Alg6|wca=(S2) Lw F2 l' F2 Lw' B2 r D2 r' D2 r F2 r' z2
 
|sign=(s2) l F2 2L' F2 l' B2 2R D2 2R' D2 2R F2 2R' z2
 
|sign=(s2) l F2 2L' F2 l' B2 2R D2 2R' D2 2R F2 2R' z2
 
|length=(21,14)|name=Mirror[Alg.4]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.4]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r' (E2) F2 l F2 l' F2 r F2 r' D2 l y2
+
{{Alg6|wca=r U2 r' (E2) F2 l F2 l' F2 r F2 r' D2 l y2
 
|sign=2R U2 2R' (e2) F2 2L F2 2L' F2 2R F2 2R' D2 2L y2
 
|sign=2R U2 2R' (e2) F2 2L F2 2L' F2 2R F2 2R' D2 2L y2
 
|length=(21,14)|name=Alg.5|wide=Y|author=Kenneth Gustavsson
 
|length=(21,14)|name=Alg.5|wide=Y|author=Kenneth Gustavsson
 
|url=https://www.speedsolving.com/forum/threads/4x4-pure-double-parity.27783/#post-539865
 
|url=https://www.speedsolving.com/forum/threads/4x4-pure-double-parity.27783/#post-539865
 
}}
 
}}
{{Alg5|wca=l' U2 l (E2) F2 r' F2 r F2 l' F2 l D2 r' y2
+
{{Alg6|wca=l' U2 l (E2) F2 r' F2 r F2 l' F2 l D2 r' y2
 
|sign=2L' U2 2L (e2) F2 2R' F2 2R F2 2L' F2 2L D2 2R' y2
 
|sign=2L' U2 2L (e2) F2 2R' F2 2R F2 2L' F2 2L D2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.5]|wide=Y|author=Kenneth Gustavsson
 
|length=(21,14)|name=Mirror[Alg.5]|wide=Y|author=Kenneth Gustavsson
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r' (E2) F2 l F2 r' D2 r D2 l' D2 l y2
+
{{Alg6|wca=r U2 r' (E2) F2 l F2 r' D2 r D2 l' D2 l y2
 
|sign=2R U2 2R' (e2) F2 2L F2 2R' D2 2R D2 2L' D2 2L y2
 
|sign=2R U2 2R' (e2) F2 2L F2 2R' D2 2R D2 2L' D2 2L y2
 
|length=(21,14)|name=Alg.6|wide=Y|author=
 
|length=(21,14)|name=Alg.6|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l (E2) F2 r' F2 l D2 l' D2 r D2 r' y2
+
{{Alg6|wca=l' U2 l (E2) F2 r' F2 l D2 l' D2 r D2 r' y2
 
|sign=2L' U2 2L (e2) F2 2R' F2 2L D2 2L' D2 2R D2 2R' y2
 
|sign=2L' U2 2L (e2) F2 2R' F2 2L D2 2L' D2 2R D2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.6]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.6]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r' (E2) F2 r U2 l' U2 l F2 r' D2 l y2
+
{{Alg6|wca=r U2 r' (E2) F2 r U2 l' U2 l F2 r' D2 l y2
 
|sign=2R U2 2R' (e2) F2 2R U2 2L' U2 2L F2 2R' D2 2L y2
 
|sign=2R U2 2R' (e2) F2 2R U2 2L' U2 2L F2 2R' D2 2L y2
 
|length=(21,14)|name=Alg.7|wide=Y|author=
 
|length=(21,14)|name=Alg.7|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l (E2) F2 l' U2 r U2 r' F2 l D2 r' y2
+
{{Alg6|wca=l' U2 l (E2) F2 l' U2 r U2 r' F2 l D2 r' y2
 
|sign=2L' U2 2L (e2) F2 2L' U2 2R U2 2R' F2 2L D2 2R' y2
 
|sign=2L' U2 2L (e2) F2 2L' U2 2R U2 2R' F2 2L D2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.7]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.7]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l (E2) F2 r' F2 l D2 r' B2 r B2 l' y2
+
{{Alg6|wca=l' U2 l (E2) F2 r' F2 l D2 r' B2 r B2 l' y2
 
|sign=2L' U2 2L (e2) F2 2R' F2 2L D2 2R' B2 2R B2 2L' y2
 
|sign=2L' U2 2L (e2) F2 2R' F2 2L D2 2R' B2 2R B2 2L' y2
 
|length=(21,14)|name=Alg.8|wide=Y|author=
 
|length=(21,14)|name=Alg.8|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r' (E2) F2 l F2 r' D2 l B2 l' B2 r y2
+
{{Alg6|wca=r U2 r' (E2) F2 l F2 r' D2 l B2 l' B2 r y2
 
|sign=2R U2 2R' (e2) F2 2L F2 2R' D2 2L B2 2L' B2 2R y2
 
|sign=2R U2 2R' (e2) F2 2L F2 2R' D2 2L B2 2L' B2 2R y2
 
|length=(21,14)|name=Mirror[Alg.8]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.8]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l F2 r' (S2) D2 l D2 r' B2 l U2 l' U2 l z2
+
{{Alg6|wca=l F2 r' (S2) D2 l D2 r' B2 l U2 l' U2 l z2
 
|sign=2L F2 2R' (s2) D2 2L D2 2R' B2 2L U2 2L' U2 2L z2
 
|sign=2L F2 2R' (s2) D2 2L D2 2R' B2 2L U2 2L' U2 2L z2
 
|length=(21,14)|name=Alg.9|wide=Y|author=
 
|length=(21,14)|name=Alg.9|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' F2 l (S2) D2 r' D2 l B2 r' U2 r U2 r' z2
+
{{Alg6|wca=r' F2 l (S2) D2 r' D2 l B2 r' U2 r U2 r' z2
 
|sign=2R' F2 2L (s2) D2 2R' D2 2L B2 2R' U2 2R U2 2R' z2
 
|sign=2R' F2 2L (s2) D2 2R' D2 2L B2 2R' U2 2R U2 2R' z2
 
|length=(21,14)|name=Mirror[Alg.9]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.9]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r D2 l' F2 l F2 r' F2 r F2 (E2) l' U2 l y2
+
{{Alg6|wca=r D2 l' F2 l F2 r' F2 r F2 (E2) l' U2 l y2
 
|sign=2R D2 2L' F2 2L F2 2R' F2 2R F2 (e2) 2L' U2 2L y2
 
|sign=2R D2 2L' F2 2L F2 2R' F2 2R F2 (e2) 2L' U2 2L y2
 
|length=(21,14)|name=Alg.10|wide=Y|author=
 
|length=(21,14)|name=Alg.10|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' D2 r F2 r' F2 l F2 l' F2 (E2) r U2 r' y2
+
{{Alg6|wca=l' D2 r F2 r' F2 l F2 l' F2 (E2) r U2 r' y2
 
|sign=2L' D2 2R F2 2R' F2 2L F2 2L' F2 (e2) 2R U2 2R' y2
 
|sign=2L' D2 2R F2 2R' F2 2L F2 2L' F2 (e2) 2R U2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.10]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.10]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r D2 r' D2 l D2 l' F2 r F2 (E2) l' U2 l y2
+
{{Alg6|wca=r D2 r' D2 l D2 l' F2 r F2 (E2) l' U2 l y2
 
|sign=2R D2 2R' D2 2L D2 2L' F2 2R F2 (e2) 2L' U2 2L y2
 
|sign=2R D2 2R' D2 2L D2 2L' F2 2R F2 (e2) 2L' U2 2L y2
 
|length=(21,14)|name=Alg.11|wide=Y|author=
 
|length=(21,14)|name=Alg.11|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' D2 l D2 r' D2 r F2 l' F2 (E2) r U2 r' y2
+
{{Alg6|wca=l' D2 l D2 r' D2 r F2 l' F2 (E2) r U2 r' y2
 
|sign=2L' D2 2L D2 2R' D2 2R F2 2L' F2 (e2) 2R U2 2R' y2
 
|sign=2L' D2 2L D2 2R' D2 2R F2 2L' F2 (e2) 2R U2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.11]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.11]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r D2 l' F2 r U2 r' U2 l F2 (E2) l' U2 l y2
+
{{Alg6|wca=r D2 l' F2 r U2 r' U2 l F2 (E2) l' U2 l y2
 
|sign=2R D2 2L' F2 2R U2 2R' U2 2L F2 (e2) 2L' U2 2L y2
 
|sign=2R D2 2L' F2 2R U2 2R' U2 2L F2 (e2) 2L' U2 2L y2
 
|length=(21,14)|name=Alg.12|wide=Y|author=
 
|length=(21,14)|name=Alg.12|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' D2 r F2 l' U2 l U2 r' F2 (E2) r U2 r' y2
+
{{Alg6|wca=l' D2 r F2 l' U2 l U2 r' F2 (E2) r U2 r' y2
 
|sign=2L' D2 2R F2 2L' U2 2L U2 2R' F2 (e2) 2R U2 2R' y2
 
|sign=2L' D2 2R F2 2L' U2 2L U2 2R' F2 (e2) 2R U2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.12]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.12]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l B2 r' B2 r D2 l' F2 r F2 (E2) l' U2 l y2
+
{{Alg6|wca=l B2 r' B2 r D2 l' F2 r F2 (E2) l' U2 l y2
 
|sign=2L B2 2R' B2 2R D2 2L' F2 2R F2 (e2) 2L' U2 2L y2
 
|sign=2L B2 2R' B2 2R D2 2L' F2 2R F2 (e2) 2L' U2 2L y2
 
|length=(21,14)|name=Alg.13|wide=Y|author=
 
|length=(21,14)|name=Alg.13|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' B2 l B2 l' D2 r F2 l' F2 (E2) r U2 r' y2
+
{{Alg6|wca=r' B2 l B2 l' D2 r F2 l' F2 (E2) r U2 r' y2
 
|sign=2R' B2 2L B2 2L' D2 2R F2 2L' F2 (e2) 2R U2 2R' y2
 
|sign=2R' B2 2L B2 2L' D2 2R F2 2L' F2 (e2) 2R U2 2R' y2
 
|length=(21,14)|name=Mirror[Alg.13]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.13]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' D2 l D2 l' F2 r U2 l' U2 (S2) r B2 l' z2
+
{{Alg6|wca=l' D2 l D2 l' F2 r U2 l' U2 (S2) r B2 l' z2
 
|sign=2L' D2 2L D2 2L' F2 2R U2 2L' U2 (s2) 2R B2 2L' z2
 
|sign=2L' D2 2L D2 2L' F2 2R U2 2L' U2 (s2) 2R B2 2L' z2
 
|length=(21,14)|name=Alg.14|wide=Y|author=
 
|length=(21,14)|name=Alg.14|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r D2 r' D2 r F2 l' U2 r U2 (S2) l' B2 r z2
+
{{Alg6|wca=r D2 r' D2 r F2 l' U2 r U2 (S2) l' B2 r z2
 
|sign=2R D2 2R' D2 2R F2 2L' U2 2R U2 (s2) 2L' B2 2R z2
 
|sign=2R D2 2R' D2 2R F2 2L' U2 2R U2 (s2) 2L' B2 2R z2
 
|length=(21,14)|name=Mirror[Alg.14]|wide=Y|author=
 
|length=(21,14)|name=Mirror[Alg.14]|wide=Y|author=
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x
+
{{Alg6|wca=r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x
 
|sign=2R2 B2 2R' U2 2R' U2 x' U2 2R' U2 2R U2 2R' U2 2R2 U2 x
 
|sign=2R2 B2 2R' U2 2R' U2 x' U2 2R' U2 2R U2 2R' U2 2R2 U2 x
 
|length=(25,15)|name=|wide=Y|author=Frédérick Badie
 
|length=(25,15)|name=|wide=Y|author=Frédérick Badie
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x r F2 Lw' F r' F' U2 F r F' U2 Lw x' E2 l' U2 l y2
+
{{Alg6|wca=x r F2 Lw' F r' F' U2 F r F' U2 Lw x' E2 l' U2 l y2
 
|sign=x 2R F2 l' F 2R' F' U2 F 2R F' U2 l x' e2 2L' U2 2L y2
 
|sign=x 2R F2 l' F 2R' F' U2 F 2R F' U2 l x' e2 2L' U2 2L y2
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x r F2 Lw' F' r' F U2 F' r F U2 Lw x' E2 l' U2 l y2
+
{{Alg6|wca=x r F2 Lw' F' r' F U2 F' r F U2 Lw x' E2 l' U2 l y2
 
|sign=x 2R F2 l' F' 2R' F U2 F' 2R F U2 l x' e2 2L' U2 2L y2
 
|sign=x 2R F2 l' F' 2R' F U2 F' 2R F U2 l x' e2 2L' U2 2L y2
 
|length=(21,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(21,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 B2 U2 l r2 U2 r' U2 r U2 F2 r F2 l' B2 Rw2
+
{{Alg6|wca=Rw2 B2 U2 l r2 U2 r' U2 r U2 F2 r F2 l' B2 Rw2
 
|sign=r2 B2 U2 2L 2R2 U2 2R' U2 2R U2 F2 2R F2 2L' B2 r2
 
|sign=r2 B2 U2 2L 2R2 U2 2R' U2 2R U2 F2 2R F2 2L' B2 r2
 
|length=(27,16)|name=|wide=Y|author=Alexander Ooms
 
|length=(27,16)|name=|wide=Y|author=Alexander Ooms
 
|url=https://www.speedsolving.com/forum/threads/double-parity-4x4.243/
 
|url=https://www.speedsolving.com/forum/threads/double-parity-4x4.243/
 
}}
 
}}
{{Alg5|wca=Rw U2 r' U2 r2 U2 M' U2 r U2 r' U2 l U2 r' U2 Rw'
+
{{Alg6|wca=Rw U2 r' U2 r2 U2 M' U2 r U2 r' U2 l U2 r' U2 Rw'
 
|sign=r U2 2R' U2 2R2 U2 m' U2 2R U2 2R' U2 2L U2 2R' U2 r'
 
|sign=r U2 2R' U2 2R2 U2 m' U2 2R U2 2R' U2 2L U2 2R' U2 r'
 
|length=(26,17)|name=|wide=N|author=Jayden McNeill
 
|length=(26,17)|name=|wide=N|author=Jayden McNeill
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-51#post-741687
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-51#post-741687
 
}}
 
}}
{{Alg5|wca=Rw' U2 r' U2 l U2 Rw' U2 r U2 3Rw U2 r2 U2 r' U2 Rw
+
{{Alg6|wca=Rw' U2 r' U2 l U2 Rw' U2 r U2 3Rw U2 r2 U2 r' U2 Rw
 
|sign=r' U2 2R' U2 2L U2 r' U2 2R U2 3r U2 2R2 U2 2R' U2 r
 
|sign=r' U2 2R' U2 2L U2 r' U2 2R U2 3r U2 2R2 U2 2R' U2 r
 
|length=(26,17)|name=|wide=Y|author=|url=
 
|length=(26,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 3Rw' U2 r' U2 Rw U2 l' U2 Rw U2 r U2 Rw' U2 r
+
{{Alg6|wca=r2 U2 3Rw' U2 r' U2 Rw U2 l' U2 Rw U2 r U2 Rw' U2 r
 
|sign=2R2 U2 3r' U2 2R' U2 r U2 2L' U2 r U2 2R U2 r' U2 2R
 
|sign=2R2 U2 3r' U2 2R' U2 r U2 2L' U2 r U2 2R U2 r' U2 2R
 
|length=(26,17)|name=|wide=Y|author=|url=
 
|length=(26,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 r' U2 r' U2 r U2 M' U2 r U2 r' U2 M U2 Rw2
+
{{Alg6|wca=Rw2 U2 r' U2 r' U2 r U2 M' U2 r U2 r' U2 M U2 Rw2
 
|sign=r2 U2 2R' U2 2R' U2 2R U2 m' U2 2R U2 2R' U2 m U2 r2
 
|sign=r2 U2 2R' U2 2R' U2 2R U2 m' U2 2R U2 2R' U2 m U2 r2
 
|length=(27,17)|name=|wide=N|author=Thom Barlow
 
|length=(27,17)|name=|wide=N|author=Thom Barlow
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-44#post-673711
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-44#post-673711
 
}}
 
}}
{{Alg5|wca=Rw2 U B2 U' r' U B2 U' Rw r U B2 U r' U' B2 U' Rw
+
{{Alg6|wca=Rw2 U B2 U' r' U B2 U' Rw r U B2 U r' U' B2 U' Rw
 
|sign=r2 U B2 U' 2R' U B2 U' r 2R U B2 U 2R' U' B2 U' r
 
|sign=r2 U B2 U' 2R' U B2 U' r 2R U B2 U 2R' U' B2 U' r
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 6,061: Line 6,307:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 3Dw L2 3Dw' r' 3Dw L2 3Dw' Rw r 3Dw L2 3Dw l' 3Dw' L2 3Dw' Rw
+
{{Alg6|wca=Rw2 3Dw L2 3Dw' r' 3Dw L2 3Dw' Rw r 3Dw L2 3Dw l' 3Dw' L2 3Dw' Rw
 
|sign=r2 3d L2 3d' 2R' 3d L2 3d' r 2R 3d L2 3d 2L' 3d' L2 3d' r
 
|sign=r2 3d L2 3d' 2R' 3d L2 3d' r 2R 3d L2 3d 2L' 3d' L2 3d' r
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 6,067: Line 6,313:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U' B2 U r' U' B2 U r2 U' B2 U' r' U B2 U r
+
{{Alg6|wca=r2 U' B2 U r' U' B2 U r2 U' B2 U' r' U B2 U r
 
|sign=2R2 U' B2 U 2R' U' B2 U 2R2 U' B2 U' 2R' U B2 U 2R
 
|sign=2R2 U' B2 U 2R' U' B2 U 2R2 U' B2 U' 2R' U B2 U 2R
 
|length=(23,18)|name=v1
 
|length=(23,18)|name=v1
Line 6,073: Line 6,319:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 3Dw' R2 3Dw r' 3Dw' R2 3Dw r2 3Dw' R2 3Dw' l' 3Dw R2 3Dw r
+
{{Alg6|wca=r2 3Dw' R2 3Dw r' 3Dw' R2 3Dw r2 3Dw' R2 3Dw' l' 3Dw R2 3Dw r
 
|sign=2R2 3d' R2 3d 2R' 3d' R2 3d 2R2 3d' R2 3d' 2L' 3d R2 3d 2R
 
|sign=2R2 3d' R2 3d 2R' 3d' R2 3d 2R2 3d' R2 3d' 2L' 3d R2 3d 2R
 
|length=(23,18)|name=v2
 
|length=(23,18)|name=v2
Line 6,079: Line 6,325:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Lw' U2 l U2 Lw U2 Rw' U2 l U2 l' U2 x U2 l2 U2 x' U2
+
{{Alg6|wca=Rw U2 Lw' U2 l U2 Lw U2 Rw' U2 l U2 l' U2 x U2 l2 U2 x' U2
 
|sign=r U2 l' U2 2L U2 l U2 r' U2 2L U2 2L' U2 x U2 2L2 U2 x' U2
 
|sign=r U2 l' U2 2L U2 l U2 r' U2 2L U2 2L' U2 x U2 2L2 U2 x' U2
 
|length=(29,18)|name=|wide=Y|author=|url=
 
|length=(29,18)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 x' r' (F2 U' l' U)5 r x
+
{{Alg6|wca=r' f R' f Uw f' Uw' Rw u f' Uw' R' Uw' r' Uw R f' U r
 +
|sign=2R' 2F R' 2F u 2F' u' r 2U 2F' u' R' u' 2R' u R 2F' U 2R
 +
|length=(19,19)|name=Alg.1|wide=N|author=Ben Whitmore
 +
|url=
 +
}}
 +
{{Alg6|wca=U2 x' r' (F2 U' l' U)5 r x
 
|sign=U2 x' 2R' (F2 U' 2L' U)5 2R x
 
|sign=U2 x' 2R' (F2 U' 2L' U)5 2R x
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
}}
 
}}
{{Alg5|wca=U2 x' r' (F2 U' l U)5 r x
+
{{Alg6|wca=U2 x' r' (F2 U' l U)5 r x
 
|sign=U2 x' 2R' (F2 U' 2L U)5 2R x
 
|sign=U2 x' 2R' (F2 U' 2L U)5 2R x
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
}}
 
}}
{{Alg5|wca=U2 x' r' (U' l' U F2)5 r x
+
{{Alg6|wca=U2 x' r' (U' l' U F2)5 r x
 
|sign=U2 x' 2R' (U' 2L' U F2)5 2R x
 
|sign=U2 x' 2R' (U' 2L' U F2)5 2R x
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
}}
 
}}
{{Alg5|wca=U2 x' r' (U' l U F2)5 r x
+
{{Alg6|wca=U2 x' r' (U' l U F2)5 r x
 
|sign=U2 x' 2R' (U' 2L U F2)5 2R x
 
|sign=U2 x' 2R' (U' 2L U F2)5 2R x
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|length=(29,23)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
|url=https://www.reddit.com/r/Cubers/comments/7mda6x/by_far_the_easiest_oll_parity_alg_to_memorize_for/
 
}}
 
}}
{{Alg5|wca=(F d' S r F Rw2 f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 Rw2 F' r' S' d F')
+
{{Alg6|wca=(F d' S r F Rw2 f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 Rw2 F' r' S' d F')
 
|sign=(F 2D' s 2R F r2 2F2 2U' 2R2 u2 s') 2R (s u2 2R2 2U 2F2 r2 F' 2R' s' 2D F')
 
|sign=(F 2D' s 2R F r2 2F2 2U' 2R2 u2 s') 2R (s u2 2R2 2U 2F2 r2 F' 2R' s' 2D F')
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(B Lw2 U' L' U r u2 b' r2 Bw2 E) r' (E' Bw2 r2 b u2 r' U' L U Lw2 B')
+
{{Alg6|wca=(B Lw2 U' L' U r u2 b' r2 Bw2 E) r' (E' Bw2 r2 b u2 r' U' L U Lw2 B')
 
|sign=(B l2 U' L' U 2R 2U2 2B' 2R2 b2 e) 2R' (e' b2 2R2 2B 2U2 2R' U' L U l2 B')
 
|sign=(B l2 U' L' U 2R 2U2 2B' 2R2 b2 e) 2R' (e' b2 2R2 2B 2U2 2R' U' L U l2 B')
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2
+
{{Alg6|wca=r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2
 
|sign=2R' U' R' U' 2R' U R U 2R U2 2R' U' R' U' 2R2 U R U 2R U2 2R U2 2R' U2
 
|sign=2R' U' R' U' 2R' U R U 2R U2 2R' U' R' U' 2R2 U R U 2R U2 2R U2 2R' U2
 
|length=(29,24)|name=|wide=N|author=Christopher Mowla
 
|length=(29,24)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-495801
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-495801
 
}}
 
}}
{{Alg5|wca=R U Rw U2 Rw U2 Rw' U' Rw2 U2 R2 Rw U' R' U' Rw U2 R' Rw2 U Rw2 U' R' U
+
{{Alg6|wca=R U Rw U2 Rw U2 Rw' U' Rw2 U2 R2 Rw U' R' U' Rw U2 R' Rw2 U Rw2 U' R' U
 
|sign=R U r U2 r U2 r' U' r2 U2 R2 r U' R' U' r U2 R' r2 U r2 U' R' U
 
|sign=R U r U2 r U2 r' U' r2 U2 R2 r U' R' U' r U2 R' r2 U r2 U' R' U
 
|length=(30,24)|name=|wide=N|author=xyzzy
 
|length=(30,24)|name=|wide=N|author=xyzzy
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
}}
 
}}
{{Alg5|wca=U R' U' Rw2 U R' Rw2 U2 Rw U' R' U' R2 Rw U2 Rw2 U' Rw' U2 Rw U2 Rw U R
+
{{Alg6|wca=U R' U' Rw2 U R' Rw2 U2 Rw U' R' U' R2 Rw U2 Rw2 U' Rw' U2 Rw U2 Rw U R
 
|sign=U R' U' r2 U R' r2 U2 r U' R' U' R2 r U2 r2 U' r' U2 r U2 r U R
 
|sign=U R' U' r2 U R' r2 U2 r U' R' U' R2 r U2 r2 U' r' U2 r U2 r U R
 
|length=(30,24)|name=|wide=N|author=xyzzy
 
|length=(30,24)|name=|wide=N|author=xyzzy
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
}}
 
}}
{{Alg5|wca=U Rw U2 Rw U2 Rw' U' Rw2 U2 R2 Rw U' R' U' Rw U2 R' Rw2 U Rw2 U' R' U R
+
{{Alg6|wca=U Rw U2 Rw U2 Rw' U' Rw2 U2 R2 Rw U' R' U' Rw U2 R' Rw2 U Rw2 U' R' U R
 
|sign=U r U2 r U2 r' U' r2 U2 R2 r U' R' U' r U2 R' r2 U r2 U' R' U R
 
|sign=U r U2 r U2 r' U' r2 U2 R2 r U' R' U' r U2 R' r2 U r2 U' R' U R
 
|length=(30,24)|name=|wide=N|author=xyzzy
 
|length=(30,24)|name=|wide=N|author=xyzzy
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
}}
 
}}
{{Alg5|wca=R U R' U' Rw2 U R' Rw2 U2 Rw U' R' U' R2 Rw U2 Rw2 U' Rw' U2 Rw U2 Rw U
+
{{Alg6|wca=R U R' U' Rw2 U R' Rw2 U2 Rw U' R' U' R2 Rw U2 Rw2 U' Rw' U2 Rw U2 Rw U
 
|sign=R U R' U' r2 U R' r2 U2 r U' R' U' R2 r U2 r2 U' r' U2 r U2 r U
 
|sign=R U R' U' r2 U R' r2 U2 r U' R' U' R2 r U2 r2 U' r' U2 r U2 r U
 
|length=(31,24)|name=|wide=N|author=xyzzy
 
|length=(31,24)|name=|wide=N|author=xyzzy
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
}}
 
}}
{{Alg5|wca=(z' Lw Uw2 U' Rw L2 U2 Lw' U' Lw R F2 U' R' U) r' (U' R U F2 R' Lw' U Lw U2 L2 Rw' U Uw2 Lw' z)
+
{{Alg6|wca=(z' Lw Uw2 U' Rw L2 U2 Lw' U' Lw R F2 U' R' U) r' (U' R U F2 R' Lw' U Lw U2 L2 Rw' U Uw2 Lw' z)
 
|sign=(z' l u2 U' r L2 U2 l' U' l R F2 U' R' U) 2R' (U' R U F2 R' l' U l U2 L2 r' U u2 l' z)
 
|sign=(z' l u2 U' r L2 U2 l' U' l R F2 U' R' U) 2R' (U' R U F2 R' l' U l U2 L2 r' U u2 l' z)
 
|length=(33,29)|name=1 Slicer|wide=N|author=Christopher Mowla
 
|length=(33,29)|name=1 Slicer|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U' r U r2 U2 r U2 r2 U' r' U' r' U2 r2 U r2 U r U2 r' U r' U' r' U2 r2 U' r' U' r2//Safe
+
{{Alg6|wca=U' r U r2 U2 r U2 r2 U' r' U' r' U2 r2 U r2 U r U2 r' U r' U' r' U2 r2 U' r' U' r2 //Safe
 
|sign=U' 2R U 2R2 U2 2R U2 2R2 U' 2R' U' 2R' U2 2R2 U 2R2 U 2R U2 2R' U 2R' U' 2R' U2 2R2 U' 2R' U' 2R2
 
|sign=U' 2R U 2R2 U2 2R U2 2R2 U' 2R' U' 2R' U2 2R2 U 2R2 U 2R U2 2R' U 2R' U' 2R' U2 2R2 U' 2R' U' 2R2
 
|length=(41,30)|name=|wide=N|author=Ben Whitmore
 
|length=(41,30)|name=|wide=N|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_U/index.html
 
}}
 
}}
{{Alg5|wca=(z' Lw Uw2 U' Rw L2 U2 Lw' U' Rw R U2 3Lw U' R2 U) r' (U' R2 U 3Lw' U2 R' Rw' U Lw U2 L2 Rw' U Uw2 Lw' z)
+
{{Alg6|wca=(z' Lw Uw2 U' Rw L2 U2 Lw' U' Rw R U2 3Lw U' R2 U) r' (U' R2 U 3Lw' U2 R' Rw' U Lw U2 L2 Rw' U Uw2 Lw' z)
 
|sign=(z' l u2 U' r L2 U2 l' U' r R U2 3l U' R2 U) 2R' (U' R2 U 3l' U2 R' r' U l U2 L2 r' U u2 l' z)
 
|sign=(z' l u2 U' r L2 U2 l' U' r R U2 3l U' R2 U) 2R' (U' R2 U 3l' U2 R' r' U l U2 L2 r' U u2 l' z)
 
|length=(37,31)|name=1 Slicer(2)|wide=N|author=Christopher Mowla
 
|length=(37,31)|name=1 Slicer(2)|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y Rw' U2 Rw U' Rw' U Rw' U' Rw2 U Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U Rw' U' Rw U' Rw U2 Rw U2 Rw2 U2 Rw U2 Rw2 y'
+
{{Alg6|wca=y Rw' U2 Rw U' Rw' U Rw' U' Rw2 U Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U Rw' U' Rw U' Rw U2 Rw U2 Rw2 U2 Rw U2 Rw2 y'
 
|sign=y r' U2 r U' r' U r' U' r2 U r2 U2 r' U2 r U2 r' U2 r' U r' U' r U' r U2 r U2 r2 U2 r U2 r2 y'
 
|sign=y r' U2 r U' r' U r' U' r2 U r2 U2 r' U2 r U2 r' U2 r' U r' U' r U' r U2 r U2 r2 U2 r U2 r2 y'
 
|length=(46,33)|name=|wide=Y|author=Ben Whitmore
 
|length=(46,33)|name=|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
}}
 
}}
 
+
{{br|b=1}}
===Adjacent double parity===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Adjacent double parity</span>===
 
[[Image:Adj.dblparity.png|110px|]]
 
[[Image:Adj.dblparity.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=y' l' f U R D U L' u L D' U' R' U' f l f2 y
{{Alg5|wca=(y' r2 F Rw' F') r2 U2 (r' U2)3 (F Rw F' r2 y)
+
|sign=y' 2L' 2F U R D U L' 2U L D' U' R' U' 2F 2L 2F2 y
 +
|length=(17,16)|name=|wide=N|author=Tom Rokicki
 +
|url=https://www.speedsolving.com/threads/a-collection-of-algorithms.708/page-124#post-1428087
 +
}}
 +
{{Alg6|wca=y' l2 f l U' B' D' U' F u F' D U B U l f' y
 +
|sign=y' 2L2 2F 2L U' B' D' U' F 2U F' D U B U 2L 2F' y
 +
|length=(17,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' r b' U R D U L' d' L D' U' R' U' b' r' b2 y
 +
|sign=y' 2R 2B' U R D U L' 2D' L D' U' R' U' 2B' 2R' 2B2 y
 +
|length=(17,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' r2 b' r' U' B' D' U' F d' F' D U B U r' b y
 +
|sign=y' 2R2 2B' 2R' U' B' D' U' F 2D' F' D U B U 2R' 2B y
 +
|length=(17,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' l f U2 L2 U' L' R' d L R U L2 U2 f l' f2 y
 +
|sign=y' 2L 2F U2 L2 U' L' R' 2D L R U L2 U2 2F 2L' 2F2 y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' l2 f' l U2 F2 U F B d F' B' U' F2 U2 l f y
 +
|sign=y' 2L2 2F' 2L U2 F2 U F B 2D F' B' U' F2 U2 2L 2F y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' r2 b r' U2 F2 U F B u' F' B' U' F2 U2 r' b' y
 +
|sign=y' 2R2 2B 2R' U2 F2 U F B 2U' F' B' U' F2 U2 2R' 2B' y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' r' b' U2 L2 U' L' R' u' L R U L2 U2 b' r b2 y
 +
|sign=y' 2R' 2B' U2 L2 U' L' R' 2U' L R U L2 U2 2B' 2R 2B2 y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' f2 l f' U2 L2 U L' R' d' L R U' L2 U2 f' l' y
 +
|sign=y' 2F2 2L 2F' U2 L2 U L' R' 2D' L R U' L2 U2 2F' 2L' y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' f' l' U2 F2 U' F B d' F' B' U F2 U2 l' f l2 y
 +
|sign=y' 2F' 2L' U2 F2 U' F B 2D' F' B' U F2 U2 2L' 2F 2L2 y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' b r U2 F2 U' F B u F' B' U F2 U2 r b' r2 y
 +
|sign=y' 2B 2R U2 F2 U' F B 2U F' B' U F2 U2 2R 2B' 2R2 y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=y' b2 r' b U2 L2 U L' R' u L R U' L2 U2 b r y
 +
|sign=y' 2B2 2R' 2B U2 L2 U L' R' 2U L R U' L2 U2 2B 2R y
 +
|length=(21,16)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=(y' r2 F Rw' F') r2 U2 (r' U2)3 (F Rw F' r2 y)
 
|sign=(y' 2R2 F r' F') 2R2 U2 (2R' U2)3 (F r F' 2R2 y)
 
|sign=(y' 2R2 F r' F') 2R2 U2 (2R' U2)3 (F r F' 2R2 y)
 
|length=(23,16)|name=|wide=N|author=Christopher Mowla
 
|length=(23,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652052
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652052
 
}}
 
}}
{{Alg5|wca=(y Rw' z' L' U r F) r2 U2 (r' U2)3 (F' r' U' L z Rw y')
+
{{Alg6|wca=(y Rw' z' L' U r F) r2 U2 (r' U2)3 (F' r' U' L z Rw y')
 
|sign=(y r' z' L' U 2R F) 2R2 U2 (2R' U2)3 (F' 2R' U' L z r y')
 
|sign=(y r' z' L' U 2R F) 2R2 U2 (2R' U2)3 (F' 2R' U' L z r y')
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652052
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652052
 
}}
 
}}
{{Alg5|wca=Dw2 D F2 U l' F2 l F2 U l D' U2 r' D F2 D' r Dw2
+
{{Alg6|wca=Dw2 D F2 U l' F2 l F2 U l D' U2 r' D F2 D' r Dw2
 
|sign=d2 D F2 U 2L' F2 2L F2 U 2L D' U2 2R' D F2 D' 2R d2
 
|sign=d2 D F2 U 2L' F2 2L F2 U 2L D' U2 2R' D F2 D' 2R d2
 
|length=(23,18)|name=|wide=N|author=Clément Gallet
 
|length=(23,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw2 D F2 U l' F2 l F2 U l D U2 r' D' F2 D r d2
+
{{Alg6|wca=Dw2 D F2 U l' F2 l F2 U l D U2 r' D' F2 D r d2
 
|sign=d2 D F2 U 2L' F2 2L F2 U 2L D U2 2R' D' F2 D 2R 2D2
 
|sign=d2 D F2 U 2L' F2 2L F2 U 2L D U2 2R' D' F2 D 2R 2D2
 
|length=(23,18)|name=|wide=N|author=Clément Gallet
 
|length=(23,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x' r2 U' Rw U) M' U2 (r' U2)3 l r (U' Rw' U r2 x)
+
{{Alg6|wca=(x' r2 U' Rw U) M' U2 (r' U2)3 l r (U' Rw' U r2 x)
 
|sign=(x' 2R2 U' r U) m' U2 (2R' U2)3 2L 2R (U' r' U 2R2 x)
 
|sign=(x' 2R2 U' r U) m' U2 (2R' U2)3 2L 2R (U' r' U 2R2 x)
 
|length=(24,18)|name=|wide=N|author=Christopher Mowla
 
|length=(24,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
}}
 
}}
{{Alg5|wca=u2 D' F2 U l' F2 l F2 U l D U2 r' D' F2 D r u2
+
{{Alg6|wca=u2 D' F2 U l' F2 l F2 U l D U2 r' D' F2 D r u2
 
|sign=2U2 D' F2 U 2L' F2 2L F2 U 2L D U2 2R' D' F2 D 2R 2U2
 
|sign=2U2 D' F2 U 2L' F2 2L F2 U 2L D U2 2R' D' F2 D 2R 2U2
 
|length=(24,18)|name=|wide=N|author=Clément Gallet
 
|length=(24,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R B y2 r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l B' R'
+
{{Alg6|wca=R B y2 r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l B' R'
 
|sign=R B y2 2R U2 2R' e2 F2 2L F2 2L' F2 2R F2 2R' D2 2L B' R'
 
|sign=R B y2 2R U2 2R' e2 F2 2L F2 2L' F2 2R F2 2R' D2 2L B' R'
 
|length=(25,18)|name=|wide=N|author=Kenneth Gustavsson
 
|length=(25,18)|name=|wide=N|author=Kenneth Gustavsson
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 U' B2 U l' U' l' B2 l U F2 U' B2 l B2 U F2 l'
+
{{Alg6|wca=l2 U' B2 U l' U' l' B2 l U F2 U' B2 l B2 U F2 l'
 
|sign=2L2 U' B2 U 2L' U' 2L' B2 2L U F2 U' B2 2L B2 U F2 2L'
 
|sign=2L2 U' B2 U 2L' U' 2L' B2 2L U F2 U' B2 2L B2 U F2 2L'
 
|length=(25,18)|name=|wide=N|author=Clément Gallet
 
|length=(25,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 U' B2 U l' F2 U' Lw' B2 l B2 Lw U F2 U' B2 U l'
+
{{Alg6|wca=l2 U' B2 U l' F2 U' Lw' B2 l B2 Lw U F2 U' B2 U l'
 
|sign=2L2 U' B2 U 2L' F2 U' l' B2 2L B2 l U F2 U' B2 U 2L'
 
|sign=2L2 U' B2 U 2L' F2 U' l' B2 2L B2 l U F2 U' B2 U 2L'
 
|length=(25,18)|name=|wide=N|author=Clément Gallet
 
|length=(25,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 U' B2 U l' F2 U' Rw' U2 l U2 Rw U F2 U' B2 U l'
+
{{Alg6|wca=l2 U' B2 U l' F2 U' Rw' U2 l U2 Rw U F2 U' B2 U l'
 
|sign=2L2 U' B2 U 2L' F2 U' r' U2 2L U2 r U F2 U' B2 U 2L'
 
|sign=2L2 U' B2 U 2L' F2 U' r' U2 2L U2 r U F2 U' B2 U 2L'
 
|length=(25,18)|name=|wide=N|author=Clément Gallet
 
|length=(25,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R B' r2 B2 r B2 r' B2 r B2 U2 r U2 r B2 r2 B' R'
+
{{Alg6|wca=R B' r2 B2 r B2 r' B2 r B2 U2 r U2 r B2 r2 B' R'
 
|sign=R B' 2R2 B2 2R B2 2R' B2 2R B2 U2 2R U2 2R B2 2R2 B' R'
 
|sign=R B' 2R2 B2 2R B2 2R' B2 2R B2 U2 2R U2 2R B2 2R2 B' R'
 
|length=(27,18)|name=|wide=N|author=|url=
 
|length=(27,18)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 U' B2 U F2 l' F2 U' Lw' B2 l B2 Lw B2 U F2 l'
+
{{Alg6|wca=l2 F2 U' B2 U F2 l' F2 U' Lw' B2 l B2 Lw B2 U F2 l'
 
|sign=2L2 F2 U' B2 U F2 2L' F2 U' l' B2 2L B2 l B2 U F2 2L'
 
|sign=2L2 F2 U' B2 U F2 2L' F2 U' l' B2 2L B2 l B2 U F2 2L'
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 U' B2 U F2 l' F2 U' Rw' U2 l U2 Rw B2 U F2 l'
+
{{Alg6|wca=l2 F2 U' B2 U F2 l' F2 U' Rw' U2 l U2 Rw B2 U F2 l'
 
|sign=2L2 F2 U' B2 U F2 2L' F2 U' r' U2 2L U2 r B2 U F2 2L'
 
|sign=2L2 F2 U' B2 U F2 2L' F2 U' r' U2 2L U2 r B2 U F2 2L'
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 l2 U' r' B2 r U l U' B2 U l B2 D2 l' D2 r2
+
{{Alg6|wca=r2 B2 l2 U' r' B2 r U l U' B2 U l B2 D2 l' D2 r2
 
|sign=2R2 B2 2L2 U' 2R' B2 2R U 2L U' B2 U 2L B2 D2 2L' D2 2R2
 
|sign=2R2 B2 2L2 U' 2R' B2 2R U 2L U' B2 U 2L B2 D2 2L' D2 2R2
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|length=(27,18)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x Rw F2 U' R Rw) U' (r U2)3 r2 U' (Rw' R' U F2 Rw' x')
+
{{Alg6|wca=(x Rw F2 U' R Rw) U' (r U2)3 r2 U' (Rw' R' U F2 Rw' x')
 
|sign=(x r F2 U' R r) U' (2R U2)3 2R2 U' (r' R' U F2 r' x')
 
|sign=(x r F2 U' R r) U' (2R U2)3 2R2 U' (r' R' U F2 r' x')
 
|length=(25,19)|name=|wide=N|author=Christopher Mowla
 
|length=(25,19)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
}}
 
}}
{{Alg5|wca=(y Rw2 U x') l U' L' U' l' U L U F2 l' F2 r U2 r' U2 (x U' Rw2 y')
+
{{Alg6|wca=(y Rw2 U x') l U' L' U' l' U L U F2 l' F2 r U2 r' U2 (x U' Rw2 y')
 
|sign=(y r2 U x') 2L U' L' U' 2L' U L U F2 2L' F2 2R U2 2R' U2 (x U' r2 y')
 
|sign=(y r2 U x') 2L U' L' U' 2L' U L U F2 2L' F2 2R U2 2R' U2 (x U' r2 y')
 
|length=(25,19)|name=|wide=N|author=Christopher Mowla
 
|length=(25,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(r2 F') Rw' F' U2 F r F l D2 r' D2 F2 l' U2 F R (F r2)
+
{{Alg6|wca=(r2 F') Rw' F' U2 F r F l D2 r' D2 F2 l' U2 F R (F r2)
 
|sign=(2R2 F') r' F' U2 F 2R F 2L D2 2R' D2 F2 2L' U2 F R (F 2R2)
 
|sign=(2R2 F') r' F' U2 F 2R F 2L D2 2R' D2 F2 2L' U2 F R (F 2R2)
 
|length=(26,19)|name=|wide=N|author=Christopher Mowla
 
|length=(26,19)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
}}
 
}}
{{Alg5|wca=r' B L' B l' B' L B' l U l B2 Lw' F2 l' F2 Lw B2 U' M'
+
{{Alg6|wca=r' B L' B l' B' L B' l U l B2 Lw' F2 l' F2 Lw B2 U' M'
 
|sign=2R' B L' B 2L' B' L B' 2L U 2L B2 l' F2 2L' F2 l B2 U' m'
 
|sign=2R' B L' B 2L' B' L B' 2L U 2L B2 l' F2 2L' F2 l B2 U' m'
 
|length=(24,20)|name=|wide=N|author=Christopher Mowla
 
|length=(24,20)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-590058
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-590058
 
}}
 
}}
{{Alg5|wca=(y Rw2 U x') l U' L' U' l' U L U M' U2 l' U2 l U2 r' U2 (x U' Rw2 y')
+
{{Alg6|wca=(y Rw2 U x') l U' L' U' l' U L U M' U2 l' U2 l U2 r' U2 (x U' Rw2 y')
 
|sign=(y r2 U x') 2L U' L' U' 2L' U L U m' U2 2L' U2 2L U2 2R' U2 (x U' r2 y')
 
|sign=(y r2 U x') 2L U' L' U' 2L' U L U m' U2 2L' U2 2L U2 2R' U2 (x U' r2 y')
 
|length=(26,20)|name=|wide=N|author=Christopher Mowla
 
|length=(26,20)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y Rw2 F L) F U2 l F2 D2 r D2 l' F r' F U2 F' r (L' F' Rw2 y')
+
{{Alg6|wca=(y Rw2 F L) F U2 l F2 D2 r D2 l' F r' F U2 F' r (L' F' Rw2 y')
 
|sign=(y r2 F L) F U2 2L F2 D2 2R D2 2L' F 2R' F U2 F' 2R (L' F' r2 y')
 
|sign=(y r2 F L) F U2 2L F2 D2 2R D2 2L' F 2R' F U2 F' 2R (L' F' r2 y')
 
|length=(27,20)|name=|wide=N|author=Christopher Mowla
 
|length=(27,20)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
}}
 
}}
{{Alg5|wca=(z' Rw' U' Rw' l' U L') U' r2 (U2 r')3 U' (L U' l Rw U Rw z)
+
{{Alg6|wca=(z' Rw' U' Rw' l' U L') U' r2 (U2 r')3 U' (L U' l Rw U Rw z)
 
|sign=(z' r' U' r' 2L' U L') U' 2R2 (U2 2R')3 U' (L U' 2L r U r z)
 
|sign=(z' r' U' r' 2L' U L') U' 2R2 (U2 2R')3 U' (L U' 2L r U r z)
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-37#post-586149
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-37#post-586149
 
}}
 
}}
{{Alg5|wca=(Lw2 B' R B l b2 u' l2 Uw2 S) l' (S' Uw2 l2 u b2 l' B' R' B Lw2)
+
{{Alg6|wca=(Lw2 B' R B l b2 u' l2 Uw2 S) l' (S' Uw2 l2 u b2 l' B' R' B Lw2)
 
|sign=(l2 B' R B 2L 2B2 2U' 2L2 u2 s) 2L' (s' u2 2L2 2U 2B2 2L' B' R' B l2)
 
|sign=(l2 B' R B 2L 2B2 2U' 2L2 u2 s) 2L' (s' u2 2L2 2U 2B2 2L' B' R' B l2)
 
|length=(29,21)|name=|wide=N|author=Christopher Mowla
 
|length=(29,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y x' Lw2 F' L2 F r f2 u' r2 Uw2 S') r' (S Uw2 r2 u f2 r' F' L2 F Lw2 x y')
+
{{Alg6|wca=(y x' Lw2 F' L2 F r f2 u' r2 Uw2 S') r' (S Uw2 r2 u f2 r' F' L2 F Lw2 x y')
 
|sign=(y x' l2 F' L2 F 2R 2F2 2U' 2R2 u2 s') 2R' (s u2 2R2 2U 2F2 2R' F' L2 F l2 x y')
 
|sign=(y x' l2 F' L2 F 2R 2F2 2U' 2R2 u2 s') 2R' (s u2 2R2 2U 2F2 2R' F' L2 F l2 x y')
 
|length=(31,21)|name=|wide=N|author=Christopher Mowla
 
|length=(31,21)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
}}
 
}}
{{Alg5|wca=(y Bw' R U b' R' Bw' Uw2 Rw' u2 l2 S') u (S l2 u2 Rw Uw2 Bw R b U' R' Bw y')
+
{{Alg6|wca=(y Bw' R U b' R' Bw' Uw2 Rw' u2 l2 S') u (S l2 u2 Rw Uw2 Bw R b U' R' Bw y')
 
|sign=(y b' R U 2B' R' b' u2 r' 2U2 2L2 s') 2U (s 2L2 2U2 r u2 b R 2B U' R' b y')
 
|sign=(y b' R U 2B' R' b' u2 r' 2U2 2L2 s') 2U (s 2L2 2U2 r u2 b R 2B U' R' b y')
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
}}
 
}}
{{Alg5|wca=Rw2 U2 R2 Rw U' R' U' Rw U2 R2 U' R Rw2 U2 Rw' U R U Rw U2 Rw2 U Rw U2
+
{{Alg6|wca=Rw2 U2 R2 Rw U' R' U' Rw U2 R2 U' R Rw2 U2 Rw' U R U Rw U2 Rw2 U Rw U2
 
|sign=r2 U2 R2 r U' R' U' r U2 R2 U' R r2 U2 r' U R U r U2 r2 U r U2
 
|sign=r2 U2 R2 r U' R' U' r U2 R2 U' R r2 U2 r' U R U r U2 r2 U r U2
 
|length=(32,24)|name=|wide=N|author=xyzzy
 
|length=(32,24)|name=|wide=N|author=xyzzy
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
}}
 
}}
{{Alg5|wca=U2 Lw2 U2 Lw L2 U' L' U' Lw U2 L2 U' Lw2 L U2 Lw' U L U Lw U2 Lw2 U Lw
+
{{Alg6|wca=U2 Lw2 U2 Lw L2 U' L' U' Lw U2 L2 U' Lw2 L U2 Lw' U L U Lw U2 Lw2 U Lw
 
|sign=U2 l2 U2 l L2 U' L' U' l U2 L2 U' l2 L U2 l' U L U l U2 l2 U l
 
|sign=U2 l2 U2 l L2 U' L' U' l U2 L2 U' l2 L U2 l' U L U l U2 l2 U l
 
|length=(32,24)|name=|wide=N|author=xyzzy
 
|length=(32,24)|name=|wide=N|author=xyzzy
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
|url=https://gist.github.com/torchlight/fdc0cdd7949925da192268ccade28820
 
}}
 
}}
{{Alg5|wca=(z Rw' Uw2 U Lw' R2 U2 Rw U Lw' U2 F' R2 F) l' (F' R2 F U2 Lw U' Rw' U2 R2 Lw U' Uw2 Rw z')
+
{{Alg6|wca=(z Rw' Uw2 U Lw' R2 U2 Rw U Lw' U2 F' R2 F) l' (F' R2 F U2 Lw U' Rw' U2 R2 Lw U' Uw2 Rw z')
 
|sign=(z r' u2 U l' R2 U2 r U l' U2 F' R2 F) 2L' (F' R2 F U2 l U' r' U2 R2 l U' u2 r z')
 
|sign=(z r' u2 U l' R2 U2 r U l' U2 F' R2 F) 2L' (F' R2 F U2 l U' r' U2 R2 l U' u2 r z')
 
|length=(33,27)|name=1 Slicer(1)
 
|length=(33,27)|name=1 Slicer(1)
Line 6,299: Line 6,609:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Lw U Rw2 F Rw U' Rw U' F2 U Rw2 U' R' U') r (U R U Rw2 U' F2 U Rw' U Rw' F' Rw2 U' Lw')
+
{{Alg6|wca=(Lw U Rw2 F Rw U' Rw U' F2 U Rw2 U' R' U') r (U R U Rw2 U' F2 U Rw' U Rw' F' Rw2 U' Lw')
 
|sign=(l U r2 F r U' r U' F2 U r2 U' R' U') 2R (U R U r2 U' F2 U r' U r' F' r2 U' l')
 
|sign=(l U r2 F r U' r U' F2 U r2 U' R' U') 2R (U R U r2 U' F2 U r' U r' F' r2 U' l')
 
|length=(35,29)|name=1 Slicer(2)
 
|length=(35,29)|name=1 Slicer(2)
Line 6,305: Line 6,615:
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-55#post-812403
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-55#post-812403
 
}}
 
}}
{{Alg5|wca=Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' B' L B U' L U l U' L' U B' L' B L Uw R Uw2 l2 Bw
+
{{Alg6|wca=Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' B' L B U' L U l U' L' U B' L' B L Uw R Uw2 l2 Bw
 
|sign=u b' 2L b u' b' 2L u2 R' u' L' B' L B U' L U 2L U' L' U B' L' B L u R u2 2L2 b
 
|sign=u b' 2L b u' b' 2L u2 R' u' L' B' L B U' L U 2L U' L' U B' L' B L u R u2 2L2 b
 
|length=(33,30)|name=|wide=N|author=Christopher Mowla
 
|length=(33,30)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' U' B' L B L U l U' L' B' L' B U L Uw R Uw2 l2 Bw
+
{{Alg6|wca=Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' U' B' L B L U l U' L' B' L' B U L Uw R Uw2 l2 Bw
 
|sign=u b' 2L b u' b' 2L u2 R' u' L' U' B' L B L U 2L U' L' B' L' B U L u R u2 2L2 b
 
|sign=u b' 2L b u' b' 2L u2 R' u' L' U' B' L B L U 2L U' L' B' L' B U L u R u2 2L2 b
 
|length=(33,30)|name=|wide=N|author=Christopher Mowla
 
|length=(33,30)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=((Lw x) Uw2 Lw Rw Uw2 Rw2 U2 Rw U' Lw U2 F L2 U F' U') l' (U F U' L2 F' U2 Lw' U Rw' U2 Rw2 Uw2 Lw' Rw' Uw2 (Lw' x'))
+
{{Alg6|wca=((Lw x) Uw2 Lw Rw Uw2 Rw2 U2 Rw U' Lw U2 F L2 U F' U') l' (U F U' L2 F' U2 Lw' U Rw' U2 Rw2 Uw2 Lw' Rw' Uw2 (Lw' x'))
 
|sign=((l x) u2 l r u2 r2 U2 r U' l U2 F L2 U F' U') 2L' (U F U' L2 F' U2 l' U r' U2 r2 u2 l' r' u2 (l' x'))
 
|sign=((l x) u2 l r u2 r2 U2 r U' l U2 F L2 U F' U') 2L' (U F U' L2 F' U2 l' U r' U2 r2 u2 l' r' u2 (l' x'))
 
|length=(45,33)|name=5x5x5 1 Slicer
 
|length=(45,33)|name=5x5x5 1 Slicer
Line 6,321: Line 6,631:
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Three flips===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Three flips</span>===
 
[[Image:Dp3flip.png|110px|]]
 
[[Image:Dp3flip.png|110px|]]
 
*Note that there are <i>several</i> possible dedge flip <b>double parity</b> cases for the last layer.  This case is probably just the first of many to come on this page, as fast algorithms for other cases are quite possible to achieve.
 
*Note that there are <i>several</i> possible dedge flip <b>double parity</b> cases for the last layer.  This case is probably just the first of many to come on this page, as fast algorithms for other cases are quite possible to achieve.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=u2 f' U' f2 Lw2 U2 f' U2 B2 Lw2 f2 U' f u2 Lw2 B2 Lw2
{{Alg5|wca=u2 f' U' f2 Lw2 U2 f' U2 B2 Lw2 f2 U' f u2 Lw2 B2 Lw2
 
 
|sign=2U2 2F' U' 2F2 l2 U2 2F' U2 B2 l2 2F2 U' 2F 2U2 l2 B2 l2
 
|sign=2U2 2F' U' 2F2 l2 U2 2F' U2 B2 l2 2F2 U' 2F 2U2 l2 B2 l2
 
|length=(29,17)|name=|wide=N|author=Clément Gallet
 
|length=(29,17)|name=|wide=N|author=Clément Gallet
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw R U2 x
+
{{Alg6|wca=Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw R U2 x
 
|sign=r' U2 2R U2 r' x' U2 2R' U' R' U' r' U2 r U R U' r R U2 x
 
|sign=r' U2 2R U2 r' x' U2 2R' U' R' U' r' U2 r U R U' r R U2 x
 
|length=(24,19)|name=|wide=N|author=Christopher Mowla
 
|length=(24,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y M U r U2 r2 U2 r' U2 F2 r' F2 r2 U2 l F2 l' F2 r2 U' M' y'
+
{{Alg6|wca=y M U r U2 r2 U2 r' U2 F2 r' F2 r2 U2 l F2 l' F2 r2 U' M' y'
 
|sign=y m U 2R U2 2R2 U2 2R' U2 F2 2R' F2 2R2 U2 2L F2 2L' F2 2R2 U' m' y'
 
|sign=y m U 2R U2 2R2 U2 2R' U2 F2 2R' F2 2R2 U2 2L F2 2L' F2 2R2 U' m' y'
 
|length=(31,20)|name=|wide=N|author=|url=
 
|length=(31,20)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(y' r' U2 M l U)(r' U' F' R' F R2 U') r' (U R2 F' R F U r) r U2 r' U2 (U' M' l' U2 r y)
+
{{Alg6|wca=(y' r' U2 M l U)(r' U' F' R' F R2 U') r' (U R2 F' R F U r) r U2 r' U2 (U' M' l' U2 r y)
 
|sign=(y' 2R' U2 m 2L U)(2R' U' F' R' F R2 U') 2R' (U R2 F' R F U 2R) 2R U2 2R' U2 (U' m' 2L' U2 2R y)
 
|sign=(y' 2R' U2 m 2L U)(2R' U' F' R' F R2 U') 2R' (U R2 F' R F U 2R) 2R U2 2R' U2 (U' m' 2L' U2 2R y)
 
|length=(33,27)|name=|wide=N|author=Christopher Mowla
 
|length=(33,27)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">In the M layer</span>==
==In the M layer==
 
 
[[Image:MLyrparity.png|100px|]]
 
[[Image:MLyrparity.png|100px|]]
 
*Note that none of these algorithms affect the cube in the same manner as their inverses.
 
*Note that none of these algorithms affect the cube in the same manner as their inverses.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=r U2 r' U2 r' D2 r D2 r' B2 r B2 r'
{{Alg5|wca=r U2 r' U2 r' D2 r D2 r' B2 r B2 r'
 
 
|sign=2R U2 2R' U2 2R' D2 2R D2 2R' B2 2R B2 2R'
 
|sign=2R U2 2R' U2 2R' D2 2R D2 2R' B2 2R B2 2R'
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l'
+
{{Alg6|wca=r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l'
 
|sign=2R U2 2R' U2 m' 2L' U2 2R U2 2L' U2 2R U2 2L'
 
|sign=2R U2 2R' U2 m' 2L' U2 2R U2 2L' U2 2R U2 2L'
 
|length=(20,14)|name=|wide=N|author=Christopher Mowla
 
|length=(20,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2
+
{{Alg6|wca=r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2
 
|sign=2R U2 2L' U2 2L 2R2 U2 2L U2 2R' U2 2L U2 2L 2R2
 
|sign=2R U2 2L' U2 2L 2R2 U2 2L U2 2R' U2 2L U2 2L 2R2
 
|length=(23,15)|name=reParity(v2)
 
|length=(23,15)|name=reParity(v2)
Line 6,369: Line 6,676:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(r' U' F' R' F R2 U' Lw2 E L2 E') r' (E L2 E' Lw2 U R2 F' R F U r) (r U2 r' U2)
+
{{Alg6|wca=(r' U' F' R' F R2 U' Lw2 E L2 E') r' (E L2 E' Lw2 U R2 F' R F U r) (r U2 r' U2)
 
|sign=(2R' U' F' R' F R2 U' l2 e L2 e') 2R' (e L2 e' l2 U R2 F' R F U 2R) (2R U2 2R' U2)
 
|sign=(2R' U' F' R' F R2 U' l2 e L2 e') 2R' (e L2 e' l2 U R2 F' R F U 2R) (2R U2 2R' U2)
 
|length=(35,26)|name=|wide=N|author=Christopher Mowla
 
|length=(35,26)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">OLL parity algorithms which don't preserve the last layer</span>=
 
 
=OLL parity algorithms which don't preserve the last layer=
 
 
[[Image:ImpurededgeFlip.PNG|110px|]]
 
[[Image:ImpurededgeFlip.PNG|110px|]]
 
*Some of the algorithms in this category are the most widely used speedsolving algorithms.
 
*Some of the algorithms in this category are the most widely used speedsolving algorithms.
*<b>None of these algorithms will result in a single dedge flip or the [https://www.speedsolving.com/wiki/images/9/95/DblParity.png "pure form"] of double parity if single slices are substituted for the wide turns</b>.
+
*None of these algorithms will result in a single dedge flip or the {{LinkColorE|u=https://www.speedsolving.com/wiki/images/9/95/DblParity.png|c=rgb(229,148,0)|t="pure form"}} of double parity if single slices are substituted for the wide turns.
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Single parity</span>==
==Single parity==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">1 flip</span>===
===1 flip===
+
*With the exception of Kåre Krig's 2 gen algorithms, all algorithms listed in this section can be derived from algorithms from the {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php?title=4x4x4_parity_algorithms#Longer.2Ffaster_algorithms|c=rgb(229,148,0)|t=Longer/Faster Algorithms}} section by using 4x4x4 wide turn equivalences such as Rw = (Lw x), Lw2 = (Rw2 x2), etc.
*With the exception of Kåre Krig's 2 gen algorithms, all algorithms listed in this section can be derived from algorithms from the [https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms#Longer.2FFaster_Algorithms Longer/Faster Algorithms] section by using 4x4x4 wide turn equivalences such as Rw = (Lw x), Lw2 = (Rw2 x2), etc.
+
*Specifically, these algorithms were derived from the {{LinkColorE|u=https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2|c=rgb(229,148,0)|t=3x3x3 Classic Setup's}} solutions which are at most 18 single slice half turns.  They only involve 2 face turns and thus there are additional transformations which are "legal" in wide turns, but "illegal" transformations to keep these algorithms pure dedge flips.
*Specifically, these algorithms were derived from the [https://alg.cubing.net/?alg=R2_B2_U2_L_U2_R-_U2_R_U2_F2_R_F2_L-_B2_R2 3x3x3 Classic Setup]'s solutions which are at most 18 single slice half turns.  They only involve 2 face turns and thus there are additional transformations which are "legal" in wide turns, but "illegal" transformations to keep these algorithms pure dedge flips.
 
 
**Therefore we have more 15 BHTM solutions which preserve F3L in wide turns than we have for pure dedge flips, for example.
 
**Therefore we have more 15 BHTM solutions which preserve F3L in wide turns than we have for pure dedge flips, for example.
**<b>Most of these algorithms need to be adjusted to work on the 5x5x5</b>.
+
**<u>Most of these algorithms need to be adjusted to work on the 5x5x5</u>.
 
+
{{br|b=1}}
 
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
<b>Interesting Fact:</b><br>
| bgcolor="fbfb8b" |
+
The following algorithm cannot be used to solve any form of OLL parity if any of its wide turns are converted to single slice turns!
It's interesting to note that the following algorithm cannot even be used to solve any form of OLL parity if all of its wide turns are converted into single slice turns!
+
{{br|b=1}}
 
+
{{Alg6|wca=Rw2 F2 U2 Rw' F' Uw L' U2 L Uw' F' Rw' U2 Rw2 F2 Rw
{{Alg5|wca=Rw2 F2 U2 Rw' F' Uw L' U2 L Uw' F' Rw' U2 Rw2 F2 Rw
 
 
|sign=r2 F2 U2 r' F' u L' U2 L u' F' r' U2 r2 F2 r
 
|sign=r2 F2 U2 r' F' u L' U2 L u' F' r' U2 r2 F2 r
 
|length=(23,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
}}
+
}}</ul>
|}
+
{{br|b=1}}
 
 
  
{{Alg5|wca=Rw' U2 Rw U2 Rw U2 Rw2 F2 Rw' U2 Rw' U2 F2 Rw2 F2
+
{{Alg6|wca=Rw' U2 Rw U2 Rw U2 Rw2 F2 Rw' U2 Rw' U2 F2 Rw2 F2
 
|sign=r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 r2 F2
 
|sign=r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 r2 F2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2
+
{{Alg6|wca=Rw' U2 Rw U2 Rw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2
 
|sign=r' U2 r U2 r' F2 r2 U2 r U2 r' U2 F2 r2 F2
 
|sign=r' U2 r U2 r' F2 r2 U2 r U2 r' U2 F2 r2 F2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Lw F2 Rw' U2 Rw2 U2 F2 Lw' U2 Lw F2 Rw2 U2 x
+
{{Alg6|wca=Rw' U2 Lw F2 Rw' U2 Rw2 U2 F2 Lw' U2 Lw F2 Rw2 U2 x
 
|sign=r' U2 l F2 r' U2 r2 U2 F2 l' U2 l F2 r2 U2 x
 
|sign=r' U2 l F2 r' U2 r2 U2 F2 l' U2 l F2 r2 U2 x
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Lw' B2 Lw U2 Rw2 B2
+
{{Alg6|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Lw' B2 Lw U2 Rw2 B2
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 l' B2 l U2 r2 B2
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 l' B2 l U2 r2 B2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw U2 Rw2 B2
+
{{Alg6|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw U2 Rw2 B2
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Lw' U2 Rw2 B2 Lw U2 Lw' B2 U2 Rw2 U2 x'
+
{{Alg6|wca=Rw' U2 Rw U2 Lw' U2 Rw2 B2 Lw U2 Lw' B2 U2 Rw2 U2 x'
 
|sign=r' U2 r U2 l' U2 r2 B2 l U2 l' B2 U2 r2 U2 x'
 
|sign=r' U2 r U2 l' U2 r2 B2 l U2 l' B2 U2 r2 U2 x'
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw' U2 Rw U2 B2 Rw2 B2 Rw U2 Rw' U2 Rw B2
+
{{Alg6|wca=Rw2 U2 Rw' U2 Rw U2 B2 Rw2 B2 Rw U2 Rw' U2 Rw B2
 
|sign=r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 r B2
 
|sign=r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 r B2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=x' Rw2 B2 Lw B2 Rw' U2 B2 Lw2 B2 Lw' U2 Lw U2 Lw' B2
+
{{Alg6|wca=x' Rw2 B2 Lw B2 Rw' U2 B2 Lw2 B2 Lw' U2 Lw U2 Lw' B2
 
|sign=x' r2 B2 l B2 r' U2 B2 l2 B2 l' U2 l U2 l' B2
 
|sign=x' r2 B2 l B2 r' U2 B2 l2 B2 l' U2 l U2 l' B2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Lw Rw U2 F2 Lw' F2 Rw F2 Rw' F2 U2 Rw' U2 Lw U2 Lw2 x'
+
{{Alg6|wca=Lw Rw U2 F2 Lw' F2 Rw F2 Rw' F2 U2 Rw' U2 Lw U2 Lw2 x'
 
|sign=l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l2 x'
 
|sign=l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l2 x'
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw Rw U2 F2 Lw' F2 Rw F2 Rw' F2 U2 Rw' U2 Lw U2 Rw2 x
+
{{Alg6|wca=Lw Rw U2 F2 Lw' F2 Rw F2 Rw' F2 U2 Rw' U2 Lw U2 Rw2 x
 
|sign=l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 r2 x
 
|sign=l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 r2 x
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw U2 Lw Rw U2 x
+
{{Alg6|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw U2 Lw Rw U2 x
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 x
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 x
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw U2 Lw' Rw' U2 Rw' B2 Rw' B2 U2 Rw2 U2 x'
+
{{Alg6|wca=Rw' U2 Rw U2 Rw U2 Lw' Rw' U2 Rw' B2 Rw' B2 U2 Rw2 U2 x'
 
|sign=r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 x'
 
|sign=r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 x'
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw' U2 Rw U2 Lw Rw2 U2 Rw2 U2 F2 Lw' U2 Lw F2 Rw2 U2 x
+
{{Alg6|wca=Rw' U2 Rw U2 Lw Rw2 U2 Rw2 U2 F2 Lw' U2 Lw F2 Rw2 U2 x
 
|sign=r' U2 r U2 l r2 U2 r2 U2 F2 l' U2 l F2 r2 U2 x
 
|sign=r' U2 r U2 l r2 U2 r2 U2 F2 l' U2 l F2 r2 U2 x
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Lw Rw2 U2 Rw2 U2 F2 Lw' U2 Rw U2 Lw2 F2 x2
+
{{Alg6|wca=Rw' U2 Rw U2 Lw Rw2 U2 Rw2 U2 F2 Lw' U2 Rw U2 Lw2 F2 x2
 
|sign=r' U2 r U2 l r2 U2 r2 U2 F2 l' U2 r U2 l2 F2 x2
 
|sign=r' U2 r U2 l r2 U2 r2 U2 F2 l' U2 r U2 l2 F2 x2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Lw2 Rw B2 Lw2 U2 Rw U2 Lw' B2 U2 Rw2 U2 x'
+
{{Alg6|wca=Rw' U2 Rw U2 Lw2 Rw B2 Lw2 U2 Rw U2 Lw' B2 U2 Rw2 U2 x'
 
|sign=r' U2 r U2 l2 r B2 l2 U2 r U2 l' B2 U2 r2 U2 x'
 
|sign=r' U2 r U2 l2 r B2 l2 U2 r U2 l' B2 U2 r2 U2 x'
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw' B2 Rw2 U2 Rw2
+
{{Alg6|wca=Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw' B2 Rw2 U2 Rw2
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 r2 U2 r2
 
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 r2 U2 r2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw U2 Rw U2 Lw2 B2 Lw Rw2 B2 Rw' B2 U2 Rw2 U2 x'
+
{{Alg6|wca=Rw' U2 Rw U2 Rw U2 Lw2 B2 Lw Rw2 B2 Rw' B2 U2 Rw2 U2 x'
 
|sign=r' U2 r U2 r U2 l2 B2 l r2 B2 r' B2 U2 r2 U2 x'
 
|sign=r' U2 r U2 r U2 l2 B2 l r2 B2 r' B2 U2 r2 U2 x'
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw2 U2 Rw' B2 Rw2 U2 Lw' B2 Lw U2 Rw2 B2
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw2 U2 Rw' B2 Rw2 U2 Lw' B2 Lw U2 Rw2 B2
 
|sign=r' U2 r' U2 r2 U2 r' B2 r2 U2 l' B2 l U2 r2 B2
 
|sign=r' U2 r' U2 r2 U2 r' B2 r2 U2 l' B2 l U2 r2 B2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw2 U2 Rw' B2 Rw2 U2 Rw' U2 Rw U2 Rw2 B2
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw2 U2 Rw' B2 Rw2 U2 Rw' U2 Rw U2 Rw2 B2
 
|sign=r' U2 r' U2 r2 U2 r' B2 r2 U2 r' U2 r U2 r2 B2
 
|sign=r' U2 r' U2 r2 U2 r' B2 r2 U2 r' U2 r U2 r2 B2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 B2 Rw B2 Rw B2 U2 Rw U2 Rw' U2 Rw' U2 Rw2 U2 B2
+
{{Alg6|wca=Rw2 U2 B2 Rw B2 Rw B2 U2 Rw U2 Rw' U2 Rw' U2 Rw2 U2 B2
 
|sign=r2 U2 B2 r B2 r B2 U2 r U2 r' U2 r' U2 r2 U2 B2
 
|sign=r2 U2 B2 r B2 r B2 U2 r U2 r' U2 r' U2 r2 U2 B2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw' U2 Rw' B2 Rw2 U2 Rw' U2 Rw2 U2 Rw U2 Lw U2 x
+
{{Alg6|wca=Rw2 U2 Rw' U2 Rw' B2 Rw2 U2 Rw' U2 Rw2 U2 Rw U2 Lw U2 x
 
|sign=r2 U2 r' U2 r' B2 r2 U2 r' U2 r2 U2 r U2 l U2 x
 
|sign=r2 U2 r' U2 r' B2 r2 U2 r' U2 r2 U2 r U2 l U2 x
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=x' Rw2 B2 Lw2 Rw' U2 Lw' U2 B2 Lw2 B2 Lw' U2 Lw U2 Lw' B2
+
{{Alg6|wca=x' Rw2 B2 Lw2 Rw' U2 Lw' U2 B2 Lw2 B2 Lw' U2 Lw U2 Lw' B2
 
|sign=x' r2 B2 l2 r' U2 l' U2 B2 l2 B2 l' U2 l U2 l' B2
 
|sign=x' r2 B2 l2 r' U2 l' U2 B2 l2 B2 l' U2 l U2 l' B2
 
|length=(27,16)|name=|wide=Y|author=|url=
 
|length=(27,16)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw' U' Rw' U B2 U' Rw U' Rw' U2 Rw' x' U2 Rw U2 Lw' U2 Rw2
+
{{Alg6|wca=Rw' U' Rw' U B2 U' Rw U' Rw' U2 Rw' x' U2 Rw U2 Lw' U2 Rw2
 
|sign=r' U' r' U B2 U' r U' r' U2 r' x' U2 r U2 l' U2 r2
 
|sign=r' U' r' U B2 U' r U' r' U2 r' x' U2 r U2 l' U2 r2
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Lw' U2 Rw U' Rw' U B2 U' Rw U' Rw' U2 Rw' x' U2 Rw'
+
{{Alg6|wca=Rw2 U2 Lw' U2 Rw U' Rw' U B2 U' Rw U' Rw' U2 Rw' x' U2 Rw'
 
|sign=r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' x' U2 r'
 
|sign=r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' x' U2 r'
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw Rw U' Rw U' F2 U Rw' U' x U2 Rw' U2 Rw' U2 Lw U2 Rw2 x
+
{{Alg6|wca=Lw Rw U' Rw U' F2 U Rw' U' x U2 Rw' U2 Rw' U2 Lw U2 Rw2 x
 
|sign=l r U' r U' F2 U r' U' x U2 r' U2 r' U2 l U2 r2 x
 
|sign=l r U' r U' F2 U r' U' x U2 r' U2 r' U2 l U2 r2 x
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
 
|sign=r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
 
|sign=r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
 
|length=(25,17)|name=lucasparity
 
|length=(25,17)|name=lucasparity
Line 6,516: Line 6,819:
 
|url=https://www.speedsolving.com/forum/threads/4x4-oll-parity.4237/#post-52481
 
|url=https://www.speedsolving.com/forum/threads/4x4-oll-parity.4237/#post-52481
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' Rw' U2 Rw'
 
|sign=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'
 
|sign=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'
 
|length=(25,17)|name=lucasparity
 
|length=(25,17)|name=lucasparity
Line 6,522: Line 6,825:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Lw' B2 Lw U2 Lw' U2 Rw U2 Rw' U2 Rw' x' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U2 Lw' B2 Lw U2 Lw' U2 Rw U2 Rw' U2 Rw' x' U2 Rw'
 
|sign=r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' x' U2 r'
 
|sign=r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' x' U2 r'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Rw' U2 Rw U2 Rw' F2 Rw F2 Rw' F2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U2 Rw' U2 Rw U2 Rw' F2 Rw F2 Rw' F2 Rw' U2 Rw'
 
|sign=r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 r' U2 r'
 
|sign=r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 r' U2 r'
 
|length=(25,17)|name=|wide=Y|author=|url=
 
|length=(25,17)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw' U2 Rw U2 Rw U2 Lw' Rw' U2 Lw2 Rw F2 Lw' U2 F2 Rw2 F2
+
{{Alg6|wca=Rw' U2 Rw U2 Rw U2 Lw' Rw' U2 Lw2 Rw F2 Lw' U2 F2 Rw2 F2
 
|sign=r' U2 r U2 r U2 l' r' U2 l2 r F2 l' U2 F2 r2 F2
 
|sign=r' U2 r U2 r U2 l' r' U2 l2 r F2 l' U2 F2 r2 F2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw2 U2 Rw U2 Lw Rw U2 Rw F2 Rw F2 Rw2 U2 x
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw2 U2 Rw U2 Lw Rw U2 Rw F2 Rw F2 Rw2 U2 x
 
|sign=r' U2 r' U2 r2 U2 r U2 l r U2 r F2 r F2 r2 U2 x
 
|sign=r' U2 r' U2 r2 U2 r U2 l r U2 r F2 r F2 r2 U2 x
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw U2 Rw' B2 Rw' B2 Rw2 U2 Rw' B2 Lw' B2 Lw2 x
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw U2 Rw' B2 Rw' B2 Rw2 U2 Rw' B2 Lw' B2 Lw2 x
 
|sign=r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l2 x
 
|sign=r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l2 x
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw U2 Rw' B2 Rw' B2 Rw2 U2 Rw' B2 Rw' U2 Rw2
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw U2 Rw' B2 Rw' B2 Rw2 U2 Rw' B2 Rw' U2 Rw2
 
|sign=r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 r' U2 r2
 
|sign=r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 r' U2 r2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Lw' U2 Rw U2 Lw' B2 Lw U2 Rw' B2 Rw' B2 Rw2 U2 Lw
+
{{Alg6|wca=Rw2 U2 Lw' U2 Rw U2 Lw' B2 Lw U2 Rw' B2 Rw' B2 Rw2 U2 Lw
 
|sign=r2 U2 l' U2 r U2 l' B2 l U2 r' B2 r' B2 r2 U2 l
 
|sign=r2 U2 l' U2 r U2 l' B2 l U2 r' B2 r' B2 r2 U2 l
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw Rw U2 Lw' Rw2 U2 Rw' U2 B2 Rw' B2 Lw U2 Lw' U2 B2 Rw2
+
{{Alg6|wca=Lw Rw U2 Lw' Rw2 U2 Rw' U2 B2 Rw' B2 Lw U2 Lw' U2 B2 Rw2
 
|sign=l r U2 l' r2 U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2
 
|sign=l r U2 l' r2 U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2
 
|length=(27,17)|name=|wide=Y|author=|url=
 
|length=(27,17)|name=|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=Rw U2 Rw U2 Rw' U2 Lw U Rw U' F2 U Rw' U' x U2 Rw2 U2 Rw'
+
{{Alg6|wca=Rw U2 Rw U2 Rw' U2 Lw U Rw U' F2 U Rw' U' x U2 Rw2 U2 Rw'
 
|sign=r U2 r U2 r' U2 l U r U' F2 U r' U' x U2 r2 U2 r'
 
|sign=r U2 r U2 r' U2 l U r U' F2 U r' U' x U2 r2 U2 r'
 
|length=(25,18)|name=|wide=Y|author=Christopher Mowla
 
|length=(25,18)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
{{Alg5|wca=R U r U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
+
{{Alg6|wca=R U r U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
 
|sign=R U 2R U R' U' r2 R U2 r2 U r U2 r' U2 r U' r2 U2 r'
 
|sign=R U 2R U R' U' r2 R U2 r2 U r U2 r' U2 r U' r2 U2 r'
 
|length=(27,20)|name=|wide=N|author=Kåre Krig &xyzzy
 
|length=(27,20)|name=|wide=N|author=Kåre Krig &xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-103#post-1270971
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-103#post-1270971
 
}}
 
}}
{{Alg5|wca=Rw' U' Rw2 U' Rw' U Rw' U' Rw' U2 Rw U Rw U' Rw U Rw2 U Rw2 U2 Rw U2 Rw2 U2 Rw
+
{{Alg6|wca=Rw' U' Rw2 U' Rw' U Rw' U' Rw' U2 Rw U Rw U' Rw U Rw2 U Rw2 U2 Rw U2 Rw2 U2 Rw
 
|sign=r' U' r2 U' r' U r' U' r' U2 r U r U' r U r2 U r2 U2 r U2 r2 U2 r
 
|sign=r' U' r2 U' r' U r' U' r' U2 r U r U' r U r2 U r2 U2 r U2 r2 U2 r
 
|length=(33,25)|name=|wide=Y|author=Kåre Krig
 
|length=(33,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw U Rw' U Rw' U2 Rw2 U Rw2 U' Rw2 U' Rw' U' Rw U Rw' U2 Rw2 U2 Rw
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw U Rw' U Rw' U2 Rw2 U Rw2 U' Rw2 U' Rw' U' Rw U Rw' U2 Rw2 U2 Rw
 
|sign=r' U2 r' U2 r U r' U r' U2 r2 U r2 U' r2 U' r' U' r U r' U2 r2 U2 r
 
|sign=r' U2 r' U2 r U r' U r' U2 r2 U r2 U' r2 U' r' U' r U r' U2 r2 U2 r
 
|length=(34,25)|name=|wide=Y|author=Kåre Krig
 
|length=(34,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw U Rw' U Rw U' Rw2 U' Rw2 U2 Rw2 U' Rw U' Rw U Rw' U2 Rw2 U2 Rw
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw U Rw' U Rw U' Rw2 U' Rw2 U2 Rw2 U' Rw U' Rw U Rw' U2 Rw2 U2 Rw
 
|sign=r' U2 r' U2 r U r' U r U' r2 U' r2 U2 r2 U' r U' r U r' U2 r2 U2 r
 
|sign=r' U2 r' U2 r U r' U r U' r2 U' r2 U2 r2 U' r U' r U r' U2 r2 U2 r
 
|length=(34,25)|name=|wide=Y|author=Kåre Krig
 
|length=(34,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw U Rw' U Rw U Rw2 U2 Rw2 U' Rw2 U Rw U' Rw U Rw' U2 Rw2 U2 Rw
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw U Rw' U Rw U Rw2 U2 Rw2 U' Rw2 U Rw U' Rw U Rw' U2 Rw2 U2 Rw
 
|sign=r' U2 r' U2 r U r' U r U r2 U2 r2 U' r2 U r U' r U r' U2 r2 U2 r
 
|sign=r' U2 r' U2 r U r' U r U r2 U2 r2 U' r2 U r U' r U r' U2 r2 U2 r
 
|length=(34,25)|name=|wide=Y|author=Kåre Krig
 
|length=(34,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U' Rw U2 Rw U2 Rw' U2 Rw' U' Rw2 U Rw2 U Rw' U2 Rw
+
{{Alg6|wca=Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U' Rw U2 Rw U2 Rw' U2 Rw' U' Rw2 U Rw2 U Rw' U2 Rw
 
|sign=r' U r' U' r' U2 r2 U2 r2 U' r U2 r U2 r' U2 r' U' r2 U r2 U r' U2 r
 
|sign=r' U r' U' r' U2 r2 U2 r2 U' r U2 r U2 r' U2 r' U' r2 U r2 U r' U2 r
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U Rw U2 Rw U2 Rw' U2 Rw' U Rw2 U Rw2 U Rw' U2 Rw
+
{{Alg6|wca=Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U Rw U2 Rw U2 Rw' U2 Rw' U Rw2 U Rw2 U Rw' U2 Rw
 
|sign=r' U r' U' r' U2 r2 U2 r2 U r U2 r U2 r' U2 r' U r2 U r2 U r' U2 r
 
|sign=r' U r' U' r' U2 r2 U2 r2 U r U2 r U2 r' U2 r' U r2 U r2 U r' U2 r
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U Rw U2 Rw U2 Rw' U2 Rw U' Rw2 U' Rw2 U' Rw U2 Rw
+
{{Alg6|wca=Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U Rw U2 Rw U2 Rw' U2 Rw U' Rw2 U' Rw2 U' Rw U2 Rw
 
|sign=r' U r' U' r' U2 r2 U2 r2 U r U2 r U2 r' U2 r U' r2 U' r2 U' r U2 r
 
|sign=r' U r' U' r' U2 r2 U2 r2 U r U2 r U2 r' U2 r U' r2 U' r2 U' r U2 r
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw U' Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U' Rw2 U Rw2 U Rw' U2 Rw
+
{{Alg6|wca=Rw' U Rw' U' Rw U' Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U' Rw2 U Rw2 U Rw' U2 Rw
 
|sign=r' U r' U' r U' r2 U2 r2 U2 r' U2 r U2 r' U2 r' U' r2 U r2 U r' U2 r
 
|sign=r' U r' U' r U' r2 U2 r2 U2 r' U2 r U2 r' U2 r' U' r2 U r2 U r' U2 r
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw U Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U Rw2 U Rw2 U Rw' U2 Rw
+
{{Alg6|wca=Rw' U Rw' U' Rw U Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U Rw2 U Rw2 U Rw' U2 Rw
 
|sign=r' U r' U' r U r2 U2 r2 U2 r' U2 r U2 r' U2 r' U r2 U r2 U r' U2 r
 
|sign=r' U r' U' r U r2 U2 r2 U2 r' U2 r U2 r' U2 r' U r2 U r2 U r' U2 r
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw U Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw U' Rw2 U' Rw2 U' Rw U2 Rw
+
{{Alg6|wca=Rw' U Rw' U' Rw U Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw U' Rw2 U' Rw2 U' Rw U2 Rw
 
|sign=r' U r' U' r U r2 U2 r2 U2 r' U2 r U2 r' U2 r U' r2 U' r2 U' r U2 r
 
|sign=r' U r' U' r U r2 U2 r2 U2 r' U2 r U2 r' U2 r U' r2 U' r2 U' r U2 r
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
===3 flip===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Three flip</span>===
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
| bgcolor="fbfb8b" |
 
 
One can make a 3 dedge flip algorithm from a 1 dedge flip algorithm by conjugating the 1 dedge flip algorithm with moves which change the way the last layer pieces are in the last layer while keeping all pieces affected by the particular 1 dedge flip algorithm in the last layer.
 
One can make a 3 dedge flip algorithm from a 1 dedge flip algorithm by conjugating the 1 dedge flip algorithm with moves which change the way the last layer pieces are in the last layer while keeping all pieces affected by the particular 1 dedge flip algorithm in the last layer.
 
+
{{br|b=1}}
 
 
 
The shortest of such conjugations is (B' R'),
 
The shortest of such conjugations is (B' R'),
 
+
{{br|b=1}}
{{Alg5|wca=(B' R') Rw U2' x Rw U2' Rw U2' Rw' U2 Lw U2' Rw' U2 Rw U2' Rw' U2 Rw' (R B)
+
{{Alg6|wca=(B' R') Rw U2' x Rw U2' Rw U2' Rw' U2 Lw U2' Rw' U2 Rw U2' Rw' U2 Rw' (R B)
 
|sign=(B' R') r U2' x r U2' r U2' r' U2 l U2' r' U2 r U2' r' U2 r' (R B)
 
|sign=(B' R') r U2' x r U2' r U2' r' U2 l U2' r' U2 r U2' r' U2 r' (R B)
 
|length=(27,21)|name=|wide=Y|author=Lucas Garron
 
|length=(27,21)|name=|wide=Y|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/4x4-oll-parity-idea.22568/#post-417375
 
|url=https://www.speedsolving.com/forum/threads/4x4-oll-parity-idea.22568/#post-417375
 
}}
 
}}
but one can see longer conjugations which solve different [[OLL]] + OLL parity cases in [http://www.speedsolving.com/forum/showthread.php?24658-1LOLL-even-parity this thread] and in the Word document "OLLparity+OLL 3flip" from [https://web.archive.org/web/20090808131640/http://www.math.leidenuniv.nl/~mfung/speedcubing/algs/4x4x4/ Michael Fung's old page], for example.
+
but one can see longer conjugations which solve different {{LinkColorI|p=OLL|c=rgb(229,148,0)|t=OLL}} + OLL parity cases in {{LinkColorE|u=http://www.speedsolving.com/forum/showthread.php?24658-1LOLL-even-parity|c=rgb(229,148,0)|t=this thread}} and in the Word document "OLLparity+OLL 3flip" from {{LinkColorE|u=https://web.archive.org/web/20090808131640/http://www.math.leidenuniv.nl/~mfung/speedcubing/algs/4x4x4/|c=rgb(229,148,0)|t=Michael Fung's old page}}, for example.
  
 
+
On the other hand, the algorithms provided in this section are algorithms which flip 3 dedges <i>without using this conjugation technique</i></ul>
On the other hand, the algorithms provided in this section are algorithms which flip 3 dedges <b>without using this conjugation technique</b>
+
{{br|b=1}}
|}
+
{{Alg6|wca=Rw F U2 F' Rw U2 Rw U2 Rw U' L' U2 L F 3Lw' U' R U' x' U F Rw
 
 
 
 
{{Alg5|wca=Rw F U2 F' Rw U2 Rw U2 Rw U' L' U2 L F 3Lw' U' R U' x' U F Rw
 
 
|sign=r F U2 F' r U2 r U2 r U' L' U2 L F 3l' U' R U' x' U F r
 
|sign=r F U2 F' r U2 r U2 r U' L' U2 L F 3l' U' R U' x' U F r
 
|length=(25,21)|name=|wide=Y|author=Christopher Mowla
 
|length=(25,21)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' R' U2 R' U2 R U' Rw
+
{{Alg6|wca=Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' R' U2 R' U2 R U' Rw
 
|sign=r U' R U2 R' U2 R' U' r U2 r R U2 r U' R' U2 R' U2 R U' r
 
|sign=r U' R U2 R' U2 R' U' r U2 r R U2 r U' R' U2 R' U2 R U' r
 
|length=(28,22)|name=|wide=Y|author=Kåre Krig
 
|length=(28,22)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw
+
{{Alg6|wca=Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw
 
|sign=r U' R U2 R' U2 R' U' r U2 r R U2 r U' r' U2 R' U2 r U' r
 
|sign=r U' R U2 R' U2 R' U' r U2 r R U2 r U' r' U2 R' U2 r U' r
 
|length=(28,22)|name=|wide=Y|author=Kåre Krig
 
|length=(28,22)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' Rw U2 R' U2 Rw' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw
+
{{Alg6|wca=Rw U' Rw U2 R' U2 Rw' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw
 
|sign=r U' r U2 R' U2 r' U' r U2 r R U2 r U' r' U2 R' U2 r U' r
 
|sign=r U' r U2 R' U2 r' U' r U2 r R U2 r U' r' U2 R' U2 r U' r
 
|length=(28,22)|name=|wide=Y|author=Kåre Krig
 
|length=(28,22)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Double parity</span>==
==Double parity==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">1 flip</span>===
===1 flip===
+
{{Alg6|wca=Rw' U2 Rw' U2 Lw U2 Rw' U2 Rw U2 x U2 Rw2 U2 Rw' U2 Rw
{{Alg5|wca=Rw' U2 Rw' U2 Lw U2 Rw' U2 Rw U2 x U2 Rw2 U2 Rw' U2 Rw
 
 
|sign=r' U2 r' U2 l U2 r' U2 r U2 x U2 r2 U2 r' U2 r
 
|sign=r' U2 r' U2 l U2 r' U2 r U2 x U2 r2 U2 r' U2 r
 
|length=(25,16)|name=v1
 
|length=(25,16)|name=v1
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw U2 Lw U2 Rw' U2 Lw U2 Lw' U2 x U2 Lw2 U2 Lw U2 Lw'
+
{{Alg6|wca=Lw U2 Lw U2 Rw' U2 Lw U2 Lw' U2 x U2 Lw2 U2 Lw U2 Lw'
 
|sign=l U2 l U2 r' U2 l U2 l' U2 x U2 l2 U2 l U2 l'
 
|sign=l U2 l U2 r' U2 l U2 l' U2 x U2 l2 U2 l U2 l'
 
|length=(25,16)|name=v2
 
|length=(25,16)|name=v2
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw' U2 Rw U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' U2 Rw2
+
{{Alg6|wca=Rw U2 Rw' U2 Rw U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' U2 Rw2
 
|sign=r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2
 
|sign=r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2
 
|length=(25,16)|name=v1
 
|length=(25,16)|name=v1
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 Lw U2 Lw' U2 Lw' U2 Rw U2 Lw' U2 Lw U2 x' U2 Lw2
+
{{Alg6|wca=Lw' U2 Lw U2 Lw' U2 Lw' U2 Rw U2 Lw' U2 Lw U2 x' U2 Lw2
 
|sign=l' U2 l U2 l' U2 l' U2 r U2 l' U2 l U2 x' U2 l2
 
|sign=l' U2 l U2 l' U2 l' U2 r U2 l' U2 l U2 x' U2 l2
 
|length=(25,16)|name=v2
 
|length=(25,16)|name=v2
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 x' U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw U2 Rw' U2 Rw
+
{{Alg6|wca=Rw2 U2 x' U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw U2 Rw' U2 Rw
 
|sign=r2 U2 x' U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r
 
|sign=r2 U2 x' U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r
 
|length=(25,16)|name=v1
 
|length=(25,16)|name=v1
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw2 U2 x' U2 Lw U2 Lw' U2 Rw U2 Lw' U2 Lw' U2 Lw U2 Lw'
+
{{Alg6|wca=Lw2 U2 x' U2 Lw U2 Lw' U2 Rw U2 Lw' U2 Lw' U2 Lw U2 Lw'
 
|sign=l2 U2 x' U2 l U2 l' U2 r U2 l' U2 l' U2 l U2 l'
 
|sign=l2 U2 x' U2 l U2 l' U2 r U2 l' U2 l' U2 l U2 l'
 
|length=(25,16)|name=v2
 
|length=(25,16)|name=v2
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw' U2 Rw2 U2 x U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw'
+
{{Alg6|wca=Rw U2 Rw' U2 Rw2 U2 x U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw'
 
|sign=r U2 r' U2 r2 U2 x U2 r U2 r' U2 l U2 r' U2 r'
 
|sign=r U2 r' U2 r2 U2 x U2 r U2 r' U2 l U2 r' U2 r'
 
|length=(25,16)|name=v1
 
|length=(25,16)|name=v1
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 Lw U2 Lw2 U2 x U2 Lw' U2 Lw U2 Rw' U2 Lw U2 Lw
+
{{Alg6|wca=Lw' U2 Lw U2 Lw2 U2 x U2 Lw' U2 Lw U2 Rw' U2 Lw U2 Lw
 
|sign=l' U2 l U2 l2 U2 x U2 l' U2 l U2 r' U2 l U2 l
 
|sign=l' U2 l U2 l2 U2 x U2 l' U2 l U2 r' U2 l U2 l
 
|length=(25,16)|name=v2
 
|length=(25,16)|name=v2
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U Rw2 R U Rw U' Rw
+
{{Alg6|wca=Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U Rw2 R U Rw U' Rw
 
|sign=r U2 r U2 r U R r U2 R2 U r U r2 R U r U' r
 
|sign=r U2 r U2 r U R r U2 R2 U r U r2 R U r U' r
 
|length=(23,19)|name=v1
 
|length=(23,19)|name=v1
Line 6,708: Line 7,006:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' Rw2 R' U' Rw' U Rw'
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' Rw2 R' U' Rw' U Rw'
 
|sign=r' U2 r' U2 r' U' R' r' U2 R2 U' r' U' r2 R' U' r' U r'
 
|sign=r' U2 r' U2 r' U' R' r' U2 R2 U' r' U' r2 R' U' r' U r'
 
|length=(23,19)|name=v2
 
|length=(23,19)|name=v2
Line 6,714: Line 7,012:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw R U Rw2 R' U2 Rw' R' U R U Rw' U2 Rw2 U' Rw2
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw R U Rw2 R' U2 Rw' R' U R U Rw' U2 Rw2 U' Rw2
 
|sign=r' U2 r' U2 r R U r2 R' U2 r' R' U R U r' U2 r2 U' r2
 
|sign=r' U2 r' U2 r R U r2 R' U2 r' R' U R U r' U2 r2 U' r2
 
|length=(26,20)|name=|wide=Y|author=Kåre Krig
 
|length=(26,20)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' U2 Lw' R2 x U' F2 U Lw' U2 r' U2 Rw F' L2 F r2 U2 x' U' F2 U x U2 Lw' U2 z
+
{{Alg6|wca=z' U2 Lw' R2 x U' F2 U Lw' U2 r' U2 Rw F' L2 F r2 U2 x' U' F2 U x U2 Lw' U2 z
 
|sign=z' U2 l' R2 x U' F2 U l' U2 2R' U2 r F' L2 F 2R2 U2 x' U' F2 U x U2 l' U2 z
 
|sign=z' U2 l' R2 x U' F2 U l' U2 2R' U2 r F' L2 F 2R2 U2 x' U' F2 U x U2 l' U2 z
 
|length=(32,22)|name=|wide=N|author=Christopher Mowla
 
|length=(32,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' Rw' U' Rw U Rw U2 Rw2 U2 Rw U2 Rw U Rw' U Rw U Rw2 U2 Rw' U2 Rw U2 Rw'
+
{{Alg6|wca=Rw' U' Rw' U' Rw U Rw U2 Rw2 U2 Rw U2 Rw U Rw' U Rw U Rw2 U2 Rw' U2 Rw U2 Rw'
 
|sign=r' U' r' U' r U r U2 r2 U2 r U2 r U r' U r U r2 U2 r' U2 r U2 r'
 
|sign=r' U' r' U' r U r U2 r2 U2 r U2 r U r' U r U r2 U2 r' U2 r U2 r'
 
|length=(33,25)|name=|wide=Y|author=Kåre Krig
 
|length=(33,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw2 U Rw2 U2 Rw U2 Rw' U2 Rw U Rw U Rw U2 Rw' U2 Rw' U2 Rw2 U' Rw2 U Rw'
+
{{Alg6|wca=Rw' U Rw2 U Rw2 U2 Rw U2 Rw' U2 Rw U Rw U Rw U2 Rw' U2 Rw' U2 Rw2 U' Rw2 U Rw'
 
|sign=r' U r2 U r2 U2 r U2 r' U2 r U r U r U2 r' U2 r' U2 r2 U' r2 U r'
 
|sign=r' U r2 U r2 U2 r U2 r' U2 r U r U r U2 r' U2 r' U2 r2 U' r2 U r'
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|length=(35,25)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw' U2 Rw U2 Rw2 U' Rw' U' Rw U' Rw' U2 Rw' U2 Rw2 U2 Rw' U' Rw' U Rw U Rw
+
{{Alg6|wca=Rw U2 Rw' U2 Rw U2 Rw2 U' Rw' U' Rw U' Rw' U2 Rw' U2 Rw2 U2 Rw' U' Rw' U Rw U Rw
 
|sign=r U2 r' U2 r U2 r2 U' r' U' r U' r' U2 r' U2 r2 U2 r' U' r' U r U r
 
|sign=r U2 r' U2 r U2 r2 U' r' U' r U' r' U2 r' U2 r2 U2 r' U' r' U r U r
 
|length=(33,25)|name=|wide=Y|author=Ben Whitmore
 
|length=(33,25)|name=|wide=Y|author=Ben Whitmore
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
 
}}
 
}}
 
+
{{br|b=1}}
===3 flip===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Three flip</span>===
{{Alg5|wca=Rw U' Rw U' Rw2 U Rw' U2 Rw U2 Rw' U Rw' U' Rw U2 Rw U2 Rw U2 Rw U' Rw' U2 Rw' U2 Rw
+
{{Alg6|wca=Rw U' Rw U' Rw2 U Rw' U2 Rw U2 Rw' U Rw' U' Rw U2 Rw U2 Rw U2 Rw U' Rw' U2 Rw' U2 Rw
 
|sign=r U' r U' r2 U r' U2 r U2 r' U r' U' r U2 r U2 r U2 r U' r' U2 r' U2 r
 
|sign=r U' r U' r2 U r' U2 r U2 r' U r' U' r U2 r U2 r U2 r U' r' U2 r' U2 r
 
|length=(35,27)|name=|wide=Y|author=Kåre Krig
 
|length=(35,27)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">OLL parity algorithms which don't preserve F3L</span>=
 
 
=OLL parity algorithms which don't preserve F3L=
 
  
 
*One advantage of having access to algorithms which don't preserve the first three layers of the 4x4x4 is that the shortest algorithms that this category of algorithms has to offer have fewer  moves than algorithms which preserve the first three layers.  (This is of interest to certain cubers.)
 
*One advantage of having access to algorithms which don't preserve the first three layers of the 4x4x4 is that the shortest algorithms that this category of algorithms has to offer have fewer  moves than algorithms which preserve the first three layers.  (This is of interest to certain cubers.)
*Unlike algorithms which preserve the first three layers, which are at minimum 14 block half turns (<b>double parity</b>) and 18 block quarter turns (one dedge flip), some algorithms in this section are just 13 block half turns, and some are just 15 block quarter turns.
+
{{br|b=1}}
 
+
*Unlike algorithms which preserve the first three layers, which are at minimum 14 block half turns (opposite double parity) and 18 block quarter turns (one dedge flip), some algorithms in this section are just 13 block half turns, and some are just 15 block quarter turns.
 
+
{{br|b=1}}
==Corner permuters==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Corner permuters</span>==
 
[[Image:CrnersParity.png‎|110px|]]
 
[[Image:CrnersParity.png‎|110px|]]
 
*Most of these algorithms are also just front right F3L slot destroyers.
 
*Most of these algorithms are also just front right F3L slot destroyers.
 
+
{{br|b=1}}
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Single Parity</b></span>
<b>Single Parity</b>
+
{{Alg6|wca=r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r'
{{Alg5|wca=r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r'
 
 
|sign=2R' U2 F' U2 F U2 2R' U2 2R' U2 2R' F' U2 F 2R'
 
|sign=2R' U2 F' U2 F U2 2R' U2 2R' U2 2R' F' U2 F 2R'
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-721562
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-721562
 
}}
 
}}
{{Alg5|wca=l U2 F' U2 F U2 l U2 l U2 l F' U2 F l
+
{{Alg6|wca=l U2 F' U2 F U2 l U2 l U2 l F' U2 F l
 
|sign=2L U2 F' U2 F U2 2L U2 2L U2 2L F' U2 F 2L
 
|sign=2L U2 F' U2 F U2 2L U2 2L U2 2L F' U2 F 2L
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-721562
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-721562
 
}}
 
}}
{{Alg5|wca=r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'
+
{{Alg6|wca=r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'
 
|sign=2R' U R U2 R' U' 2R' U2 2R' U2 2R' U' R U2 R' U 2R'
 
|sign=2R' U R U2 R' U' 2R' U2 2R' U2 2R' U' R U2 R' U 2R'
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l'
+
{{Alg6|wca=l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l'
 
|sign=2L' U' R U2 R' U 2L' U2 2L' U2 2L' U R U2 R' U' 2L'
 
|sign=2L' U' R U2 R' U 2L' U2 2L' U2 2L' U R U2 R' U' 2L'
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2
+
{{Alg6|wca=r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2
 
|sign=2R2 s' 2R U' R U' 2R U2 2R U2 2R U' R' U' 2R s 2R2
 
|sign=2R2 s' 2R U' R U' 2R U2 2R U2 2R U' R' U' 2R s 2R2
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2
+
{{Alg6|wca=r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2
 
|sign=2R2 s 2R U' R U' 2R U2 2R U2 2R U' R' U' 2R s' 2R2
 
|sign=2R2 s 2R U' R U' 2R U2 2R U2 2R U' R' U' 2R s' 2R2
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2
+
{{Alg6|wca=Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2
 
|sign=r U' R' U2 R U 2R U2 2R U2 2R U R' U2 R U' r R2
 
|sign=r U' R' U2 R U 2R U2 2R U2 2R U R' U2 R U' r R2
 
|length=(22,18)|name=|wide=N|author=Kåre Krig
 
|length=(22,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw
+
{{Alg6|wca=Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw
 
|sign=r U' R' U2 R U 2R U2 r R U2 2R U R U2 R' U' r
 
|sign=r U' R' U2 R U 2R U2 r R U2 2R U R U2 R' U' r
 
|length=(22,18)|name=|wide=N|author=Kåre Krig
 
|length=(22,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw
+
{{Alg6|wca=Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw
 
|sign=r U' R U2 R' U 2R U2 r R U2 2R U R' U2 R U' r
 
|sign=r U' R U2 R' U 2R U2 r R U2 2R U R' U2 R U' r
 
|length=(22,18)|name=|wide=N|author=Kåre Krig
 
|length=(22,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw
+
{{Alg6|wca=Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw
 
|sign=r R U' R2 U2 R2 U 2R U2 r U2 2R U R U2 R' U' r
 
|sign=r R U' R2 U2 R2 U 2R U2 r U2 2R U R U2 R' U' r
 
|length=(24,18)|name=|wide=N|author=Kåre Krig
 
|length=(24,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2
+
{{Alg6|wca=Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2
 
|sign=r U' R' U2 R U r R2 U2 2R U2 r U R' U2 R U' r R2
 
|sign=r U' R' U2 R U r R2 U2 2R U2 r U R' U2 R U' r R2
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2
+
{{Alg6|wca=Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2
 
|sign=r U' R' U2 R U r U2 2R U2 r R2 U R' U2 R U' r R2
 
|sign=r U' R' U2 R U r U2 2R U2 r R2 U R' U2 R U' r R2
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw
+
{{Alg6|wca=Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw
 
|sign=r U' R' U2 R U' R U2 2R U2 r U2 2R U R U2 R' U' r
 
|sign=r U' R' U2 R U' R U2 2R U2 r U2 2R U R U2 R' U' r
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(r' U' R U r)(r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r)(r U R' U' r')
+
{{Alg6|wca=(r' U' R U r)(r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r)(r U R' U' r')
 
|sign=(2R' U' R U 2R)(2R U2 2R2 U2 2R' U2 2R U2 2R' U2 2R2 U2 2R)(2R U R' U' 2R')
 
|sign=(2R' U' R U 2R)(2R U2 2R2 U2 2R' U2 2R U2 2R' U2 2R2 U2 2R)(2R U R' U' 2R')
 
|length=(31,21)|name=|wide=N|author=Christopher Mowla
 
|length=(31,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Front-right F3L slot destroyers</span>==
==Front-right F3L slot destroyers==
 
 
[[Image:FRF3Lslot.png|110px|]]
 
[[Image:FRF3Lslot.png|110px|]]
  
<b>Single Parity</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Single Parity</b></span>
{{Alg5|wca=l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F
+
{{Alg6|wca=l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F
 
|sign=2L U2 2L' F U R U' l' D2 2R D2 2R U2 r' U2 l F
 
|sign=2L U2 2L' F U R U' l' D2 2R D2 2R U2 r' U2 l F
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-13#post-419116
 
|url=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-13#post-419116
 
}}
 
}}
{{Alg5|wca=Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F
+
{{Alg6|wca=Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F
 
|sign=r U2 l' U2 2L D2 2L D2 r' U' L U F 2R' U2 2R F
 
|sign=r U2 l' U2 2L D2 2L D2 r' U' L U F 2R' U2 2R F
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-13#post-419116
 
|url=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-13#post-419116
 
}}
 
}}
{{Alg5|wca=Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
+
{{Alg6|wca=Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
 
|sign=r U R' U' r2 R U2 r2 U r U2 r' U2 r U' r2 U2 r'
 
|sign=r U R' U' r2 R U2 r2 U r U2 r' U2 r U' r2 U2 r'
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r'
+
{{Alg6|wca=Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r'
 
|sign=r U R' U' r2 U2 r2 R U r U2 r' U2 r U' r2 U2 2R'
 
|sign=r U R' U' r2 U2 r2 R U r U2 r' U2 r U' r2 U2 2R'
 
|length=(24,18)|name=|wide=N|author=Kåre Krig
 
|length=(24,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw
+
{{Alg6|wca=Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw
 
|sign=r U2 R U R' U2 R U 2R U2 r U2 r U R U2 R' U' r
 
|sign=r U2 R U R' U2 R U 2R U2 r U2 r U R U2 R' U' r
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
 
|length=(24,19)|name=|wide=N|author=Kåre Krig
Line 6,863: Line 7,158:
 
}}
 
}}
  
<b>Double Parity</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Double Parity</b></span>
{{Alg5|wca=Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw
+
{{Alg6|wca=Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw
 
|sign=r U2 r U2 r U r U2 R' U r U r2 R U r U' r
 
|sign=r U2 r U2 r U r U2 R' U r U r2 R U r U' r
 
|length=(21,18)|name=|wide=Y|author=Kåre Krig
 
|length=(21,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2
+
{{Alg6|wca=Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2
 
|sign=r U2 r U2 r' U' R' r2 U2 2R U' R' U' r U2 2R2 U r2
 
|sign=r U2 r U2 r' U' R' r2 U2 2R U' R' U' r U2 2R2 U r2
 
|length=(24,18)|name=|wide=N|author=Kåre Krig
 
|length=(24,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(r' U' R U r)(r2 F2 Uw2 r Uw2 F2 r2)(r U R' U' r')(Fw2 l' Uw2 l r Uw2 r' Fw2)
+
{{Alg6|wca=(r' U' R U r)(r2 F2 Uw2 r Uw2 F2 r2)(r U R' U' r')(Fw2 l' Uw2 l r Uw2 r' Fw2)
 
|sign=(2R' U' R U 2R)(2R2 F2 u2 2R u2 F2 2R2)(2R U R' U' 2R')(f2 2L' u2 2L 2R u2 2R' f2)
 
|sign=(2R' U' R U 2R)(2R2 F2 u2 2R u2 F2 2R2)(2R U R' U' 2R')(f2 2L' u2 2L 2R u2 2R' f2)
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Petrus</span>==
==Petrus==
 
 
[[Image:Pparity.png|110px|]]
 
[[Image:Pparity.png|110px|]]
 
*These algorithms "just" scramble two adjacent faces' worth of pieces.
 
*These algorithms "just" scramble two adjacent faces' worth of pieces.
 +
{{br|b=1}}
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Single Parity</b></span>
<b>Single Parity</b>
+
{{Alg6|wca=Rw B' U2 B Rw B2 Lw B2 Rw B D2 B' Rw
{{Alg5|wca=Rw B' U2 B Rw B2 Lw B2 Rw B D2 B' Rw
 
 
|sign=r B' U2 B r B2 l B2 r B D2 B' r
 
|sign=r B' U2 B r B2 l B2 r B D2 B' r
 
|length=(17,13)|name=v1
 
|length=(17,13)|name=v1
Line 6,893: Line 7,187:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' Rw' U F2 U' Lw' U2 Rw' U2 Rw' F' U2 F Rw'
+
{{Alg6|wca=x' Rw' U F2 U' Lw' U2 Rw' U2 Rw' F' U2 F Rw'
 
|sign=x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'
 
|sign=x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'
 
|length=(17,13)|name=v2
 
|length=(17,13)|name=v2
Line 6,899: Line 7,193:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=x' Rw' U F2 U' Lw' U2 Rw' U2 Lw' U' B2 U Rw' x'
+
{{Alg6|wca=x' Rw' U F2 U' Lw' U2 Rw' U2 Lw' U' B2 U Rw' x'
 
|sign=x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'
 
|sign=x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'
 
|length=(17,13)|name=v3
 
|length=(17,13)|name=v3
Line 6,905: Line 7,199:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=x' Rw' U F2 U' Lw' U2 Rw' 3Dw2 Rw' U' F2 U Lw' x
+
{{Alg6|wca=x' Rw' U F2 U' Lw' U2 Rw' 3Dw2 Rw' U' F2 U Lw' x
 
|sign=x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x
 
|sign=x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x
 
|length=(17,13)|name=v4
 
|length=(17,13)|name=v4
Line 6,911: Line 7,205:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'
+
{{Alg6|wca=Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'
 
|sign=r' s' L2 s r' U2 r' U2 r' F U2 F' U' L' U r'
 
|sign=r' s' L2 s r' U2 r' U2 r' F U2 F' U' L' U r'
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'
+
{{Alg6|wca=Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'
 
|sign=r' s R2 s' r' U2 r' U2 r' F' U2 F U R U' r'
 
|sign=r' s R2 s' r' U2 r' U2 r' F' U2 F U R U' r'
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x'
+
{{Alg6|wca=Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x'
 
|sign=r U2 r' U2 r D2 2R D2 2L' U L' U' B' 2L' U2 2L x'
 
|sign=r U2 r' U2 r D2 2R D2 2L' U L' U' B' 2L' U2 2L x'
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'
+
{{Alg6|wca=Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'
 
|sign=r' U R' U2 R U' r' U2 r' U2 r' U' R U2 R' U r'
 
|sign=r' U R' U2 R U' r' U2 r' U2 r' U' R U2 R' U r'
 
|length=(21,17)|name=|wide=Y|author=Kåre Krig, Bruce Norskog, & Christopher Mowla
 
|length=(21,17)|name=|wide=Y|author=Kåre Krig, Bruce Norskog, & Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-803970
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-803970
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw
+
{{Alg6|wca=Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw
 
|sign=r U' R' U2 R U 2R U2 2R U2 2R U R' U2 R U' r
 
|sign=r U' R' U2 R U 2R U2 2R U2 2R U R' U2 R U' r
 
|length=(21,17)|name=|wide=N|author=Kåre Krig
 
|length=(21,17)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw
+
{{Alg6|wca=Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw
 
|sign=r U' R' U2 R U r U2 r U2 2R U R U2 R' U' r
 
|sign=r U' R' U2 R U r U2 r U2 2R U R U2 R' U' r
 
|length=(21,17)|name=|wide=N|author=Kåre Krig
 
|length=(21,17)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw'
+
{{Alg6|wca=Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw'
 
|sign=r' U' L' U2 L U r' U2 r' U2 r' U L' U2 L U' r'
 
|sign=r' U' L' U2 L U r' U2 r' U2 r' U L' U2 L U' r'
 
|length=(21,17)|name=|wide=Y|author=Bruce Norskog & Christopher Mowla
 
|length=(21,17)|name=|wide=Y|author=Bruce Norskog & Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/page-2#post-806608
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/page-2#post-806608
 
}}
 
}}
{{Alg5|wca=Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F
+
{{Alg6|wca=Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F
 
|sign=r U2 l' U2 2L D2 2L D2 r' U' L U F r' U2 r F
 
|sign=r U2 l' U2 2L D2 2L D2 r' U' L U F r' U2 r F
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw
+
{{Alg6|wca=Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw
 
|sign=r U' R2 U2 R2 U 2R U2 r U2 2R U R U2 R' U' r
 
|sign=r U' R2 U2 R2 U 2R U2 r U2 2R U R U2 R' U' r
 
|length=(23,17)|name=|wide=N|author=Kåre Krig
 
|length=(23,17)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'
+
{{Alg6|wca=Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'
 
|sign=r U2 r2 U' r' U2 r U2 r' U r2 U2 r2 U R2 U' r'
 
|sign=r U2 r2 U' r' U2 r U2 r' U r2 U2 r2 U R2 U' r'
 
|length=(25,17)|name=|wide=Y|author=Kåre Krig & Christopher Mowla
 
|length=(25,17)|name=|wide=Y|author=Kåre Krig & Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-753184
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-753184
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw'
+
{{Alg6|wca=Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw'
 
|sign=r U2 r2 U r' U2 r U2 r' U' r2 U2 2R2 U R2 U' r'
 
|sign=r U2 r2 U r' U2 r U2 r' U' r2 U2 2R2 U R2 U' r'
 
|length=(25,17)|name=|wide=N|author=Kåre Krig & Christopher Mowla
 
|length=(25,17)|name=|wide=N|author=Kåre Krig & Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-753184
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-753184
 
}}
 
}}
{{Alg5|wca=Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw
+
{{Alg6|wca=Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw
 
|sign=r U' R2 U2 R2 U 2R U2 2R U2 2R U R2 U2 R2 U' r
 
|sign=r U' R2 U2 R2 U 2R U2 2R U2 2R U R2 U2 R2 U' r
 
|length=(25,17)|name=|wide=N|author=Kåre Krig
 
|length=(25,17)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw'
+
{{Alg6|wca=Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw'
 
|sign=r' U R U2 R' U' 2R' U2 r' U2 r' F' U' R' U' R F r'
 
|sign=r' U R U2 R' U' 2R' U2 r' U2 r' F' U' R' U' R F r'
 
|length=(21,18)|name=|wide=N|author=Kåre Krig
 
|length=(21,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R' U' R U2 R' U Rw'
+
{{Alg6|wca=Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R' U' R U2 R' U Rw'
 
|sign=r' U R U2 R' U' r' U2 r' U2 r' R' U' R U2 R' U r'
 
|sign=r' U R U2 R' U' r' U2 r' U2 r' R' U' R U2 R' U r'
 
|length=(22,18)|name=|wide=Y|author=Kåre Krig
 
|length=(22,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw
+
{{Alg6|wca=Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw
 
|sign=r U' R' U2 R U r U2 2R U2 r R2 U R' U2 R U' r
 
|sign=r U' R' U2 R U r U2 2R U2 r R2 U R' U2 R U' r
 
|length=(23,18)|name=|wide=N|author=Kåre Krig
 
|length=(23,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw
+
{{Alg6|wca=Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw
 
|sign=r U' R U2 R' U r U2 2R U2 r R2 U R U2 R' U' r
 
|sign=r U' R U2 R' U r U2 2R U2 r R2 U R U2 R' U' r
 
|length=(23,18)|name=|wide=N|author=Kåre Krig
 
|length=(23,18)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw
+
{{Alg6|wca=Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw
 
|sign=r U' R U2 R' U r U2 r R2 U2 r U R' U2 R U' r
 
|sign=r U' R U2 R' U r U2 r R2 U2 r U R' U2 R U' r
 
|length=(23,18)|name=|wide=Y|author=Kåre Krig
 
|length=(23,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw'
+
{{Alg6|wca=Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw'
 
|sign=r U R U' r2 R U2 r2 U' r U2 r' U2 r U r2 U2 r'
 
|sign=r U R U' r2 R U2 r2 U' r U2 r' U2 r U r2 U2 r'
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw'
+
{{Alg6|wca=Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw'
 
|sign=r' U R U2 R' U' r' U2 r' U2 r' R2 U' R2 U2 R2 U r'
 
|sign=r' U R U2 R' U' r' U2 r' U2 r' R2 U' R2 U2 R2 U r'
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
+
{{Alg6|wca=Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
 
|sign=r U R' U' r2 U2 r2 R U r U2 r' U2 r U' r2 U2 r'
 
|sign=r U R' U' r2 U2 r2 R U r U2 r' U2 r U' r2 U2 r'
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|length=(24,18)|name=|wide=Y|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw
+
{{Alg6|wca=Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw
 
|sign=r U R' U r U2 2R U2 2R U' r' U R U R' U2 r U' r
 
|sign=r U R' U r U2 2R U2 2R U' r' U R U R' U2 r U' r
 
|length=(22,19)|name=|wide=N|author=Kåre Krig
 
|length=(22,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw
+
{{Alg6|wca=Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw
 
|sign=r U R' U 2R U2 2R U2 r U' r' U R U R' U2 r U' r
 
|sign=r U R' U 2R U2 2R U2 r U' r' U R U R' U2 r U' r
 
|length=(22,19)|name=|wide=N|author=Kåre Krig
 
|length=(22,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw
+
{{Alg6|wca=Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw
 
|sign=r U' r U2 R' U R U r' U' 2R U2 r U2 r U R' U r
 
|sign=r U' r U2 R' U R U r' U' 2R U2 r U2 r U R' U r
 
|length=(22,19)|name=|wide=N|author=Kåre Krig
 
|length=(22,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw
+
{{Alg6|wca=Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw
 
|sign=r U' R' U2 R U r R U2 2R U2 r R U R' U2 R U' r
 
|sign=r U' R' U2 R U r R U2 2R U2 r R U R' U2 R U' r
 
|length=(23,19)|name=|wide=N|author=Kåre Krig
 
|length=(23,19)|name=|wide=N|author=Kåre Krig
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw
+
{{Alg6|wca=Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw
 
|sign=r U' r U2 R' U R U r' U' r U2 2R U2 r U R2 U r
 
|sign=r U' r U2 R' U R U r' U' r U2 2R U2 r U R2 U r
 
|length=(23,19)|name=|wide=N|author=Kåre Krig
 
|length=(23,19)|name=|wide=N|author=Kåre Krig
Line 7,037: Line 7,331:
 
}}
 
}}
  
<b>Double Parity</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Double Parity</b></span>
{{Alg5|wca=Lw' U2 F2 Lw' U' F R' F Lw2 U2 Rw U2 Lw2 U' x'
+
{{Alg6|wca=Lw' U2 F2 Lw' U' F R' F Lw2 U2 Rw U2 Lw2 U' x'
 
|sign=l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'
 
|sign=l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'
 
|length=(20,14)|name=v1
 
|length=(20,14)|name=v1
Line 7,044: Line 7,338:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=Lw' U2 F2 Lw' U' F 3Lw' U Lw2 x' U2 Rw U2 Lw2 U' x'
+
{{Alg6|wca=Lw' U2 F2 Lw' U' F 3Lw' U Lw2 x' U2 Rw U2 Lw2 U' x'
 
|sign=l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'
 
|sign=l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'
 
|length=(20,14)|name=v2
 
|length=(20,14)|name=v2
Line 7,050: Line 7,344:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 Rw U' F R' F Rw2 U2 Lw' U2 Rw2 U' x'
+
{{Alg6|wca=Rw U2 F2 Rw U' F R' F Rw2 U2 Lw' U2 Rw2 U' x'
 
|sign=r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'
 
|sign=r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'
 
|length=(20,14)|name=v1
 
|length=(20,14)|name=v1
Line 7,056: Line 7,350:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 Rw U' F 3Lw' U Rw2 x' U2 Lw' U2 Rw2 U' x'
+
{{Alg6|wca=Rw U2 F2 Rw U' F 3Lw' U Rw2 x' U2 Lw' U2 Rw2 U' x'
 
|sign=r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'
 
|sign=r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'
 
|length=(20,14)|name=v2
 
|length=(20,14)|name=v2
Line 7,062: Line 7,356:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-722738
 
}}
 
}}
{{Alg5|wca=r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw
+
{{Alg6|wca=r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw
 
|sign=2R' U R U' 2R' U2 2R U R' U 2R U2 2R F2 l' U2 l
 
|sign=2R' U R U' 2R' U2 2R U R' U 2R U2 2R F2 l' U2 l
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'
+
{{Alg6|wca=Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'
 
|sign=r' U R U (r' U2)3 r2 U R' U' r2 U' R' U r'
 
|sign=r' U R U (r' U2)3 r2 U R' U' r2 U' R' U r'
 
|length=(24,19)|name=|wide=Y|author=Stefan Pochmann
 
|length=(24,19)|name=|wide=Y|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/13698
+
|url=https://web.archive.org/web/20191022175231/https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/13698?guccounter=1
 
}}
 
}}
 
+
{{br|b=1}}
==X-Cross preservers==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">X-Cross preservers</span>==
 
[[Image:MoreT1F3Lslot.png|110px|]]
 
[[Image:MoreT1F3Lslot.png|110px|]]
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Single Parity</b></span>
<b>Single Parity</b>
+
{{Alg6|wca=Rw' U2 F U2 F' U2 Rw' U2 Rw' U2 Rw' F U2 F' Rw'
{{Alg5|wca=Rw' U2 F U2 F' U2 Rw' U2 Rw' U2 Rw' F U2 F' Rw'
 
 
|sign=r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r'
 
|sign=r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r'
 
|length=(21,15)|name=|wide=Y|author=Bruce Norskog & Christopher Mowla
 
|length=(21,15)|name=|wide=Y|author=Bruce Norskog & Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw
+
{{Alg6|wca=Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw
 
|sign=r U D' R2 U' R2 D x' U2 l U2 l U2 l F' U2 F l
 
|sign=r U D' R2 U' R2 D x' U2 l U2 l U2 l F' U2 F l
 
|length=(22,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(22,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r
+
{{Alg6|wca=Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r
 
|sign=r F U2 F' r U2 r U2 r R U2 F U2 F' U2 2R
 
|sign=r F U2 F' r U2 r U2 r R U2 F U2 F' U2 2R
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|length=(22,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z'
+
{{Alg6|wca=Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z'
 
|sign=r' U R U2 R' U' r' U2 r' U2 r' F U' B' U' s d' z'
 
|sign=r' U R U2 R' U' r' U2 r' U2 r' F U' B' U' s d' z'
 
|length=(20,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(20,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x'
+
{{Alg6|wca=Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x'
 
|sign=l U' L' R U2 L U l U2 l U2 l U' R' U2 R U 2R x'
 
|sign=l U' L' R U2 L U l U2 l U2 l U' R' U2 R U 2R x'
 
|length=(22,18)|name=|wide=N|author=Christopher Mowla
 
|length=(22,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R
+
{{Alg6|wca=Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R
 
|sign=l U' L' R' U2 L U l U2 l U2 l U' R U2 R' U l R
 
|sign=l U' L' R' U2 L U l U2 l U2 l U' R U2 R' U l R
 
|length=(23,19)|name=|wide=Y|author=Christopher Mowla
 
|length=(23,19)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Random pseudo-3x3x3 positions</span>==
==Random pseudo-3x3x3 positions==
 
 
[[Image:Pseudo3.png|110px|]]
 
[[Image:Pseudo3.png|110px|]]
*Bruce Norskog explained how he found the algorithms (the algorithms in this section attributed solely to him) in [http://cubezzz.dyndns.org/drupal/?q=node/view/230 this post].
+
*Bruce Norskog explained how he found the algorithms (the algorithms in this section attributed solely to him) in {{LinkColorE|u=http://cubezzz.dyndns.org/drupal/?q=node/view/230|c=rgb(229,148,0)|t=this post}}.
 
 
*To see a large list of (U,Rw,R) solutions (several of the algorithms in this list are listed in this section already) that have been found by Kåre Krig, see [http://www.speedsolving.com/forum/showthread.php?30127-New-4x4-parity-algs-using-R-Rw-U&p=806576&viewfull=1#post806576 this thread].
 
  
 +
*To see a large list of (U,Rw,R) solutions that have been found by Kåre Krig, see {{LinkColorE|u=http://www.speedsolving.com/forum/showthread.php?30127-New-4x4-parity-algs-using-R-Rw-U&p=806576&viewfull=1#post806576|c=rgb(229,148,0)|t=this thread}}.  (Several of the algorithms in that list are listed in this section already.)
  
<b>Single Parity</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Single Parity</b></span>
{{Alg5|wca=Rw B U2 B' r B2 l B2 r B' D2 B Rw
+
{{Alg6|wca=Rw B U2 B' r B2 l B2 r B' D2 B Rw
 
|sign=r B U2 B' 2R B2 2L B2 2R B' D2 B r
 
|sign=r B U2 B' 2R B2 2L B2 2R B' D2 B r
 
|length=(17,13)|name=|wide=N|author=Bruce Norskog
 
|length=(17,13)|name=|wide=N|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U F2 U' Lw F2 r U2 Rw U B2 U' Rw
+
{{Alg6|wca=Rw U F2 U' Lw F2 r U2 Rw U B2 U' Rw
 
|sign=r U F2 U' l F2 2R U2 r U B2 U' r
 
|sign=r U F2 U' l F2 2R U2 r U B2 U' r
 
|length=(17,13)|name=|wide=N|author=Bruce Norskog
 
|length=(17,13)|name=|wide=N|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' F2 U Lw F2 r U2 Rw U' B2 U Rw
+
{{Alg6|wca=Rw U' F2 U Lw F2 r U2 Rw U' B2 U Rw
 
|sign=r U' F2 U l F2 2R U2 r U' B2 U r
 
|sign=r U' F2 U l F2 2R U2 r U' B2 U r
 
|length=(17,13)|name=|wide=N|author=Bruce Norskog
 
|length=(17,13)|name=|wide=N|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw M R D R' Bw f M d' M' Fw b M' F Uw
+
{{Alg6|wca=Uw M R D R' Bw f M d' M' Fw b M' F Uw
 
|sign=u m R D R' b 2F m 2D' m' f 2B m' F u
 
|sign=u m R D R' b 2F m 2D' m' f 2B m' F u
 
|length=(15,15)|name=|wide=N|author=Bruce Norskog
 
|length=(15,15)|name=|wide=N|author=Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
}}
 
}}
{{Alg5|wca=Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'
+
{{Alg6|wca=Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'
 
|sign=r' s' L2 s r' U2 r' U2 r' F' U2 F U R U' r'
 
|sign=r' s' L2 s r' U2 r' U2 r' F' U2 F U R U' r'
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'
+
{{Alg6|wca=Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'
 
|sign=r' s R2 s' r' U2 r' U2 r' F U2 F' U' L' U r'
 
|sign=r' s R2 s' r' U2 r' U2 r' F U2 F' U' L' U r'
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw' U2 Rw D2 Rw D2 Rw' F L' F' U' Rw' D2 Rw
+
{{Alg6|wca=Rw U2 Rw' U2 Rw D2 Rw D2 Rw' F L' F' U' Rw' D2 Rw
 
|sign=r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r
 
|sign=r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r
 
|length=(21,16)|name=|wide=Y|author=Christopher Mowla
 
|length=(21,16)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-8#post-304604
 
|url=https://www.speedsolving.com/forum/threads/wanted-new-dedge-flip-algorithm.17839/page-8#post-304604
 
}}
 
}}
{{Alg5|wca=r U' M' U M' U' M' U' M Uw2 r Uw2 U' M' U2 M' U M U2 M U M' U M U M' U' l'
+
{{Alg6|wca=r U' M' U M' U' M' U' M Uw2 r Uw2 U' M' U2 M' U M U2 M U M' U M U M' U' l'
 
|sign=2R U' m' U m' U' m' U' m u2 2R u2 U' m' U2 m' U m U2 m U m' U m U m' U' 2L'
 
|sign=2R U' m' U m' U' m' U' m u2 2R u2 U' m' U2 m' U m U2 m U m' U m U m' U' 2L'
 
|length=(31,28)|name=|wide=N|author=Christopher Mowla
 
|length=(31,28)|name=|wide=N|author=Christopher Mowla
Line 7,159: Line 7,450:
 
}}
 
}}
  
<b>Double Parity</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Double Parity</b></span>
{{Alg5|wca=Rw F2 U2 Lw F U' R U' Rw2 B2 Rw' B2 Rw2
+
{{Alg6|wca=Rw F2 U2 Lw F U' R U' Rw2 B2 Rw' B2 Rw2
 
|sign=r F2 U2 l F U' R U' r2 B2 r' B2 r2
 
|sign=r F2 U2 l F U' R U' r2 B2 r' B2 r2
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw F2 U2 Lw F' U L' U Rw2 B2 Rw' B2 Rw2
+
{{Alg6|wca=Rw F2 U2 Lw F' U L' U Rw2 B2 Rw' B2 Rw2
 
|sign=r F2 U2 l F' U L' U r2 B2 r' B2 r2
 
|sign=r F2 U2 l F' U L' U r2 B2 r' B2 r2
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw F2 U2 Lw F U' (L' R) U' Rw2 B2 Rw' B2 Rw2
+
{{Alg6|wca=Rw F2 U2 Lw F U' (L' R) U' Rw2 B2 Rw' B2 Rw2
 
|sign=r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2
 
|sign=r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw F2 U2 Lw F' U (L' R) U Rw2 B2 Rw' B2 Rw2
+
{{Alg6|wca=Rw F2 U2 Lw F' U (L' R) U Rw2 B2 Rw' B2 Rw2
 
|sign=r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2
 
|sign=r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U2 Lw' U2 x' (Rw' U2 Lw U2)2 Lw'
+
{{Alg6|wca=Rw U2 Lw' U2 x' (Rw' U2 Lw U2)2 Lw'
 
|sign=r U2 l' U2 x' (r' U2 l U2)2 l'
 
|sign=r U2 l' U2 x' (r' U2 l U2)2 l'
 
|length=(19,13)|name=reParity
 
|length=(19,13)|name=reParity
Line 7,186: Line 7,477:
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' b M r' D' b D l' b2 Lw E' B' Rw
+
{{Alg6|wca=Rw U' b M r' D' b D l' b2 Lw E' B' Rw
 
|sign=r U' 2B m 2R' D' 2B D 2L' 2B2 l e' B' r
 
|sign=r U' 2B m 2R' D' 2B D 2L' 2B2 l e' B' r
 
|length=(15,14)|name=|wide=N|author=Bruce Norskog
 
|length=(15,14)|name=|wide=N|author=Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw U2 Rw U2 Rw U2 D' Rw F' U2 F Rw'
+
{{Alg6|wca=Rw2 U2 Rw U2 Rw U2 Rw U2 D' Rw F' U2 F Rw'
 
|sign=r2 U2 r U2 r U2 r U2 D' r F' U2 F r'
 
|sign=r2 U2 r U2 r U2 r U2 D' r F' U2 F r'
 
|length=(20,14)|name=|wide=Y|author=xyzzy
 
|length=(20,14)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw' U2 Rw' U2 Rw' U2 D Rw' B U2 B' Rw
+
{{Alg6|wca=Rw2 U2 Rw' U2 Rw' U2 Rw' U2 D Rw' B U2 B' Rw
 
|sign=r2 U2 r' U2 r' U2 r' U2 D r' B U2 B' r
 
|sign=r2 U2 r' U2 r' U2 r' U2 D r' B U2 B' r
 
|length=(20,14)|name=|wide=Y|author=xyzzy
 
|length=(20,14)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw' U F2 U' Rw F2 B' Rw F2 Rw F2 Rw F2 Rw2
+
{{Alg6|wca=Rw' U F2 U' Rw F2 B' Rw F2 Rw F2 Rw F2 Rw2
 
|sign=r' U F2 U' r F2 B' r F2 r F2 r F2 r2
 
|sign=r' U F2 U' r F2 B' r F2 r F2 r F2 r2
 
|length=(20,14)|name=|wide=Y|author=xyzzy
 
|length=(20,14)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Uw M F R' B u d l' u d F R' B M Uw
+
{{Alg6|wca=Uw M F R' B u d l' u d F R' B M Uw
 
|sign=u m F R' B 2U 2D 2L' 2U 2D F R' B m u
 
|sign=u m F R' B 2U 2D 2L' 2U 2D F R' B m u
 
|length=(15,15)|name=|wide=N|author=Bruce Norskog
 
|length=(15,15)|name=|wide=N|author=Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
}}
 
}}
{{Alg5|wca=Uw M F' L B' u d l' u d F' L B' M Uw
+
{{Alg6|wca=Uw M F' L B' u d l' u d F' L B' M Uw
 
|sign=u m F' L B' 2U 2D 2L' 2U 2D F' L B' m u
 
|sign=u m F' L B' 2U 2D 2L' 2U 2D F' L B' m u
 
|length=(15,15)|name=|wide=N|author=Bruce Norskog
 
|length=(15,15)|name=|wide=N|author=Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-540571
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw' U2 D' Rw D F2 Rw F2 Rw F2 Rw' D' Rw'
+
{{Alg6|wca=Rw U2 Rw' U2 D' Rw D F2 Rw F2 Rw F2 Rw' D' Rw'
 
|sign=r U2 r' U2 D' r D F2 r F2 r F2 r' D' r'
 
|sign=r U2 r' U2 D' r D F2 r F2 r F2 r' D' r'
 
|length=(20,15)|name=|wide=Y|author=xyzzy
 
|length=(20,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw' U2 Rw' U2 Rw' U2 Rw2 B R D' Rw B' U2 B Rw'
+
{{Alg6|wca=Rw' U2 Rw' U2 Rw' U2 Rw2 B R D' Rw B' U2 B Rw'
 
|sign=r' U2 r' U2 r' U2 r2 B R D' r B' U2 B r'
 
|sign=r' U2 r' U2 r' U2 r2 B R D' r B' U2 B r'
 
|length=(20,15)|name=|wide=Y|author=xyzzy
 
|length=(20,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw U2 Rw U2 Rw U2 D L' Rw F U2 F' Rw'
+
{{Alg6|wca=Rw2 U2 Rw U2 Rw U2 Rw U2 D L' Rw F U2 F' Rw'
 
|sign=r2 U2 r U2 r U2 r U2 D L' r F U2 F' r'
 
|sign=r2 U2 r U2 r U2 r U2 D L' r F U2 F' r'
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw U2 Rw U2 Rw D L' U2 Rw F U2 F' Rw'
+
{{Alg6|wca=Rw2 U2 Rw U2 Rw U2 Rw D L' U2 Rw F U2 F' Rw'
 
|sign=r2 U2 r U2 r U2 r D L' U2 r F U2 F' r'
 
|sign=r2 U2 r U2 r U2 r D L' U2 r F U2 F' r'
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw' F2 Rw2 U F R' L U F' Rw U2 F2 Rw
+
{{Alg6|wca=Rw2 U2 Rw' F2 Rw2 U F R' L U F' Rw U2 F2 Rw
 
|sign=r2 U2 r' F2 r2 U F R' L U F' r U2 F2 r
 
|sign=r2 U2 r' F2 r2 U F R' L U F' r U2 F2 r
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 U2 Rw' F2 Rw2 U' F R' L U' F Rw U2 F2 Rw
+
{{Alg6|wca=Rw2 U2 Rw' F2 Rw2 U' F R' L U' F Rw U2 F2 Rw
 
|sign=r2 U2 r' F2 r2 U' F R' L U' F r U2 F2 r
 
|sign=r2 U2 r' F2 r2 U' F R' L U' F r U2 F2 r
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|length=(21,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 Rw F2 Rw2 U L2 B' L B U Rw' F2 Rw2
+
{{Alg6|wca=Rw U2 F2 Rw F2 Rw2 U L2 B' L B U Rw' F2 Rw2
 
|sign=r U2 F2 r F2 r2 U L2 B' L B U r' F2 r2
 
|sign=r U2 F2 r F2 r2 U L2 B' L B U r' F2 r2
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 Rw F2 Rw2 U B' L' B L2 U Rw' F2 Rw2
+
{{Alg6|wca=Rw U2 F2 Rw F2 Rw2 U B' L' B L2 U Rw' F2 Rw2
 
|sign=r U2 F2 r F2 r2 U B' L' B L2 U r' F2 r2
 
|sign=r U2 F2 r F2 r2 U B' L' B L2 U r' F2 r2
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 Rw F2 Rw2 U' R2 B R' B' U' Rw' F2 Rw2
+
{{Alg6|wca=Rw U2 F2 Rw F2 Rw2 U' R2 B R' B' U' Rw' F2 Rw2
 
|sign=r U2 F2 r F2 r2 U' R2 B R' B' U' r' F2 r2
 
|sign=r U2 F2 r F2 r2 U' R2 B R' B' U' r' F2 r2
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw U2 F2 Rw F2 Rw2 U' B R B' R2 U' Rw' F2 Rw2
+
{{Alg6|wca=Rw U2 F2 Rw F2 Rw2 U' B R B' R2 U' Rw' F2 Rw2
 
|sign=r U2 F2 r F2 r2 U' B R B' R2 U' r' F2 r2
 
|sign=r U2 F2 r F2 r2 U' B R B' R2 U' r' F2 r2
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw D' B2 D Rw' D' Rw' U2 Rw' B2 U2 Rw U2 B2 Rw2
+
{{Alg6|wca=Rw D' B2 D Rw' D' Rw' U2 Rw' B2 U2 Rw U2 B2 Rw2
 
|sign=r D' B2 D r' D' r' U2 r' B2 U2 r U2 B2 r2
 
|sign=r D' B2 D r' D' r' U2 r' B2 U2 r U2 B2 r2
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 U2 B2 Rw B2 U2 Rw' B2 Rw' F' Rw' F U2 F' Rw
+
{{Alg6|wca=Rw2 U2 B2 Rw B2 U2 Rw' B2 Rw' F' Rw' F U2 F' Rw
 
|sign=r2 U2 B2 r B2 U2 r' B2 r' F' r' F U2 F' r
 
|sign=r2 U2 B2 r B2 U2 r' B2 r' F' r' F U2 F' r
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D L2 B L' B' D Rw2 F2 Rw F2 D2 Rw
+
{{Alg6|wca=Rw2 F2 Rw' D L2 B L' B' D Rw2 F2 Rw F2 D2 Rw
 
|sign=r2 F2 r' D L2 B L' B' D r2 F2 r F2 D2 r
 
|sign=r2 F2 r' D L2 B L' B' D r2 F2 r F2 D2 r
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D B L B' L2 D Rw2 F2 Rw F2 D2 Rw
+
{{Alg6|wca=Rw2 F2 Rw' D B L B' L2 D Rw2 F2 Rw F2 D2 Rw
 
|sign=r2 F2 r' D B L B' L2 D r2 F2 r F2 D2 r
 
|sign=r2 F2 r' D B L B' L2 D r2 F2 r F2 D2 r
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D2 B2 Rw' D B R' D F2 B' Rw2 B2 Rw'
+
{{Alg6|wca=Rw2 F2 Rw' D2 B2 Rw' D B R' D F2 B' Rw2 B2 Rw'
 
|sign=r2 F2 r' D2 B2 r' D B R' D F2 B' r2 B2 r'
 
|sign=r2 F2 r' D2 B2 r' D B R' D F2 B' r2 B2 r'
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D2 B2 Rw' D' B' L D' F2 B Rw2 B2 Rw'
+
{{Alg6|wca=Rw2 F2 Rw' D2 B2 Rw' D' B' L D' F2 B Rw2 B2 Rw'
 
|sign=r2 F2 r' D2 B2 r' D' B' L D' F2 B r2 B2 r'
 
|sign=r2 F2 r' D2 B2 r' D' B' L D' F2 B r2 B2 r'
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D2 B2 Rw' F D' L F' D' F2 Rw2 B2 Rw'
+
{{Alg6|wca=Rw2 F2 Rw' D2 B2 Rw' F D' L F' D' F2 Rw2 B2 Rw'
 
|sign=r2 F2 r' D2 B2 r' F D' L F' D' F2 r2 B2 r'
 
|sign=r2 F2 r' D2 B2 r' F D' L F' D' F2 r2 B2 r'
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D2 B2 Rw' F' D R' F D F2 Rw2 B2 Rw'
+
{{Alg6|wca=Rw2 F2 Rw' D2 B2 Rw' F' D R' F D F2 Rw2 B2 Rw'
 
|sign=r2 F2 r' D2 B2 r' F' D R' F D F2 r2 B2 r'
 
|sign=r2 F2 r' D2 B2 r' F' D R' F D F2 r2 B2 r'
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D' R2 B' R B D' Rw2 F2 Rw F2 D2 Rw
+
{{Alg6|wca=Rw2 F2 Rw' D' R2 B' R B D' Rw2 F2 Rw F2 D2 Rw
 
|sign=r2 F2 r' D' R2 B' R B D' r2 F2 r F2 D2 r
 
|sign=r2 F2 r' D' R2 B' R B D' r2 F2 r F2 D2 r
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=Rw2 F2 Rw' D' B' R' B R2 D' Rw2 F2 Rw F2 D2 Rw
+
{{Alg6|wca=Rw2 F2 Rw' D' B' R' B R2 D' Rw2 F2 Rw F2 D2 Rw
 
|sign=r2 F2 r' D' B' R' B R2 D' r2 F2 r F2 D2 r
 
|sign=r2 F2 r' D' B' R' B R2 D' r2 F2 r F2 D2 r
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|length=(22,15)|name=|wide=Y|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=r' U M' U' M' U M' U M Uw2 l' Uw2 M' U M U' M' U M' U M U2 M' U2 r
+
{{Alg6|wca=r' U M' U' M' U M' U M Uw2 l' Uw2 M' U M U' M' U M' U M U2 M' U2 r
 
|sign=2R' U m' U' m' U m' U m u2 2L' u2 m' U m U' m' U m' U m U2 m' U2 2R
 
|sign=2R' U m' U' m' U m' U m u2 2L' u2 m' U m U' m' U m' U m U2 m' U2 2R
 
|length=(29,25)|name=|wide=N|author=Christopher Mowla
 
|length=(29,25)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-12#post-874531
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-12#post-874531
 
}}
 
}}
 +
{{br|b=1}}
  
=Non Dedge-Preserving Last Layer 2-Cycle Cases=
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">Non Dedge-Preserving Last Layer 2-Cycle Cases</span>=
 
*This section contains all of the 2-cycle cases that can occur in the last layer besides the one dedge flip.
 
*This section contains all of the 2-cycle cases that can occur in the last layer besides the one dedge flip.
*These are additional cases which arise in the K4 Method and other [[direct solving]] methods.
+
*These are additional cases which arise in the {{LinkColorI|p=K4|c=rgb(229,148,0)|t=K4 Method}} and other {{LinkColorI|p=direct solving|c=rgb(229,148,0)|t=direct solving methods}}.
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">In opposite dedges</span>==
==In opposite dedges==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Opposite</span>===
===Opposite===
 
 
[[Image:Adj2swap.png|110px|]]
 
[[Image:Adj2swap.png|110px|]]
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Symmetrical algorithms</b></span>
<b>Symmetrical algorithms</b>
+
{{Alg6|wca=r U2 r U2 F2 r F2 l' U2 l U2 r2
{{Alg5|wca=r U2 r U2 F2 r F2 l' U2 l U2 r2
 
 
|sign=2R U2 2R U2 F2 2R F2 2L' U2 2L U2 2R2
 
|sign=2R U2 2R U2 F2 2R F2 2L' U2 2L U2 2R2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 l F2 D2 r D2 l' F2 r U2 r2
+
{{Alg6|wca=r U2 l F2 D2 r D2 l' F2 r U2 r2
 
|sign=2R U2 2L F2 D2 2R D2 2L' F2 2R U2 2R2
 
|sign=2R U2 2L F2 D2 2R D2 2L' F2 2R U2 2R2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 l' B2 D2 r' D2 l B2 r' U2 r2
+
{{Alg6|wca=r' U2 l' B2 D2 r' D2 l B2 r' U2 r2
 
|sign=2R' U2 2L' B2 D2 2R' D2 2L B2 2R' U2 2R2
 
|sign=2R' U2 2L' B2 D2 2R' D2 2L B2 2R' U2 2R2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r' U2 B2 r' B2 l U2 l' U2 r2
+
{{Alg6|wca=r' U2 r' U2 B2 r' B2 l U2 l' U2 r2
 
|sign=2R' U2 2R' U2 B2 2R' B2 2L U2 2L' U2 2R2
 
|sign=2R' U2 2R' U2 B2 2R' B2 2L U2 2L' U2 2R2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l F2 r F2 D2 l B2 r' B2 r D2 l2
+
{{Alg6|wca=l F2 r F2 D2 l B2 r' B2 r D2 l2
 
|sign=2L F2 2R F2 D2 2L B2 2R' B2 2R D2 2L2
 
|sign=2L F2 2R F2 D2 2L B2 2R' B2 2R D2 2L2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l F2 r F2 D2 r D2 r' D2 l D2 l2
+
{{Alg6|wca=l F2 r F2 D2 r D2 r' D2 l D2 l2
 
|sign=2L F2 2R F2 D2 2R D2 2R' D2 2L D2 2L2
 
|sign=2L F2 2R F2 D2 2R D2 2R' D2 2L D2 2L2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' B2 r' B2 D2 l' F2 r F2 r' D2 l2
+
{{Alg6|wca=l' B2 r' B2 D2 l' F2 r F2 r' D2 l2
 
|sign=2L' B2 2R' B2 D2 2L' F2 2R F2 2R' D2 2L2
 
|sign=2L' B2 2R' B2 D2 2L' F2 2R F2 2R' D2 2L2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' B2 r' B2 D2 r' D2 r D2 l' D2 l2
+
{{Alg6|wca=l' B2 r' B2 D2 r' D2 r D2 l' D2 l2
 
|sign=2L' B2 2R' B2 D2 2R' D2 2R D2 2L' D2 2L2
 
|sign=2L' B2 2R' B2 D2 2R' D2 2R D2 2L' D2 2L2
 
|length=(19,12)|name=|wide=Y|author=|url=
 
|length=(19,12)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 M' U2 r U2 r' U2 l U2 r2
+
{{Alg6|wca=r U2 r U2 M' U2 r U2 r' U2 l U2 r2
 
|sign=2R U2 2R U2 m' U2 2R U2 2R' U2 2L U2 2R2
 
|sign=2R U2 2R U2 m' U2 2R U2 2R' U2 2L U2 2R2
 
|length=(20,13)|name=|wide=N|author=|url=
 
|length=(20,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 r' U2 3Rw' U2 r' U2 r U2 l' U2 Rw2
+
{{Alg6|wca=Rw' U2 r' U2 3Rw' U2 r' U2 r U2 l' U2 Rw2
 
|sign=r' U2 2R' U2 3r' U2 2R' U2 2R U2 2L' U2 r2
 
|sign=r' U2 2R' U2 3r' U2 2R' U2 2R U2 2L' U2 r2
 
|length=(20,13)|name=|wide=N|author=|url=
 
|length=(20,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=z Rw' U l' Uw' Rw Uw l' Fw' l' Fw l2 Uw' Rw' u Rw z'
+
{{Alg6|wca=z Rw' U l' Uw' Rw Uw l' Fw' l' Fw l2 Uw' Rw' u Rw z'
 
|sign=z r' U 2L' u' r u 2L' f' 2L' f 2L2 u' r' 2U r z'
 
|sign=z r' U 2L' u' r u 2L' f' 2L' f 2L2 u' r' 2U r z'
 
|length=(16,15)|name=|wide=N|author=Christopher Mowla
 
|length=(16,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-694197
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-694197
 
}}
 
}}
{{Alg5|wca=l F2 r F2 l D f' D r D2 r' D' f D l2
+
{{Alg6|wca=l F2 r F2 l D f' D r D2 r' D' f D l2
 
|sign=2L F2 2R F2 2L D 2F' D 2R D2 2R' D' 2F D 2L2
 
|sign=2L F2 2R F2 2L D 2F' D 2R D2 2R' D' 2F D 2L2
 
|length=(19,15)|name=|wide=Y|author=Christopher Mowla
 
|length=(19,15)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b'
+
{{Alg6|wca=b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b'
 
|sign=2B 2U b' r' 2F' r b r' 2F2 u' 2F' u 2F' r 2U' 2B'
 
|sign=2B 2U b' r' 2F' r b r' 2F2 u' 2F' u 2F' r 2U' 2B'
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-5#post-626321
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-5#post-626321
 
}}
 
}}
{{Alg5|wca=z Rw U' l Uw Rw' 3Uw' l Bw l Bw' l' d' l' Uw Rw u' Rw' z'
+
{{Alg6|wca=z Rw U' l Uw Rw' 3Uw' l Bw l Bw' l' d' l' Uw Rw u' Rw' z'
 
|sign=z r U' 2L u r' 3u' 2L b 2L b' 2L' 2D' 2L' u r 2U' r' z'
 
|sign=z r U' 2L u r' 3u' 2L b 2L b' 2L' 2D' 2L' u r 2U' r' z'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' Lw U b' Uw' Fw Uw b' Lw' b' Lw b2 Uw' Fw' u Lw' Dw
+
{{Alg6|wca=Dw' Lw U b' Uw' Fw Uw b' Lw' b' Lw b2 Uw' Fw' u Lw' Dw
 
|sign=d' l U 2B' u' f u 2B' l' 2B' l 2B2 u' f' 2U l' d
 
|sign=d' l U 2B' u' f u 2B' l' 2B' l 2B2 u' f' 2U l' d
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' b U' Lw d' Lw' Uw Lw d' Fw' d' Fw d2 Lw' u' b' Dw
+
{{Alg6|wca=Dw' b U' Lw d' Lw' Uw Lw d' Fw' d' Fw d2 Lw' u' b' Dw
 
|sign=d' 2B U' l 2D' l' u l 2D' f' 2D' f 2D2 l' 2U' 2B' d
 
|sign=d' 2B U' l 2D' l' u l 2D' f' 2D' f 2D2 l' 2U' 2B' d
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' S B d' Bw' Uw Bw d' Lw' d' Lw d2 Bw' Uw' b S' Rw
+
{{Alg6|wca=Rw' S B d' Bw' Uw Bw d' Lw' d' Lw d2 Bw' Uw' b S' Rw
 
|sign=r' s B 2D' b' u b 2D' l' 2D' l 2D2 b' u' 2B s' r
 
|sign=r' s B 2D' b' u b 2D' l' 2D' l 2D2 b' u' 2B s' r
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' u' B d' Bw' Uw Bw d' Lw' d' Lw d2 Bw' Uw' b u Rw
+
{{Alg6|wca=Rw' u' B d' Bw' Uw Bw d' Lw' d' Lw d2 Bw' Uw' b u Rw
 
|sign=r' 2U' B 2D' b' u b 2D' l' 2D' l 2D2 b' u' 2B 2U r
 
|sign=r' 2U' B 2D' b' u b 2D' l' 2D' l 2D2 b' u' 2B 2U r
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' f U' Lw d' Lw' Uw Lw d' Fw' d' Fw d2 Lw' u' f' Rw
+
{{Alg6|wca=Rw' f U' Lw d' Lw' Uw Lw d' Fw' d' Fw d2 Lw' u' f' Rw
 
|sign=r' 2F U' l 2D' l' u l 2D' f' 2D' f 2D2 l' 2U' 2F' r
 
|sign=r' 2F U' l 2D' l' u l 2D' f' 2D' f 2D2 l' 2U' 2F' r
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' B Fw Uw Fw' Dw' d' Lw' d' Lw d' D Fw Uw' Fw' d' B' Dw
+
{{Alg6|wca=Dw' B Fw Uw Fw' Dw' d' Lw' d' Lw d' D Fw Uw' Fw' d' B' Dw
 
|sign=d' B f u f' d' 2D' l' 2D' l 2D' D f u' f' 2D' B' d
 
|sign=d' B f u f' d' 2D' l' 2D' l 2D' D f u' f' 2D' B' d
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' B d' Bw' Uw Bw F d' Lw' d' Lw d F' d Bw' Uw' b Dw
+
{{Alg6|wca=Dw' B d' Bw' Uw Bw F d' Lw' d' Lw d F' d Bw' Uw' b Dw
 
|sign=d' B 2D' b' u b F 2D' l' 2D' l 2D F' 2D b' u' 2B d
 
|sign=d' B 2D' b' u b F 2D' l' 2D' l 2D F' 2D b' u' 2B d
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' Lw U b' Uw' Fw l' Fw' l' Fw l Uw b Uw' Fw' u Lw' Dw
+
{{Alg6|wca=Dw' Lw U b' Uw' Fw l' Fw' l' Fw l Uw b Uw' Fw' u Lw' Dw
 
|sign=d' l U 2B' u' f 2L' f' 2L' f 2L u 2B u' f' 2U l' d
 
|sign=d' l U 2B' u' f 2L' f' 2L' f 2L u 2B u' f' 2U l' d
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw' Bw L d' Lw' Uw f' Uw' f' Uw f Lw d Lw' Uw' l Bw' Uw
+
{{Alg6|wca=Uw' Bw L d' Lw' Uw f' Uw' f' Uw f Lw d Lw' Uw' l Bw' Uw
 
|sign=u' b L 2D' l' u 2F' u' 2F' u 2F l 2D l' u' 2L b' u
 
|sign=u' b L 2D' l' u 2F' u' 2F' u 2F l 2D l' u' 2L b' u
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw R' S Lw Fw Lw' b Lw Fw' Lw' b Uw b Uw' f' b' R Dw'
+
{{Alg6|wca=Dw R' S Lw Fw Lw' b Lw Fw' Lw' b Uw b Uw' f' b' R Dw'
 
|sign=d R' s l f l' 2B l f' l' 2B u 2B u' 2F' 2B' R d'
 
|sign=d R' s l f l' 2B l f' l' 2B u 2B u' 2F' 2B' R d'
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' R S' Lw Fw Lw' b Lw Fw' Lw' b Uw b Uw' f b R' Dw
+
{{Alg6|wca=Dw' R S' Lw Fw Lw' b Lw Fw' Lw' b Uw b Uw' f b R' Dw
 
|sign=d' R s' l f l' 2B l f' l' 2B u 2B u' 2F 2B R' d
 
|sign=d' R s' l f l' 2B l f' l' 2B u 2B u' 2F 2B R' d
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' d f Lw Fw Lw' b Lw Fw' Lw' b Uw b Uw' S' b d' Rw
+
{{Alg6|wca=Rw' d f Lw Fw Lw' b Lw Fw' Lw' b Uw b Uw' S' b d' Rw
 
|sign=r' 2D 2F l f l' 2B l f' l' 2B u 2B u' s' 2B 2D' r
 
|sign=r' 2D 2F l f l' 2B l f' l' 2B u 2B u' s' 2B 2D' r
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Bw' b' M Fw Rw' u Rw u Rw' u' Fw' l' Fw Rw Fw' r b Bw
+
{{Alg6|wca=Bw' b' M Fw Rw' u Rw u Rw' u' Fw' l' Fw Rw Fw' r b Bw
 
|sign=b' 2B' m f r' 2U r 2U r' 2U' f' 2L' f r f' 2R 2B b
 
|sign=b' 2B' m f r' 2U r 2U r' 2U' f' 2L' f r f' 2R 2B b
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' L U') (r' F U2 F')4 r' (U L' y)
+
{{Alg6|wca=(y' L U') (r' F U2 F')4 r' (U L' y)
 
|sign=(y' L U') (2R' F U2 F')4 2R' (U L' y)
 
|sign=(y' L U') (2R' F U2 F')4 2R' (U L' y)
 
|length=(25,21)|name=|wide=Y|author=Floyd Newberry
 
|length=(25,21)|name=|wide=Y|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=(y' L U') (r F U2 F')4 r (U L' y)
+
{{Alg6|wca=(y' L U') (r F U2 F')4 r (U L' y)
 
|sign=(y' L U') (2R F U2 F')4 2R (U L' y)
 
|sign=(y' L U') (2R F U2 F')4 2R (U L' y)
 
|length=(25,21)|name=|wide=Y|author=Floyd Newberry
 
|length=(25,21)|name=|wide=Y|author=Floyd Newberry
Line 7,469: Line 7,759:
 
}}
 
}}
  
<b>Non-symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Non-symmetrical algorithms</b></span>
{{Alg5|wca=Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F'
+
{{Alg6|wca=Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F'
 
|sign=r U2 2R U2 r U2 r2 F 2R F' r2 U2 r2 F 2R' F'
 
|sign=r U2 2R U2 r U2 r2 F 2R F' r2 U2 r2 F 2R' F'
 
|length=(23,16)|name=|wide=N|author=Christopher Mowla
 
|length=(23,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D'
+
{{Alg6|wca=l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D'
 
|sign=2L' B2 2L D 2R' D' 2L' B2 2L D 2L 2R F2 2R' F2 2L' D'
 
|sign=2L' B2 2L D 2R' D' 2L' B2 2L D 2L 2R F2 2R' F2 2L' D'
 
|length=(21,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(21,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D'
+
{{Alg6|wca=r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D'
 
|sign=2R' U2 2R D 2R' D' 2R' U2 2L' B2 2R' B2 2L 2R D 2R D'
 
|sign=2R' U2 2R D 2R' D' 2R' U2 2L' B2 2R' B2 2L 2R D 2R D'
 
|length=(21,17)|name=|wide=Y|author=Christopher Mowla
 
|length=(21,17)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z Rw Uw' l Dw Bw' D' L' d Rw Dw l Dw' Rw' d' L d' l' Uw z'
+
{{Alg6|wca=z Rw Uw' l Dw Bw' D' L' d Rw Dw l Dw' Rw' d' L d' l' Uw z'
 
|sign=z r u' 2L d b' D' L' 2D r d 2L d' r' 2D' L 2D' 2L' u z'
 
|sign=z r u' 2L d b' D' L' 2D r d 2L d' r' 2D' L 2D' 2L' u z'
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z Rw' Uw l' Dw' Fw D L d' Rw' Dw' l' Dw Rw d L' d l Uw' z'
+
{{Alg6|wca=z Rw' Uw l' Dw' Fw D L d' Rw' Dw' l' Dw Rw d L' d l Uw' z'
 
|sign=z r' u 2L' d' f D L 2D' r' d' 2L' d r 2D L' 2D 2L u' z'
 
|sign=z r' u 2L' d' f D L 2D' r' d' 2L' d r 2D L' 2D 2L u' z'
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw' Fw l' Fw' Uw Fw l' Uw' u' R u l' u' R' Uw u l2 Fw' y'
+
{{Alg6|wca=Dw' Fw l' Fw' Uw Fw l' Uw' u' R u l' u' R' Uw u l2 Fw' y'
 
|sign=d' f 2L' f' u f 2L' u' 2U' R 2U 2L' 2U' R' u 2U 2L2 f' y'
 
|sign=d' f 2L' f' u f 2L' u' 2U' R 2U 2L' 2U' R' u 2U 2L2 f' y'
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=l U l U' l' U' l U l U l' D' b2 l b2 l' U2 D l' U//Safe
+
{{Alg6|wca=l U l U' l' U' l U l U l' D' b2 l b2 l' U2 D l' U //Safe
|sign=2L U 2L U' 2L' U' 2L U 2L U 2L' D' 2B2 2L 2B2 2L' U2 D 2L' U//Safe
+
|sign=2L U 2L U' 2L' U' 2L U 2L U 2L' D' 2B2 2L 2B2 2L' U2 D 2L' U //Safe
 
|length=(23,20)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
|length=(23,20)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
}}
 
}}
{{Alg5|wca=r' U' R U r' U R' U' r U R U2 R' U' r' U2 r' U2 r' U2 r'
+
{{Alg6|wca=r' U' R U r' U R' U' r U R U2 R' U' r' U2 r' U2 r' U2 r'
 
|sign=2R' U' R U 2R' U R' U' 2R U R U2 R' U' 2R' U2 2R' U2 2R' U2 2R'
 
|sign=2R' U' R U 2R' U R' U' 2R U R U2 R' U' 2R' U2 2R' U2 2R' U2 2R'
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U2 l' U2 r U2 r' U2 x' U2 r' U2 r' U' l r u2 l' r' U l r u2 x//Safe
+
{{Alg6|wca=U2 l' U2 r U2 r' U2 x' U2 r' U2 r' U' l r u2 l' r' U l r u2 x //Safe
|sign=U2 2L' U2 2R U2 2R' U2 x' U2 2R' U2 2R' U' 2L 2R 2U2 2L' 2R' U 2L 2R 2U2 x//Safe
+
|sign=U2 2L' U2 2R U2 2R' U2 x' U2 2R' U2 2R' U' 2L 2R 2U2 2L' 2R' U 2L 2R 2U2 x //Safe
 
|length=(29,21)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(29,21)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Diagonal===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Diagonal</span>===
 
[[Image:Diag.opp.png|110px|]]
 
[[Image:Diag.opp.png|110px|]]
 
*Note:  The mirror case can also arise as well.  One can simply apply the mirror image of this case's algorithms to get algorithms for its mirror case.
 
*Note:  The mirror case can also arise as well.  One can simply apply the mirror image of this case's algorithms to get algorithms for its mirror case.
*All 36 unique (25,14) solutions are listed.  To obtain all possible (25,14) solutions for the top/last layer, also take y2 cube rotations of all 36 and then also consider their inverses.  (This gives a total of 144 algorithms.)  
+
*All 36 unique (25,14) solutions are listed.  To obtain all possible (25,14) solutions for the top/last layer, also take y2 cube rotations of all 36 and then also consider their inverses.  (This gives a total of 144 algorithms.)
 
+
{{br|b=1}}
 
+
<ul style="font-family:Lucida Console;font-size:90%;color:rgb(235,235,0);background-color:rgb(60,60,60);">
{| style="font-family: Tahoma; font-size: 100%; line-height: 100%; border: 0px solid #CCC; border-collapse: collapse;" width="100%" valign="top" cellpadding="6"
 
| bgcolor="fbfb8b" |
 
 
It is interesting to note that due to the following algorithm's symmetry,
 
It is interesting to note that due to the following algorithm's symmetry,
{{Alg5|wca=(Rw2 F2 U2) <b>r</b> (U2 F2 Rw2) (F2 l' U2 l r U2 r' F2)
+
{{Alg6|wca=(Rw2 F2 U2) <i>r</i> (U2 F2 Rw2) (F2 l' U2 l r U2 r' F2)
 
|sign=(r2 F2 U2) 2R (U2 F2 r2) (F2 2L' U2 2L 2R U2 2R' F2)
 
|sign=(r2 F2 U2) 2R (U2 F2 r2) (F2 2L' U2 2L 2R U2 2R' F2)
 
|length=(25,15)|name=|wide=N|author=Christopher Mowla
 
|length=(25,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
 
 
the bold inner slice r turn simply can be inverted to achieve the mirror case.
 
the bold inner slice r turn simply can be inverted to achieve the mirror case.
{{Alg5|wca=(Rw2 F2 U2) (r') (U2 F2 Rw2) (F2 l' U2 l r U2 r' F2)
+
{{Alg6|wca=(Rw2 F2 U2) (r') (U2 F2 Rw2) (F2 l' U2 l r U2 r' F2)
 
|sign=(r2 F2 U2) 2R' (U2 F2 r2) (F2 2L' U2 2L 2R U2 2R' F2)
 
|sign=(r2 F2 U2) 2R' (U2 F2 r2) (F2 2L' U2 2L 2R U2 2R' F2)
 
|length=(25,15)|name=|wide=N|author=Christopher Mowla
 
|length=(25,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
 +
In fact, the combination of the first algorithm above with the inverse of the second,<br>
 +
(Rw2 F2 U2 <i>r</i> U2 F2 Rw2 F2 l' U2 l r U2 r' F2)(F2 r U2 r' l' U2 l F2 Rw2 F2 U2 (r) U2 F2 Rw2)
  
 +
cancels to:<br>
 +
Rw2 F2 U2 <i>r</i> (r) U2 F2 Rw2 = (Rw2 F2 U2) r2 (U2 F2 Rw2) = Stefan Pochmann's <i>n</i>x<i>n</i>x<i>n</i> cube PLL parity algorithm.
  
In fact, the combination of the first algorithm above with the inverse of the second,
+
This is interesting because this 2-cycle case can be thought of as "half" of the {{LinkColorE|u=https://www.speedsolving.com/wiki/images/c/c4/Opppllparity.png|c=rgb(229,148,0)|t=opposite}} parity case.  This should make perfect sense, because, as mentioned {{LinkColorE|u=https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms#Adjacent_2|c=rgb(229,148,0)|t=earlier}}, the opposite dedge swap PLL parity case is a "2 2-cycle".  This case is a "1 2-cycle" or a single 2-cycle.</ul>
 
+
{{br|b=1}}
(Rw2 F2 U2 <b>r</b> U2 F2 Rw2 F2 l' U2 l r U2 r' F2)(F2 r U2 r' l' U2 l F2 Rw2 F2 U2 (r) U2 F2 Rw2)
 
 
 
cancels to:
 
  
Rw2 F2 U2 <b>r</b> (r) U2 F2 Rw2 = (Rw2 F2 U2) r2 (U2 F2 Rw2) = Stefan Pochmann's <i>n</i>x<i>n</i>x<i>n</i> cube PLL parity algorithm.
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Symmetrical algorithms</b></span>
 
+
{{Alg6|wca=Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw'
 
 
This is interesting because this 2-cycle case can be thought of as "half" of the [https://www.speedsolving.com/wiki/images/c/c4/Opppllparity.png opposite parity] case.  This should make perfect sense, since it was mentioned [https://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms#Adjacent_2 earlier] that the opposite dedge swap PLL parity case, for example, is a "2 2-cycle".  This case is a "1 2-cycle" or a single 2-cycle.
 
|}
 
 
 
 
 
<b>Symmetrical algorithms</b>
 
{{Alg5|wca=Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw'
 
 
|sign=u l' u' 2L' u l f' l2 u' 2L' u l' L' f u'
 
|sign=u l' u' 2L' u l f' l2 u' 2L' u l' L' f u'
 
|length=(16,15)|name=|wide=N|author=Christopher Mowla
 
|length=(16,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw'
+
{{Alg6|wca=Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw'
 
|sign=u l' u' 2L' u l2 d' l u' 2L' u L' d l' u'
 
|sign=u l' u' 2L' u l2 d' l u' 2L' u L' d l' u'
 
|length=(16,15)|name=|wide=N|author=Christopher Mowla
 
|length=(16,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw Fw Dw' f' Rw Fw l Fw' Rw' F' l' Bw Rw Bw' l Dw'
+
{{Alg6|wca=Dw Fw Dw' f' Rw Fw l Fw' Rw' F' l' Bw Rw Bw' l Dw'
 
|sign=d f d' 2F' r f 2L f' r' F' 2L' b r b' 2L d'
 
|sign=d f d' 2F' r f 2L f' r' F' 2L' b r b' 2L d'
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw F Rw' Fw' l' Fw Lw Dw' Rw2 Bw' l' Bw Rw' L' f Uw'
+
{{Alg6|wca=Uw F Rw' Fw' l' Fw Lw Dw' Rw2 Bw' l' Bw Rw' L' f Uw'
 
|sign=u F r' f' 2L' f l d' r2 b' 2L' b r' L' 2F u'
 
|sign=u F r' f' 2L' f l d' r2 b' 2L' b r' L' 2F u'
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Fw U' Uw' r' Uw Lw Uw' r2 Fw' r' Fw r' Uw Lw' U Fw'
+
{{Alg6|wca=Fw U' Uw' r' Uw Lw Uw' r2 Fw' r' Fw r' Uw Lw' U Fw'
 
|sign=f U' u' 2R' u l u' 2R2 f' 2R' f 2R' u l' U f'
 
|sign=f U' u' 2R' u l u' 2R2 f' 2R' f 2R' u l' U f'
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Uw b Rw' Fw' Rw b' L Fw' Lw b Lw' Fw L' Rw' Fw Rw Uw'
+
{{Alg6|wca=Uw b Rw' Fw' Rw b' L Fw' Lw b Lw' Fw L' Rw' Fw Rw Uw'
 
|sign=u 2B r' f' r 2B' L f' l 2B l' f L' r' f r u'
 
|sign=u 2B r' f' r 2B' L f' l 2B l' f L' r' f r u'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Dw M Uw Rw' d' Fw Dw b Dw' Fw' 3Uw' l' Uw Rw Uw' r Dw'
+
{{Alg6|wca=Dw M Uw Rw' d' Fw Dw b Dw' Fw' 3Uw' l' Uw Rw Uw' r Dw'
 
|sign=d m u r' 2D' f d 2B d' f' 3u' 2L' u r u' 2R d'
 
|sign=d m u r' 2D' f d 2B d' f' 3u' 2L' u r u' 2R d'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw
+
{{Alg6|wca=Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw
 
|sign=l' U2 2L U2 2L U2 2R' U2 2L U2 2L' U2 m' U2 2L2 U2 l
 
|sign=l' U2 2L U2 2L U2 2R' U2 2L U2 2L' U2 m' U2 2L2 U2 l
 
|length=(26,17)|name=|wide=N|author=|url=
 
|length=(26,17)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=F (l' F' U2 F)4 l' F'
+
{{Alg6|wca=F (l' F' U2 F)4 l' F'
 
|sign=F (2L' F' U2 F)4 2L' F'
 
|sign=F (2L' F' U2 F)4 2L' F'
 
|length=(23,19)|name=|wide=Y|author=Floyd Newberry
 
|length=(23,19)|name=|wide=Y|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=F (l F' U2 F)4 l F'
+
{{Alg6|wca=F (l F' U2 F)4 l F'
 
|sign=F (2L F' U2 F)4 2L F'
 
|sign=F (2L F' U2 F)4 2L F'
 
|length=(23,19)|name=|wide=Y|author=Floyd Newberry
 
|length=(23,19)|name=|wide=Y|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=x' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U x//Safe
+
{{Alg6|wca=x' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U x //Safe
|sign=x' U2 2R' U' 2R U 2R U 2R' D' 2F2 2R 2F2 2R' D U2 2R' U 2R U 2R U x//Safe
+
|sign=x' U2 2R' U' 2R U 2R U 2R' D' 2F2 2R 2F2 2R' D U2 2R' U 2R U 2R U x //Safe
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
}}
 
}}
{{Alg5|wca=Rw2 U2 r' U R U r U2 r' U' R' U' r2 U R U r U2 r' U' R' U Rw2
+
{{Alg6|wca=Rw2 U2 r' U R U r U2 r' U' R' U' r2 U R U r U2 r' U' R' U Rw2
 
|sign=r2 U2 2R' U R U 2R U2 2R' U' R' U' 2R2 U R U 2R U2 2R' U' R' U r2
 
|sign=r2 U2 2R' U R U 2R U2 2R' U' R' U' 2R2 U R U 2R U2 2R' U' R' U r2
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|length=(29,23)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-495801
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-495801
 
}}
 
}}
{{Alg5|wca=Lw' U2 l U2 l U l' r' u2 l r U' l' r' u2 x U2 r U2 l' U2 l U2 Lw x'//Safe
+
{{Alg6|wca=Lw' U2 l U2 l U l' r' u2 l r U' l' r' u2 x U2 r U2 l' U2 l U2 Lw x' //Safe
|sign=l' U2 2L U2 2L U 2L' 2R' 2U2 2L 2R U' 2L' 2R' 2U2 x U2 2R U2 2L' U2 2L U2 l x'//Safe
+
|sign=l' U2 2L U2 2L U 2L' 2R' 2U2 2L 2R U' 2L' 2R' 2U2 x U2 2R U2 2L' U2 2L U2 l x' //Safe
 
|length=(31,23)|name=|wide=N|author=Per Kristen Fredlund
 
|length=(31,23)|name=|wide=N|author=Per Kristen Fredlund
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' Rw U2 Rw U2 Rw' U2 Rw' U' r U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw
+
{{Alg6|wca=Rw' U' Rw U2 Rw U2 Rw' U2 Rw' U' r U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw
 
|sign=r' U' r U2 r U2 r' U2 r' U' 2R U r U2 r U2 r' U2 r' U' 2R2 U2 r
 
|sign=r' U' r U2 r U2 r' U2 r' U' 2R U r U2 r U2 r' U2 r' U' 2R2 U2 r
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-497777
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-31#post-497777
 
}}
 
}}
{{Alg5|wca=Rw' U Rw U2 Rw U2 Rw' U2 Rw' U r U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw
+
{{Alg6|wca=Rw' U Rw U2 Rw U2 Rw' U2 Rw' U r U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw
 
|sign=r' U r U2 r U2 r' U2 r' U 2R U' r U2 r U2 r' U2 r' U 2R2 U2 r
 
|sign=r' U r U2 r U2 r' U2 r' U 2R U' r U2 r U2 r' U2 r' U 2R2 U2 r
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|length=(31,23)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
<b>Non-symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Non-symmetrical algorithms</b></span>
{{Alg5|wca=l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2
+
{{Alg6|wca=l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2
 
|sign=2L' s2 U2 2L U2 2L' U2 2R U2 2R' F2 2L B2 2R z2
 
|sign=2L' s2 U2 2L U2 2L' U2 2R U2 2R' F2 2L B2 2R z2
 
|length=(21,14)|name=|wide=Y|author=Kenneth Gustavsson
 
|length=(21,14)|name=|wide=Y|author=Kenneth Gustavsson
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2
+
{{Alg6|wca=l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2
 
|sign=2L2 B2 U2 2L U2 2L2 B2 2L U2 2L2 U2 B2 2L B2
 
|sign=2L2 B2 U2 2L U2 2L2 B2 2L U2 2L2 U2 B2 2L B2
 
|length=(25,14)|name=|wide=Y|author=Nicholas Ho
 
|length=(25,14)|name=|wide=Y|author=Nicholas Ho
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 D2 r D2 F2 l2 F2 l' F2 D2 l2 D2 r F2
+
{{Alg6|wca=r2 D2 r D2 F2 l2 F2 l' F2 D2 l2 D2 r F2
 
|sign=2R2 D2 2R D2 F2 2L2 F2 2L' F2 D2 2L2 D2 2R F2
 
|sign=2R2 D2 2R D2 F2 2L2 F2 2L' F2 D2 2L2 D2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 l' U2 l2 F2 l' U2 r2 U2 F2 r F2
+
{{Alg6|wca=r2 F2 U2 l' U2 l2 F2 l' U2 r2 U2 F2 r F2
 
|sign=2R2 F2 U2 2L' U2 2L2 F2 2L' U2 2R2 U2 F2 2R F2
 
|sign=2R2 F2 U2 2L' U2 2L2 F2 2L' U2 2R2 U2 F2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 l F2 D2 r2 D2 l' F2 r2 U2 r' F2
+
{{Alg6|wca=r2 F2 U2 l F2 D2 r2 D2 l' F2 r2 U2 r' F2
 
|sign=2R2 F2 U2 2L F2 D2 2R2 D2 2L' F2 2R2 U2 2R' F2
 
|sign=2R2 F2 U2 2L F2 D2 2R2 D2 2L' F2 2R2 U2 2R' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 l F2 D2 r2 D2 r F2 l2 U2 l F2
+
{{Alg6|wca=r2 F2 U2 l F2 D2 r2 D2 r F2 l2 U2 l F2
 
|sign=2R2 F2 U2 2L F2 D2 2R2 D2 2R F2 2L2 U2 2L F2
 
|sign=2R2 F2 U2 2L F2 D2 2R2 D2 2R F2 2L2 U2 2L F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 U2 r U2 r2 F2 r U2 r2 U2 F2 r F2
+
{{Alg6|wca=r2 F2 U2 r U2 r2 F2 r U2 r2 U2 F2 r F2
 
|sign=2R2 F2 U2 2R U2 2R2 F2 2R U2 2R2 U2 F2 2R F2
 
|sign=2R2 F2 U2 2R U2 2R2 F2 2R U2 2R2 U2 F2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r U2 F2 r2 F2 r' F2 U2 r2 U2 r' F2
+
{{Alg6|wca=r2 U2 r U2 F2 r2 F2 r' F2 U2 r2 U2 r' F2
 
|sign=2R2 U2 2R U2 F2 2R2 F2 2R' F2 U2 2R2 U2 2R' F2
 
|sign=2R2 U2 2R U2 F2 2R2 F2 2R' F2 U2 2R2 U2 2R' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r' U2 r2 B2 r' U2 l2 U2 B2 l B2
+
{{Alg6|wca=l2 B2 U2 r' U2 r2 B2 r' U2 l2 U2 B2 l B2
 
|sign=2L2 B2 U2 2R' U2 2R2 B2 2R' U2 2L2 U2 B2 2L B2
 
|sign=2L2 B2 U2 2R' U2 2R2 B2 2R' U2 2L2 U2 B2 2L B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r B2 D2 l2 D2 l B2 r2 U2 r B2
+
{{Alg6|wca=l2 B2 U2 r B2 D2 l2 D2 l B2 r2 U2 r B2
 
|sign=2L2 B2 U2 2R B2 D2 2L2 D2 2L B2 2R2 U2 2R B2
 
|sign=2L2 B2 U2 2R B2 D2 2L2 D2 2L B2 2R2 U2 2R B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 B2 U2 r B2 D2 l2 D2 r' B2 l2 U2 l' B2
+
{{Alg6|wca=l2 B2 U2 r B2 D2 l2 D2 r' B2 l2 U2 l' B2
 
|sign=2L2 B2 U2 2R B2 D2 2L2 D2 2R' B2 2L2 U2 2L' B2
 
|sign=2L2 B2 U2 2R B2 D2 2L2 D2 2R' B2 2L2 U2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 D2 l D2 B2 r2 B2 r' B2 D2 r2 D2 l B2
+
{{Alg6|wca=l2 D2 l D2 B2 r2 B2 r' B2 D2 r2 D2 l B2
 
|sign=2L2 D2 2L D2 B2 2R2 B2 2R' B2 D2 2R2 D2 2L B2
 
|sign=2L2 D2 2L D2 B2 2R2 B2 2R' B2 D2 2R2 D2 2L B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l U2 B2 l2 B2 l' B2 U2 l2 U2 l' B2
+
{{Alg6|wca=l2 U2 l U2 B2 l2 B2 l' B2 U2 l2 U2 l' B2
 
|sign=2L2 U2 2L U2 B2 2L2 B2 2L' B2 U2 2L2 U2 2L' B2
 
|sign=2L2 U2 2L U2 B2 2L2 B2 2L' B2 U2 2L2 U2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 F2 l2 F2 r' F2 D2 l2 D2 l' F2
+
{{Alg6|wca=r2 U2 r' U2 F2 l2 F2 r' F2 D2 l2 D2 l' F2
 
|sign=2R2 U2 2R' U2 F2 2L2 F2 2R' F2 D2 2L2 D2 2L' F2
 
|sign=2R2 U2 2R' U2 F2 2L2 F2 2R' F2 D2 2L2 D2 2L' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 D2 l' D2 l2 B2 r' U2 r2 U2 B2 l' B2
+
{{Alg6|wca=r2 B2 D2 l' D2 l2 B2 r' U2 r2 U2 B2 l' B2
 
|sign=2R2 B2 D2 2L' D2 2L2 B2 2R' U2 2R2 U2 B2 2L' B2
 
|sign=2R2 B2 D2 2L' D2 2L2 B2 2R' U2 2R2 U2 B2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l' U2 B2 r2 B2 l' B2 D2 r2 D2 r' B2
+
{{Alg6|wca=l2 U2 l' U2 B2 r2 B2 l' B2 D2 r2 D2 r' B2
 
|sign=2L2 U2 2L' U2 B2 2R2 B2 2L' B2 D2 2R2 D2 2R' B2
 
|sign=2L2 U2 2L' U2 B2 2R2 B2 2L' B2 D2 2R2 D2 2R' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 r' D2 r2 F2 l' U2 l2 U2 F2 r' F2
+
{{Alg6|wca=l2 F2 D2 r' D2 r2 F2 l' U2 l2 U2 F2 r' F2
 
|sign=2L2 F2 D2 2R' D2 2R2 F2 2L' U2 2L2 U2 F2 2R' F2
 
|sign=2L2 F2 D2 2R' D2 2R2 F2 2L' U2 2L2 U2 F2 2R' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r B2 l2 D2 l D2 B2 r2 U2 F2 r' F2
+
{{Alg6|wca=r2 U2 r B2 l2 D2 l D2 B2 r2 U2 F2 r' F2
 
|sign=2R2 U2 2R B2 2L2 D2 2L D2 B2 2R2 U2 F2 2R' F2
 
|sign=2R2 U2 2R B2 2L2 D2 2L D2 B2 2R2 U2 F2 2R' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l F2 r2 D2 r D2 F2 l2 U2 B2 l' B2
+
{{Alg6|wca=l2 U2 l F2 r2 D2 r D2 F2 l2 U2 B2 l' B2
 
|sign=2L2 U2 2L F2 2R2 D2 2R D2 F2 2L2 U2 B2 2L' B2
 
|sign=2L2 U2 2L F2 2R2 D2 2R D2 F2 2L2 U2 B2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' B2 r2 D2 r' D2 B2 r2 U2 F2 r' F2
+
{{Alg6|wca=r2 U2 l' B2 r2 D2 r' D2 B2 r2 U2 F2 r' F2
 
|sign=2R2 U2 2L' B2 2R2 D2 2R' D2 B2 2R2 U2 F2 2R' F2
 
|sign=2R2 U2 2L' B2 2R2 D2 2R' D2 B2 2R2 U2 F2 2R' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r' F2 l2 D2 l' D2 F2 l2 U2 B2 l' B2
+
{{Alg6|wca=l2 U2 r' F2 l2 D2 l' D2 F2 l2 U2 B2 l' B2
 
|sign=2L2 U2 2R' F2 2L2 D2 2L' D2 F2 2L2 U2 B2 2L' B2
 
|sign=2L2 U2 2R' F2 2L2 D2 2L' D2 F2 2L2 U2 B2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l' F2 D2 l2 D2 r F2 r2 D2 r F2
+
{{Alg6|wca=l2 F2 D2 l' F2 D2 l2 D2 r F2 r2 D2 r F2
 
|sign=2L2 F2 D2 2L' F2 D2 2L2 D2 2R F2 2R2 D2 2R F2
 
|sign=2L2 F2 D2 2L' F2 D2 2L2 D2 2R F2 2R2 D2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 D2 r' B2 D2 r2 D2 l B2 l2 D2 l B2
+
{{Alg6|wca=r2 B2 D2 r' B2 D2 r2 D2 l B2 l2 D2 l B2
 
|sign=2R2 B2 D2 2R' B2 D2 2R2 D2 2L B2 2L2 D2 2L B2
 
|sign=2R2 B2 D2 2R' B2 D2 2R2 D2 2L B2 2L2 D2 2L B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 D2 r D2 r2 B2 l U2 r2 U2 B2 l' B2
+
{{Alg6|wca=r2 B2 D2 r D2 r2 B2 l U2 r2 U2 B2 l' B2
 
|sign=2R2 B2 D2 2R D2 2R2 B2 2L U2 2R2 U2 B2 2L' B2
 
|sign=2R2 B2 D2 2R D2 2R2 B2 2L U2 2R2 U2 B2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l' F2 D2 l2 D2 l' F2 l2 D2 l' F2
+
{{Alg6|wca=l2 F2 D2 l' F2 D2 l2 D2 l' F2 l2 D2 l' F2
 
|sign=2L2 F2 D2 2L' F2 D2 2L2 D2 2L' F2 2L2 D2 2L' F2
 
|sign=2L2 F2 D2 2L' F2 D2 2L2 D2 2L' F2 2L2 D2 2L' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 D2 r' B2 D2 r2 D2 r' B2 r2 D2 r' B2
+
{{Alg6|wca=r2 B2 D2 r' B2 D2 r2 D2 r' B2 r2 D2 r' B2
 
|sign=2R2 B2 D2 2R' B2 D2 2R2 D2 2R' B2 2R2 D2 2R' B2
 
|sign=2R2 B2 D2 2R' B2 D2 2R2 D2 2R' B2 2R2 D2 2R' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 F2 D2 l D2 l2 F2 r U2 l2 U2 F2 r' F2
+
{{Alg6|wca=l2 F2 D2 l D2 l2 F2 r U2 l2 U2 F2 r' F2
 
|sign=2L2 F2 D2 2L D2 2L2 F2 2R U2 2L2 U2 F2 2R' F2
 
|sign=2L2 F2 D2 2L D2 2L2 F2 2R U2 2L2 U2 F2 2R' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l B2 r2 U2 l U2 B2 r2 U2 F2 r F2
+
{{Alg6|wca=r2 U2 l B2 r2 U2 l U2 B2 r2 U2 F2 r F2
 
|sign=2R2 U2 2L B2 2R2 U2 2L U2 B2 2R2 U2 F2 2R F2
 
|sign=2R2 U2 2L B2 2R2 U2 2L U2 B2 2R2 U2 F2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' B2 l2 U2 r' U2 B2 r2 U2 F2 r F2
+
{{Alg6|wca=r2 U2 r' B2 l2 U2 r' U2 B2 r2 U2 F2 r F2
 
|sign=2R2 U2 2R' B2 2L2 U2 2R' U2 B2 2R2 U2 F2 2R F2
 
|sign=2R2 U2 2R' B2 2L2 U2 2R' U2 B2 2R2 U2 F2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 l' F2 r2 U2 l' U2 F2 l2 U2 B2 l B2
+
{{Alg6|wca=l2 U2 l' F2 r2 U2 l' U2 F2 l2 U2 B2 l B2
 
|sign=2L2 U2 2L' F2 2R2 U2 2L' U2 F2 2L2 U2 B2 2L B2
 
|sign=2L2 U2 2L' F2 2R2 U2 2L' U2 F2 2L2 U2 B2 2L B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l2 U2 r F2 l2 U2 r U2 F2 l2 U2 B2 l B2
+
{{Alg6|wca=l2 U2 r F2 l2 U2 r U2 F2 l2 U2 B2 l B2
 
|sign=2L2 U2 2R F2 2L2 U2 2R U2 F2 2L2 U2 B2 2L B2
 
|sign=2L2 U2 2R F2 2L2 U2 2R U2 F2 2L2 U2 B2 2L B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 l' D2 l2 F2 r U2 r2 U2 F2 l F2
+
{{Alg6|wca=r2 F2 D2 l' D2 l2 F2 r U2 r2 U2 F2 l F2
 
|sign=2R2 F2 D2 2L' D2 2L2 F2 2R U2 2R2 U2 F2 2L F2
 
|sign=2R2 F2 D2 2L' D2 2L2 F2 2R U2 2R2 U2 F2 2L F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 r' B2 U2 r2 U2 l' B2 r2 D2 l' F2
+
{{Alg6|wca=r2 F2 D2 r' B2 U2 r2 U2 l' B2 r2 D2 l' F2
 
|sign=2R2 F2 D2 2R' B2 U2 2R2 U2 2L' B2 2R2 D2 2L' F2
 
|sign=2R2 F2 D2 2R' B2 U2 2R2 U2 2L' B2 2R2 D2 2L' F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 F2 D2 r' B2 U2 r2 U2 r B2 l2 D2 r F2
+
{{Alg6|wca=r2 F2 D2 r' B2 U2 r2 U2 r B2 l2 D2 r F2
 
|sign=2R2 F2 D2 2R' B2 U2 2R2 U2 2R B2 2L2 D2 2R F2
 
|sign=2R2 F2 D2 2R' B2 U2 2R2 U2 2R B2 2L2 D2 2R F2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2
+
{{Alg6|wca=r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2
 
|sign=2R2 B2 U2 2R U2 2R2 B2 2R' U2 2R2 U2 B2 2R' B2
 
|sign=2R2 B2 U2 2R U2 2R2 B2 2R' U2 2R2 U2 B2 2R' B2
 
|length=(25,14)|name=|wide=Y|author=Nicholas Ho
 
|length=(25,14)|name=|wide=Y|author=Nicholas Ho
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 U2 l F2 U2 r2 U2 r' F2 r2 U2 l' B2
+
{{Alg6|wca=r2 B2 U2 l F2 U2 r2 U2 r' F2 r2 U2 l' B2
 
|sign=2R2 B2 U2 2L F2 U2 2R2 U2 2R' F2 2R2 U2 2L' B2
 
|sign=2R2 B2 U2 2L F2 U2 2R2 U2 2R' F2 2R2 U2 2L' B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 B2 U2 l F2 U2 r2 U2 l F2 l2 U2 r B2
+
{{Alg6|wca=r2 B2 U2 l F2 U2 r2 U2 l F2 l2 U2 r B2
 
|sign=2R2 B2 U2 2L F2 U2 2R2 U2 2L F2 2L2 U2 2R B2
 
|sign=2R2 B2 U2 2L F2 U2 2R2 U2 2L F2 2L2 U2 2R B2
 
|length=(25,14)|name=|wide=Y|author=|url=
 
|length=(25,14)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x'
+
{{Alg6|wca=Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x'
 
|sign=r2 F2 U2 2R U2 x U2 r2 U2 2R' U2 2L 2R U2 2L' U2 x'
 
|sign=r2 F2 U2 2R U2 x U2 r2 U2 2R' U2 2L 2R U2 2L' U2 x'
 
|length=(25,15)|name=|wide=N|author=Christopher Mowla
 
|length=(25,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw Fw r' Fw' Rw' Dw R' U Rw' Fw r' Fw' Rw U' Rw Dw'
+
{{Alg6|wca=Rw Fw r' Fw' Rw' Dw R' U Rw' Fw r' Fw' Rw U' Rw Dw'
 
|sign=r f 2R' f' r' d R' U r' f 2R' f' r U' r d'
 
|sign=r f 2R' f' r' d R' U r' f 2R' f' r U' r d'
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r
+
{{Alg6|wca=l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r
 
|sign=2L' U2 2L U2 2L U2 2R' U2 2L U2 2L' U2 F2 2L2 F2 2R
 
|sign=2L' U2 2L U2 2L U2 2R' U2 2L U2 2L' U2 F2 2L2 F2 2R
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' F2 D2 r' D2 F' l2 U2 l2 F' l F l2 U2 l2 F'
+
{{Alg6|wca=l' F2 D2 r' D2 F' l2 U2 l2 F' l F l2 U2 l2 F'
 
|sign=2L' F2 D2 2R' D2 F' 2L2 U2 2L2 F' 2L F 2L2 U2 2L2 F'
 
|sign=2L' F2 D2 2R' D2 F' 2L2 U2 2L2 F' 2L F 2L2 U2 2L2 F'
 
|length=(25,16)|name=|wide=N|author=Christopher Mowla
 
|length=(25,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' Uw' r Uw Rw Bw' F' R' r Uw' r Uw r' R F r' Bw
+
{{Alg6|wca=Rw' Uw' r Uw Rw Bw' F' R' r Uw' r Uw r' R F r' Bw
 
|sign=r' u' 2R u r b' F' R' 2R u' 2R u 2R' R F 2R' b
 
|sign=r' u' 2R u r b' F' R' 2R u' 2R u 2R' R F 2R' b
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' Uw' r Uw Rw Bw' R' F' r Uw' r Uw r' F R r' Bw
+
{{Alg6|wca=Rw' Uw' r Uw Rw Bw' R' F' r Uw' r Uw r' F R r' Bw
 
|sign=r' u' 2R u r b' R' F' 2R u' 2R u 2R' F R 2R' b
 
|sign=r' u' 2R u r b' R' F' 2R u' 2R u 2R' F R 2R' b
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' r U2 r U u' r' U r' U' r' u r u' r' U' r' U r' Uw x//Safe
+
{{Alg6|wca=x' r U2 r U u' r' U r' U' r' u r u' r' U' r' U r' Uw x //Safe
|sign=x' 2R U2 2R U 2U' 2R' U 2R' U' 2R' 2U 2R 2U' 2R' U' 2R' U 2R' u x//Safe
+
|sign=x' 2R U2 2R U 2U' 2R' U 2R' U' 2R' 2U 2R 2U' 2R' U' 2R' U 2R' u x //Safe
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=x' l' Uw Rw' Uw' l Uw Fw Uw B' l2 B r' B' l2 B Uw' Fw' Rw Uw' x
+
{{Alg6|wca=x' l' Uw Rw' Uw' l Uw Fw Uw B' l2 B r' B' l2 B Uw' Fw' Rw Uw' x
 
|sign=x' 2L' u r' u' 2L u f u B' 2L2 B 2R' B' 2L2 B u' f' r u' x
 
|sign=x' 2L' u r' u' 2L u f u B' 2L2 B 2R' B' 2L2 B u' f' r u' x
 
|length=(21,19)|name=|wide=N|author=Christopher Mowla
 
|length=(21,19)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=x l U2 l' U2 l U2 l2 U' l' U l U2 l U2 l2 U2 l U l U l U2 x'
+
{{Alg6|wca=x l U2 l' U2 l U2 l2 U' l' U l U2 l U2 l2 U2 l U l U l U2 x'
 
|sign=x 2L U2 2L' U2 2L U2 2L2 U' 2L' U 2L U2 2L U2 2L2 U2 2L U 2L U 2L U2 x'
 
|sign=x 2L U2 2L' U2 2L U2 2L2 U' 2L' U 2L U2 2L U2 2L2 U2 2L U 2L U 2L U2 x'
 
|length=(31,22)|name=|wide=N|author=Lucas Garron
 
|length=(31,22)|name=|wide=N|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
}}
 
}}
{{Alg5|wca=x l U2 l' U2 l U2 l2 U l' U' l U2 l U2 l2 U2 l U' l U' l U2 x'
+
{{Alg6|wca=x l U2 l' U2 l U2 l2 U l' U' l U2 l U2 l2 U2 l U' l U' l U2 x'
 
|sign=x 2L U2 2L' U2 2L U2 2L2 U 2L' U' 2L U2 2L U2 2L2 U2 2L U' 2L U' 2L U2 x'
 
|sign=x 2L U2 2L' U2 2L U2 2L2 U 2L' U' 2L U2 2L U2 2L2 U2 2L U' 2L U' 2L U2 x'
 
|length=(31,22)|name=|wide=N|author=Lucas Garron
 
|length=(31,22)|name=|wide=N|author=Lucas Garron
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
|url=https://www.speedsolving.com/forum/threads/acube4x4-question.3498/#post-299278
 
}}
 
}}
{{Alg5|wca=Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U'
+
{{Alg6|wca=Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U'
 
|sign=r U r' U' r U2 r' U2 r' U' r U' r U r2 U' r2 U2 r U2 r' U2 r U2 r U'
 
|sign=r U r' U' r U2 r' U2 r' U' r U' r U r2 U' r2 U2 r U2 r' U2 r U2 r U'
 
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
 
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
 
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
 
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
 
}}
 
}}
{{Alg5|wca=Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U
+
{{Alg6|wca=Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U
 
|sign=r U r' U' r U2 r' U2 r' U' r U' r U' r2 U2 r2 U' r U2 r' U2 r U2 r U
 
|sign=r U r' U' r U2 r' U2 r' U' r U' r U' r2 U2 r2 U' r U2 r' U2 r U2 r U
 
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
 
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
 
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
 
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
 
}}
 
}}
 
+
{{br|b=1}}
==In adjacent dedges==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">In adjacent dedges</span>==
===Close unoriented===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Close unoriented</span>===
 
[[Image:Adj.case1.png|110px|]]
 
[[Image:Adj.case1.png|110px|]]
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Symmetrical algorithms</b></span>
<b>Symmetrical algorithms</b>
+
{{Alg6|wca=l2' U Lw U2 r' U2 Rw' U2 x U' r' U x' U2 x U' M' l'
{{Alg5|wca=l2' U Lw U2 r' U2 Rw' U2 x U' r' U x' U2 x U' M' l'
 
 
|sign=2L2' U l U2 2R' U2 r' U2 x U' 2R' U x' U2 x U' m' 2L'
 
|sign=2L2' U l U2 2R' U2 r' U2 x U' 2R' U x' U2 x U' m' 2L'
 
|length=(20,15)|name=|wide=N|author=Christopher Mowla
 
|length=(20,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
}}
 
}}
{{Alg5|wca=x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x
+
{{Alg6|wca=x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x
 
|sign=x' 2L2 F U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' F' 2L2 x
 
|sign=x' 2L2 F U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' F' 2L2 x
 
|length=(23,15)|name=|wide=N|author=reThinking the Cube
 
|length=(23,15)|name=|wide=N|author=reThinking the Cube
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 F' L F' r F L' F l' U2 l U2 r2
+
{{Alg6|wca=r U2 r U2 F' L F' r F L' F l' U2 l U2 r2
 
|sign=2R U2 2R U2 F' L F' 2R F L' F 2L' U2 2L U2 2R2
 
|sign=2R U2 2R U2 F' L F' 2R F L' F 2L' U2 2L U2 2R2
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' l2 F U2 l U2 r' U2 r U2 3Rw U2 r U2 Rw' F' l2 x
+
{{Alg6|wca=x' l2 F U2 l U2 r' U2 r U2 3Rw U2 r U2 Rw' F' l2 x
 
|sign=x' 2L2 F U2 2L U2 2R' U2 2R U2 3r U2 2R U2 r' F' 2L2 x
 
|sign=x' 2L2 F U2 2L U2 2R' U2 2R U2 3r U2 2R U2 r' F' 2L2 x
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Bw l' Uw' r' Uw Lw Uw' Rw' r' Fw' r' Fw r' R Uw L' Bw'
+
{{Alg6|wca=Bw l' Uw' r' Uw Lw Uw' Rw' r' Fw' r' Fw r' R Uw L' Bw'
 
|sign=b 2L' u' 2R' u l u' r' 2R' f' 2R' f 2R' R u L' b'
 
|sign=b 2L' u' 2R' u l u' r' 2R' f' 2R' f 2R' R u L' b'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2
+
{{Alg6|wca=r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2
 
|sign=2R2 U2 2L U2 2R' U2 2R U2 F' L F' 2R F L' F 2L' 2R2
 
|sign=2R2 U2 2L U2 2R' U2 2R U2 F' L F' 2R F L' F 2L' 2R2
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2
+
{{Alg6|wca=l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2
 
|sign=2L2 U m U2 2L U2 2R' U2 2R U2 m' U2 2R U2 2L' U' 2L2
 
|sign=2L2 U m U2 2L U2 2R' U2 2R U2 m' U2 2R U2 2L' U' 2L2
 
|length=(25,17)|name=|wide=N|author=Christopher Mowla
 
|length=(25,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z Uw' Lw M' Bw l Bw' Rw' Bw Lw l Uw l Uw' L' l Bw' M x Uw z'
+
{{Alg6|wca=z Uw' Lw M' Bw l Bw' Rw' Bw Lw l Uw l Uw' L' l Bw' M x Uw z'
 
|sign=z u' l m' b 2L b' r' b l 2L u 2L u' L' 2L b' m x u z'
 
|sign=z u' l m' b 2L b' r' b l 2L u 2L u' L' 2L b' m x u z'
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' Lw u' Bw R r' Bw' r' Bw r R' Dw r Dw' Bw' Dw r' U' y Lw' y
+
{{Alg6|wca=y' Lw u' Bw R r' Bw' r' Bw r R' Dw r Dw' Bw' Dw r' U' y Lw' y
 
|sign=y' l 2U' b R 2R' b' 2R' b 2R R' d 2R d' b' d 2R' U' y l' y
 
|sign=y' l 2U' b R 2R' b' 2R' b 2R R' d 2R d' b' d 2R' U' y l' y
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y Fw' M Lw Fw r Fw' Lw' Fw Rw r Uw r Uw' r R' Fw' M' Fw y'
+
{{Alg6|wca=y Fw' M Lw Fw r Fw' Lw' Fw Rw r Uw r Uw' r R' Fw' M' Fw y'
 
|sign=y f' m l f 2R f' l' f r 2R u 2R u' 2R R' f' m' f y'
 
|sign=y f' m l f 2R f' l' f r 2R u 2R u' 2R R' f' m' f y'
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|length=(18,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l U l U l' U' l' U' l D f2 l' f2 l U2 D' l U' l' U' l2//Safe
+
{{Alg6|wca=l U l U l' U' l' U' l D f2 l' f2 l U2 D' l U' l' U' l2 //Safe
|sign=2L U 2L U 2L' U' 2L' U' 2L D 2F2 2L' 2F2 2L U2 D' 2L U' 2L' U' 2L2//Safe
+
|sign=2L U 2L U 2L' U' 2L' U' 2L D 2F2 2L' 2F2 2L U2 D' 2L U' 2L' U' 2L2 //Safe
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
}}
 
}}
{{Alg5|wca=(L U2)(r' F U2 F')4 r' (U2 L')
+
{{Alg6|wca=(L U2)(r' F U2 F')4 r' (U2 L')
|sign=(L U2)(2R' F U2 F')4 2R' (U2 L')
+
|sign=(L U2) (2R' F U2 F')4 2R' (U2 L')
 
|length=(27,21)|name=|wide=N|author=Floyd Newberry
 
|length=(27,21)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=(L U2)(r F U2 F')4 r (U2 L')
+
{{Alg6|wca=(L U2)(r F U2 F')4 r (U2 L')
|sign=(L U2)(2R F U2 F')4 2R (U2 L')
+
|sign=(L U2) (2R F U2 F')4 2R (U2 L')
 
|length=(27,21)|name=|wide=N|author=Floyd Newberry
 
|length=(27,21)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=x' l' Rw' U2 Rw U' L' U' r' U L U Rw' U2 Rw U' L' U' r2 U L U l x
+
{{Alg6|wca=x' l' Rw' U2 Rw U' L' U' r' U L U Rw' U2 Rw U' L' U' r2 U L U l x
 
|sign=x' 2L' r' U2 r U' L' U' 2R' U L U r' U2 r U' L' U' 2R2 U L U 2L x
 
|sign=x' 2L' r' U2 r U' L' U' 2R' U L U r' U2 r U' L' U' 2R2 U L U 2L x
 
|length=(25,22)|name=|wide=N|author=Christopher Mowla
 
|length=(25,22)|name=|wide=N|author=Christopher Mowla
Line 7,915: Line 8,197:
 
}}
 
}}
  
<b>Non-symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Non-symmetrical algorithms</b></span>
{{Alg5|wca=y' r' Uw r U2 r U u' r' U r' U' r' u r u' r' U' r' U y//Safe
+
{{Alg6|wca=y' r' Uw r U2 r U u' r' U r' U' r' u r u' r' U' r' U y //Safe
|sign=y' 2R' u 2R U2 2R U 2U' 2R' U 2R' U' 2R' 2U 2R 2U' 2R' U' 2R' U y//Safe
+
|sign=y' 2R' u 2R U2 2R U 2U' 2R' U 2R' U' 2R' 2U 2R 2U' 2R' U' 2R' U y //Safe
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=y' r' u' U r U2 r Uw r' U r' U' r' u' r u r' U' r' U y//Safe
+
{{Alg6|wca=y' r' u' U r U2 r Uw r' U r' U' r' u' r u r' U' r' U y //Safe
|sign=y' 2R' 2U' U 2R U2 2R u 2R' U 2R' U' 2R' 2U' 2R 2U 2R' U' 2R' U y//Safe
+
|sign=y' 2R' 2U' U 2R U2 2R u 2R' U 2R' U' 2R' 2U' 2R 2U 2R' U' 2R' U y //Safe
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=y' r' U' r' u r u' r' U' r' U r' Uw r U2 r U u' r' U y//Safe
+
{{Alg6|wca=y' r' U' r' u r u' r' U' r' U r' Uw r U2 r U u' r' U y //Safe
|sign=y' 2R' U' 2R' 2U 2R 2U' 2R' U' 2R' U 2R' u 2R U2 2R U 2U' 2R' U y//Safe
+
|sign=y' 2R' U' 2R' 2U 2R 2U' 2R' U' 2R' U 2R' u 2R U2 2R U 2U' 2R' U y //Safe
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=y' r' U' r' u' r u r' U' r' U r' u' U r U2 r Uw r' U y//Safe
+
{{Alg6|wca=y' r' U' r' u' r u r' U' r' U r' u' U r U2 r Uw r' U y //Safe
|sign=y' 2R' U' 2R' 2U' 2R 2U 2R' U' 2R' U 2R' 2U' U 2R U2 2R u 2R' U y//Safe
+
|sign=y' 2R' U' 2R' 2U' 2R 2U 2R' U' 2R' U 2R' 2U' U 2R U2 2R u 2R' U y //Safe
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|length=(20,19)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=l Fw' Lw Dw l' Uw2 U L2 u' L' Rw' Uw' l Uw L Rw u L2 u Bw' Uw x
+
{{Alg6|wca=l Fw' Lw Dw l' Uw2 U L2 u' L' Rw' Uw' l Uw L Rw u L2 u Bw' Uw x
 
|sign=2L f' l d 2L' u2 U L2 2U' L' r' u' 2L u L r 2U L2 2U b' u x
 
|sign=2L f' l d 2L' u2 U L2 2U' L' r' u' 2L u L r 2U L2 2U b' u x
 
|length=(23,21)|name=|wide=N|author=Christopher Mowla
 
|length=(23,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l' Fw Rw Fw' Lw L B2 L B l Uw' l' Uw l' B' L' B2 L2 Fw Rw' Fw'
+
{{Alg6|wca=l' Fw Rw Fw' Lw L B2 L B l Uw' l' Uw l' B' L' B2 L2 Fw Rw' Fw'
 
|sign=2L' f r f' l L B2 L B 2L u' 2L' u 2L' B' L' B2 L2 f r' f'
 
|sign=2L' f r f' l L B2 L B 2L u' 2L' u 2L' B' L' B2 L2 f r' f'
 
|length=(24,21)|name=|wide=N|author=Christopher Mowla
 
|length=(24,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R2 U r' U' R2 U Fw' L' Fw2 r2 Uw' z
+
{{Alg6|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R2 U r' U' R2 U Fw' L' Fw2 r2 Uw' z
 
|sign=z' f' u 2R' u' f u 2R' f2 L f U' R2 U 2R' U' R2 U f' L' f2 2R2 u' z
 
|sign=z' f' u 2R' u' f u 2R' f2 L f U' R2 U 2R' U' R2 U f' L' f2 2R2 u' z
 
|length=(27,22)|name=|wide=N|author=Christopher Mowla
 
|length=(27,22)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=l' F2 l F2 U' Rw U2 l U2 Rw' B' M U' Lw2 F2 r2 F2 Lw2 U M' B U
+
{{Alg6|wca=l' F2 l F2 U' Rw U2 l U2 Rw' B' M U' Lw2 F2 r2 F2 Lw2 U M' B U
 
|sign=2L' F2 2L F2 U' r U2 2L U2 r' B' m U' l2 F2 2R2 F2 l2 U m' B U
 
|sign=2L' F2 2L F2 U' r U2 2L U2 r' B' m U' l2 F2 2R2 F2 l2 U m' B U
 
|length=(31,22)|name=|wide=N|author=Christopher Mowla
 
|length=(31,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Far unoriented===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Far unoriented</span>===
 
[[Image:Adjcase2.png|110px|]]
 
[[Image:Adjcase2.png|110px|]]
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Symmetrical algorithms</b></span>
<b>Symmetrical algorithms</b>
+
{{Alg6|wca=l2' U' Lw U2 r' U2 Rw' U2 x U r' U' x' U2 x U M' l'
{{Alg5|wca=l2' U' Lw U2 r' U2 Rw' U2 x U r' U' x' U2 x U M' l'
 
 
|sign=2L2' U' l U2 2R' U2 r' U2 x U 2R' U' x' U2 x U m' 2L'
 
|sign=2L2' U' l U2 2R' U2 r' U2 x U 2R' U' x' U2 x U m' 2L'
 
|length=(20,15)|name=|wide=N|author=Christopher Mowla
 
|length=(20,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
}}
 
}}
{{Alg5|wca=(x Rw2 F') U2 l U2 r' U2 r U2 F2 r F2 l' (F Rw2 x')
+
{{Alg6|wca=(x Rw2 F') U2 l U2 r' U2 r U2 F2 r F2 l' (F Rw2 x')
 
|sign=(x r2 F') U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' (F r2 x')
 
|sign=(x r2 F') U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' (F r2 x')
 
|length=(23,15)|name=|wide=N|author=Christopher Mowla
 
|length=(23,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=f' R' r u Rw' Dw' Rw u2 Fw u Fw' u Rw' Dw R2 f
+
{{Alg6|wca=f' R' r u Rw' Dw' Rw u2 Fw u Fw' u Rw' Dw R2 f
 
|sign=2F' R' 2R 2U r' d' r 2U2 f 2U f' 2U r' d R2 2F
 
|sign=2F' R' 2R 2U r' d' r 2U2 f 2U f' 2U r' d R2 2F
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r F f' u' Fw Dw Fw' u2 Rw' u' Rw u' Fw Dw' F2 r'
+
{{Alg6|wca=r F f' u' Fw Dw Fw' u2 Rw' u' Rw u' Fw Dw' F2 r'
 
|sign=2R F 2F' 2U' f d f' 2U2 r' 2U' r 2U' f d' F2 2R'
 
|sign=2R F 2F' 2U' f d f' 2U2 r' 2U' r 2U' f d' F2 2R'
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(f' R') Lw' u Lw Uw2 Rw' U Lw' u Lw Uw' Rw Uw2 (R f)
+
{{Alg6|wca=(f' R') Lw' u Lw Uw2 Rw' U Lw' u Lw Uw' Rw Uw2 (R f)
 
|sign=(2F' R') l' 2U l u2 r' U l' 2U l u' r u2 (R 2F)
 
|sign=(2F' R') l' 2U l u2 r' U l' 2U l u' r u2 (R 2F)
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(f' R') Uw2 Rw' u Rw Uw2 Lw' U Rw' u Rw Uw' Lw (R f)
+
{{Alg6|wca=(f' R') Uw2 Rw' u Rw Uw2 Lw' U Rw' u Rw Uw' Lw (R f)
 
|sign=(2F' R') u2 r' 2U r u2 l' U r' 2U r u' l (R 2F)
 
|sign=(2F' R') u2 r' 2U r u2 l' U r' 2U r u' l (R 2F)
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(f' R') Uw2 Rw' Uw Lw' u' Lw U' Rw Uw2 Lw' u' Lw (R f)
+
{{Alg6|wca=(f' R') Uw2 Rw' Uw Lw' u' Lw U' Rw Uw2 Lw' u' Lw (R f)
 
|sign=(2F' R') u2 r' u l' 2U' l U' r u2 l' 2U' l (R 2F)
 
|sign=(2F' R') u2 r' u l' 2U' l U' r u2 l' 2U' l (R 2F)
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(f' R') Lw' Uw Rw' u' Rw U' Lw Uw2 Rw' u' Rw Uw2 (R f)
+
{{Alg6|wca=(f' R') Lw' Uw Rw' u' Rw U' Lw Uw2 Rw' u' Rw Uw2 (R f)
 
|sign=(2F' R') l' u r' 2U' r U' l u2 r' 2U' r u2 (R 2F)
 
|sign=(2F' R') l' u r' 2U' r U' l u2 r' 2U' r u2 (R 2F)
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|length=(18,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 r U2 F R' F r F' R F' l' U2 l U2 r2
+
{{Alg6|wca=r U2 r U2 F R' F r F' R F' l' U2 l U2 r2
 
|sign=2R U2 2R U2 F R' F 2R F' R F' 2L' U2 2L U2 2R2
 
|sign=2R U2 2R U2 F R' F 2R F' R F' 2L' U2 2L U2 2R2
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x Rw2 F') U2 l U2 r' U2 r U2 3Rw U2 r U2 Rw' (F Rw2 x')
+
{{Alg6|wca=(x Rw2 F') U2 l U2 r' U2 r U2 3Rw U2 r U2 Rw' (F Rw2 x')
 
|sign=(x r2 F') U2 2L U2 2R' U2 2R U2 3r U2 2R U2 r' (F r2 x')
 
|sign=(x r2 F') U2 2L U2 2R' U2 2R U2 3r U2 2R U2 r' (F r2 x')
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|length=(24,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r d' Fw Rw Bw' l Bw Rw' F Uw Bw r Bw' Uw' F' Fw' r'
+
{{Alg6|wca=r d' Fw Rw Bw' l Bw Rw' F Uw Bw r Bw' Uw' F' Fw' r'
 
|sign=2R 2D' f r b' 2L b r' F u b 2R b' u' F' f' 2R'
 
|sign=2R 2D' f r b' 2L b r' F u b 2R b' u' F' f' 2R'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r d Fw F Uw Fw d' Fw' Uw' F' Rw Bw' l' Bw Rw' Fw' r'
+
{{Alg6|wca=r d Fw F Uw Fw d' Fw' Uw' F' Rw Bw' l' Bw Rw' Fw' r'
 
|sign=2R 2D f F u f 2D' f' u' F' r b' 2L' b r' f' 2R'
 
|sign=2R 2D f F u f 2D' f' u' F' r b' 2L' b r' f' 2R'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=f' d Lw' Uw' Lw d' Lw' Uw R' Fw' Uw' f' Uw Fw Lw R f
+
{{Alg6|wca=f' d Lw' Uw' Lw d' Lw' Uw R' Fw' Uw' f' Uw Fw Lw R f
 
|sign=2F' 2D l' u' l 2D' l' u R' f' u' 2F' u f l R 2F
 
|sign=2F' 2D l' u' l 2D' l' u R' f' u' 2F' u f l R 2F
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=f' Lw' Uw' Lw d' Lw' Uw R' Fw' Uw' f' Uw Fw Lw R d f
+
{{Alg6|wca=f' Lw' Uw' Lw d' Lw' Uw R' Fw' Uw' f' Uw Fw Lw R d f
 
|sign=2F' l' u' l 2D' l' u R' f' u' 2F' u f l R 2D 2F
 
|sign=2F' l' u' l 2D' l' u R' f' u' 2F' u f l R 2D 2F
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(f' R') Lw' Uw' Lw d' Lw' Uw Fw' Uw' f' Uw Fw Lw d (R f)
+
{{Alg6|wca=(f' R') Lw' Uw' Lw d' Lw' Uw Fw' Uw' f' Uw Fw Lw d (R f)
 
|sign=(2F' R') l' u' l 2D' l' u f' u' 2F' u f l 2D (R 2F)
 
|sign=(2F' R') l' u' l 2D' l' u f' u' 2F' u f l 2D (R 2F)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(f' R') d Lw' Uw' Lw d' Lw' Uw Fw' Uw' f' Uw Fw Lw (R f)
+
{{Alg6|wca=(f' R') d Lw' Uw' Lw d' Lw' Uw Fw' Uw' f' Uw Fw Lw (R f)
 
|sign=(2F' R') 2D l' u' l 2D' l' u f' u' 2F' u f l (R 2F)
 
|sign=(2F' R') 2D l' u' l 2D' l' u f' u' 2F' u f l (R 2F)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw r) Bw' Dw f' Dw' l' Uw l Bw d Bw' Uw' Bw d' (r' Rw')
+
{{Alg6|wca=(Rw r) Bw' Dw f' Dw' l' Uw l Bw d Bw' Uw' Bw d' (r' Rw')
 
|sign=(r 2R) b' d 2F' d' 2L' u 2L b 2D b' u' b 2D' (2R' r')
 
|sign=(r 2R) b' d 2F' d' 2L' u 2L b 2D b' u' b 2D' (2R' r')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw r) Bw' Dw f' Dw' Bw Dw Bw' Uw' f' Uw Bw f Dw' (r' Rw')
+
{{Alg6|wca=(Rw r) Bw' Dw f' Dw' Bw Dw Bw' Uw' f' Uw Bw f Dw' (r' Rw')
 
|sign=(r 2R) b' d 2F' d' b d b' u' 2F' u b 2F d' (2R' r')
 
|sign=(r 2R) b' d 2F' d' b d b' u' 2F' u b 2F d' (2R' r')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Lw r) Uw' Fw l' Fw' Uw Fw Lw' Uw' l' Uw Lw l Fw' (Lw' r')
+
{{Alg6|wca=(Lw r) Uw' Fw l' Fw' Uw Fw Lw' Uw' l' Uw Lw l Fw' (Lw' r')
 
|sign=(l 2R) u' f 2L' f' u f l' u' 2L' u l 2L f' (l' 2R')
 
|sign=(l 2R) u' f 2L' f' u f l' u' 2L' u l 2L f' (l' 2R')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw r z) l Fw' Uw Fw l' Fw' l' Uw' l Uw l Uw' Fw (z' Rw' r')
+
{{Alg6|wca=(Rw r z) l Fw' Uw Fw l' Fw' l' Uw' l Uw l Uw' Fw (z' Rw' r')
 
|sign=(r 2R z) 2L f' u f 2L' f' 2L' u' 2L u 2L u' f (z' r' 2R')
 
|sign=(r 2R z) 2L f' u f 2L' f' 2L' u' 2L u 2L u' f (z' r' 2R')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Bw' f') Uw Lw' d Lw b Rw' b' Uw' l' Uw Rw Uw' l (f Bw)
+
{{Alg6|wca=(Bw' f') Uw Lw' d Lw b Rw' b' Uw' l' Uw Rw Uw' l (f Bw)
 
|sign=(b' 2F') u l' 2D l 2B r' 2B' u' 2L' u r u' 2L (2F b)
 
|sign=(b' 2F') u l' 2D l 2B r' 2B' u' 2L' u r u' 2L (2F b)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Bw' f') Uw Lw' d Lw Uw' Lw' Uw Rw d Rw' d' Uw' Lw (f Bw)
+
{{Alg6|wca=(Bw' f') Uw Lw' d Lw Uw' Lw' Uw Rw d Rw' d' Uw' Lw (f Bw)
 
|sign=(b' 2F') u l' 2D l u' l' u r 2D r' 2D' u' l (2F b)
 
|sign=(b' 2F') u l' 2D l u' l' u r 2D r' 2D' u' l (2F b)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x' r E') r' Uw Lw Uw' r Uw Lw' Bw Uw l Uw' Bw' Uw' (E r' x)
+
{{Alg6|wca=(x' r E') r' Uw Lw Uw' r Uw Lw' Bw Uw l Uw' Bw' Uw' (E r' x)
 
|sign=(x' 2R e') 2R' u l u' 2R u l' b u 2L u' b' u' (e 2R' x)
 
|sign=(x' 2R e') 2R' u l u' 2R u l' b u 2L u' b' u' (e 2R' x)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x' r E') r Uw Bw Uw l' Uw' Bw' Lw Uw' r' Uw Lw' Uw' (E r' x)
+
{{Alg6|wca=(x' r E') r Uw Bw Uw l' Uw' Bw' Lw Uw' r' Uw Lw' Uw' (E r' x)
 
|sign=(x' 2R e') 2R u b u 2L' u' b' l u' 2R' u l' u' (e 2R' x)
 
|sign=(x' 2R e') 2R u b u 2L' u' b' l u' 2R' u l' u' (e 2R' x)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw
+
{{Alg6|wca=Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw
 
|sign=r' 2L' x' U2 2L U2 2R' U2 2R U2 x U R U 2R U' R' U' r
 
|sign=r' 2L' x' U2 2L U2 2R' U2 2R U2 x U R U 2R U' R' U' r
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-588960
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-588960
 
}}
 
}}
{{Alg5|wca=r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2
+
{{Alg6|wca=r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2
 
|sign=2R2 U2 2L U2 2R' U2 2R U2 F R' F 2R F' R F' 2L' 2R2
 
|sign=2R2 U2 2L U2 2R' U2 2R U2 F R' F 2R F' R F' 2L' 2R2
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|length=(23,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=R (l' B U2 B')4 l' R'
+
{{Alg6|wca=R (l' B U2 B')4 l' R'
 
|sign=R (2L' B U2 B')4 2L' R'
 
|sign=R (2L' B U2 B')4 2L' R'
 
|length=(23,19)|name=|wide=N|author=Floyd Newberry
 
|length=(23,19)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=R (l B U2 B')4 l R'
+
{{Alg6|wca=R (l B U2 B')4 l R'
 
|sign=R (2L B U2 B')4 2L R'
 
|sign=R (2L B U2 B')4 2L R'
 
|length=(23,19)|name=|wide=N|author=Floyd Newberry
 
|length=(23,19)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=Rw' U R U r2 U' R' U' Rw' U2 Rw U R U r U' R' U' Rw' U2 Rw2
+
{{Alg6|wca=Rw' U R U r2 U' R' U' Rw' U2 Rw U R U r U' R' U' Rw' U2 Rw2
 
|sign=r' U R U 2R2 U' R' U' r' U2 r U R U 2R U' R' U' r' U2 r2
 
|sign=r' U R U 2R2 U' R' U' r' U2 r U R U 2R U' R' U' r' U2 r2
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l U' l U' l' U l' U l D' b2 l' b2 l U2 D l U l' U l2//Safe
+
{{Alg6|wca=l U' l U' l' U l' U l D' b2 l' b2 l U2 D l U l' U l2 //Safe
|sign=2L U' 2L U' 2L' U 2L' U 2L D' 2B2 2L' 2B2 2L U2 D 2L U 2L' U 2L2//Safe
+
|sign=2L U' 2L U' 2L' U 2L' U 2L D' 2B2 2L' 2B2 2L U2 D 2L U 2L' U 2L2 //Safe
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
}}
 
}}
{{Alg5|wca=Rw r U' R' U r' U' R U2 R' U r U2 r U2 r U2 r2 U R U' Rw'
+
{{Alg6|wca=Rw r U' R' U r' U' R U2 R' U r U2 r U2 r U2 r2 U R U' Rw'
 
|sign=r 2R U' R' U 2R' U' R U2 R' U 2R U2 2R U2 2R U2 2R2 U R U' r'
 
|sign=r 2R U' R' U 2R' U' R U2 R' U 2R U2 2R U2 2R U2 2R2 U R U' r'
 
|length=(27,22)|name=|wide=N|author=Christopher Mowla
 
|length=(27,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 R U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw' U2 Rw' R'
+
{{Alg6|wca=Rw2 R U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw' U2 Rw' R'
 
|sign=r2 R U2 r U 2R U' r' U2 r' U2 r U2 r U 2R2 U' r' U2 r' U2 r' R'
 
|sign=r2 R U2 r U 2R U' r' U2 r' U2 r U2 r U 2R2 U' r' U2 r' U2 r' R'
 
|length=(30,23)|name=|wide=N|author=Christopher Mowla
 
|length=(30,23)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
<b>Non-symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Non-symmetrical algorithms</b></span>
{{Alg5|wca=x' U2 l' U2 l U2 r' U2 r B2 r' F D2 F' l' F D2 F' r B2 x
+
{{Alg6|wca=x' U2 l' U2 l U2 r' U2 r B2 r' F D2 F' l' F D2 F' r B2 x
 
|sign=x' U2 2L' U2 2L U2 2R' U2 2R B2 2R' F D2 F' 2L' F D2 F' 2R B2 x
 
|sign=x' U2 2L' U2 2L U2 2R' U2 2R B2 2R' F D2 F' 2L' F D2 F' 2R B2 x
 
|length=(27,19)|name=|wide=N|author=Christopher Mowla
 
|length=(27,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw2 U L U' Fw r' Fw' U L' U' Fw2 r2 Uw' z
+
{{Alg6|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw2 U L U' Fw r' Fw' U L' U' Fw2 r2 Uw' z
 
|sign=z' f' u 2R' u' f u 2R' f2 U L U' f 2R' f' U L' U' f2 2R2 u' z
 
|sign=z' f' u 2R' u' f u 2R' f2 U L U' f 2R' f' U L' U' f2 2R2 u' z
 
|length=(23,20)|name=|wide=N|author=Christopher Mowla
 
|length=(23,20)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=Lw Uw' l Uw Rw' B D' d B Fw Dw b Dw' Fw' B' D d' B' Uw' l' Uw x
+
{{Alg6|wca=Lw Uw' l Uw Rw' B D' d B Fw Dw b Dw' Fw' B' D d' B' Uw' l' Uw x
 
|sign=l u' 2L u r' B D' 2D B f d 2B d' f' B' D 2D' B' u' 2L' u x
 
|sign=l u' 2L u r' B D' 2D B f d 2B d' f' B' D 2D' B' u' 2L' u x
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|length=(21,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R U r' U' R' U Fw' L' Fw2 r2 Uw' z
+
{{Alg6|wca=z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R U r' U' R' U Fw' L' Fw2 r2 Uw' z
 
|sign=z' f' u 2R' u' f u 2R' f2 L f U' R U 2R' U' R' U f' L' f2 2R2 u' z
 
|sign=z' f' u 2R' u' f u 2R' f2 L f U' R U 2R' U' R' U f' L' f2 2R2 u' z
 
|length=(25,22)|name=|wide=N|author=Christopher Mowla
 
|length=(25,22)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
 
+
{{br|b=1}}
===Oriented===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Oriented</span>===
 
[[Image:Adjcase3.png|110px|]]
 
[[Image:Adjcase3.png|110px|]]
 
*Note:  The mirror case can also arise as well.  One can simply apply the mirror image of this case's algorithms to get algorithms for its mirror case.
 
*Note:  The mirror case can also arise as well.  One can simply apply the mirror image of this case's algorithms to get algorithms for its mirror case.
 +
{{br|b=1}}
  
 
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Symmetrical algorithms</b></span>
<b>Symmetrical algorithms</b>
+
{{Alg6|wca=Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2
{{Alg5|wca=Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2
 
 
|sign=r2 u' b 2R' b' u b r' u' 2R' u r 2R b' r2
 
|sign=r2 u' b 2R' b' u b r' u' 2R' u r 2R b' r2
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' Fw2) l Uw' Bw Uw l' Uw' l' Bw' l Bw l Bw' Uw (Fw2 y)
+
{{Alg6|wca=(y' Fw2) l Uw' Bw Uw l' Uw' l' Bw' l Bw l Bw' Uw (Fw2 y)
 
|sign=(y' f2) 2L u' b u 2L' u' 2L' b' 2L b 2L b' u (f2 y)
 
|sign=(y' f2) 2L u' b u 2L' u' 2L' b' 2L b 2L b' u (f2 y)
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' z' Fw2) Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Dw' (Fw2 z y)
+
{{Alg6|wca=(y' z' Fw2) Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Dw' (Fw2 z y)
 
|sign=(y' z' f2) r' d 2L' d' r d l' b' 2L' b l 2L d' (f2 z y)
 
|sign=(y' z' f2) r' d 2L' d' r d l' b' 2L' b l 2L d' (f2 z y)
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-650792
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-650792
 
}}
 
}}
{{Alg5|wca=Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2
+
{{Alg6|wca=Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2
 
|sign=r2 2F u' b d 2R' d' 2R' b' 2R b 2R b' u r2
 
|sign=r2 2F u' b d 2R' d' 2R' b' 2R b 2R b' u r2
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|length=(17,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-650792
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-650792
 
}}
 
}}
{{Alg5|wca=(y' z' Fw' l') Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 (l Fw z y)
+
{{Alg6|wca=(y' z' Fw' l') Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 (l Fw z y)
 
|sign=(y' z' f' 2L') u' b2 u' 2R u b2 u2 2R u 2R' u2 (2L f z y)
 
|sign=(y' z' f' 2L') u' b2 u' 2R u b2 u2 2R u 2R' u2 (2L f z y)
 
|length=(19,15)|name=1st 15 Mover
 
|length=(19,15)|name=1st 15 Mover
Line 8,176: Line 8,458:
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-641481
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-641481
 
}}
 
}}
{{Alg5|wca=Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw'
+
{{Alg6|wca=Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw'
 
|sign=u r' u' 2R' u r b' r' 2R' u' 2R' u R 2R' b u'
 
|sign=u r' u' 2R' u r b' r' 2R' u' 2R' u R 2R' b u'
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' x' Uw') r' Uw Rw Uw' l Uw Rw' Fw Uw r Uw' Fw' Uw' M' (Uw x y)
+
{{Alg6|wca=(y' x' Uw') r' Uw Rw Uw' l Uw Rw' Fw Uw r Uw' Fw' Uw' M' (Uw x y)
 
|sign=(y' x' u') 2R' u r u' 2L u r' f u 2R u' f' u' m' (u x y)
 
|sign=(y' x' u') 2R' u r u' 2L u r' f u 2R u' f' u' m' (u x y)
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|length=(16,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' Bw' R Dw r' Dw' Rw' Bw Rw' R' Dw r' Dw' Rw2 Fw' u Fw y
+
{{Alg6|wca=y' Bw' R Dw r' Dw' Rw' Bw Rw' R' Dw r' Dw' Rw2 Fw' u Fw y
 
|sign=y' b' R d 2R' d' r' b r' R' d 2R' d' r2 f' 2U f y
 
|sign=y' b' R d 2R' d' r' b r' R' d 2R' d' r2 f' 2U f y
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|length=(17,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-5#post-626321
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-5#post-626321
 
}}
 
}}
{{Alg5|wca=(y' Bw') Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r (Bw y)
+
{{Alg6|wca=(y' Bw') Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r (Bw y)
 
|sign=(y' b') u2 2R' d 2L' d' 2R u' l2 u' 2R' u l2 u' 2R (b y)
 
|sign=(y' b') u2 2R' d 2L' d' 2R u' l2 u' 2R' u l2 u' 2R (b y)
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' l' r' U Rw U2 l' U2 Lw' U2 x' U' l' U F2 U' M' l' y
+
{{Alg6|wca=y' l' r' U Rw U2 l' U2 Lw' U2 x' U' l' U F2 U' M' l' y
 
|sign=y' 2L' 2R' U r U2 2L' U2 l' U2 x' U' 2L' U F2 U' m' 2L' y
 
|sign=y' 2L' 2R' U r U2 2L' U2 l' U2 x' U' 2L' U F2 U' m' 2L' y
 
|length=(20,16)|name=|wide=N|author=Christopher Mowla
 
|length=(20,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-437212
 
}}
 
}}
{{Alg5|wca=x l' U L U l' U' L' U' F2 l' F2 r U2 r' U2 l2 x'
+
{{Alg6|wca=x l' U L U l' U' L' U' F2 l' F2 r U2 r' U2 l2 x'
 
|sign=x 2L' U L U 2L' U' L' U' F2 2L' F2 2R U2 2R' U2 2L2 x'
 
|sign=x 2L' U L U 2L' U' L' U' F2 2L' F2 2R U2 2R' U2 2L2 x'
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|length=(21,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-588960
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-588960
 
}}
 
}}
{{Alg5|wca=(L' B') l' U2 l' U2 x U2 l' U2 x' r U2 r' U2 l2 (B L)
+
{{Alg6|wca=(L' B') l' U2 l' U2 x U2 l' U2 x' r U2 r' U2 l2 (B L)
 
|sign=(L' B') 2L' U2 2L' U2 x U2 2L' U2 x' 2R U2 2R' U2 2L2 (B L)
 
|sign=(L' B') 2L' U2 2L' U2 x U2 2L' U2 x' 2R U2 2R' U2 2L2 (B L)
 
|length=(23,16)|name=|wide=N|author=|url=
 
|length=(23,16)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(x Rw E') Uw Rw Uw' l Uw Rw' Fw Uw r Uw' Fw' Uw' l' (E Rw' x')
+
{{Alg6|wca=(x Rw E') Uw Rw Uw' l Uw Rw' Fw Uw r Uw' Fw' Uw' l' (E Rw' x')
 
|sign=(x r e') u r u' 2L u r' f u 2R u' f' u' 2L' (e r' x')
 
|sign=(x r e') u r u' 2L u r' f u 2R u' f' u' 2L' (e r' x')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x Rw E') Uw Fw Uw r' Uw' Fw' Rw Uw' l' Uw Rw' Uw' l (E Rw' x')
+
{{Alg6|wca=(x Rw E') Uw Fw Uw r' Uw' Fw' Rw Uw' l' Uw Rw' Uw' l (E Rw' x')
 
|sign=(x r e') u f u 2R' u' f' r u' 2L' u r' u' 2L (e r' x')
 
|sign=(x r e') u f u 2R' u' f' r u' 2L' u r' u' 2L (e r' x')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' Bw' r') l' Bw Rw Bw' l Bw Rw' Uw Bw r Bw' Uw' Bw' (r Bw y)
+
{{Alg6|wca=(y' Bw' r') l' Bw Rw Bw' l Bw Rw' Uw Bw r Bw' Uw' Bw' (r Bw y)
 
|sign=(y' b' 2R') 2L' b r b' 2L b r' u b 2R b' u' b' (2R b y)
 
|sign=(y' b' 2R') 2L' b r b' 2L b r' u b 2R b' u' b' (2R b y)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' Bw' R) l Dw Bw Dw r' Dw' Bw' Rw Dw' l' Dw Rw' Dw' (R' Bw y)
+
{{Alg6|wca=(y' Bw' R) l Dw Bw Dw r' Dw' Bw' Rw Dw' l' Dw Rw' Dw' (R' Bw y)
 
|sign=(y' b' R) 2L d b d 2R' d' b' r d' 2L' d r' d' (R' b y)
 
|sign=(y' b' R) 2L d b d 2R' d' b' r d' 2L' d r' d' (R' b y)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' Bw') l' R Dw Rw Dw' l Dw Rw' Bw Dw r Dw' Bw' Dw' R' (Bw y)
+
{{Alg6|wca=(y' Bw') l' R Dw Rw Dw' l Dw Rw' Bw Dw r Dw' Bw' Dw' R' (Bw y)
 
|sign=(y' b') 2L' R d r d' 2L d r' b d 2R d' b' d' R' (b y)
 
|sign=(y' b') 2L' R d r d' 2L d r' b d 2R d' b' d' R' (b y)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y' Bw' M) Bw Rw Bw' l Bw Rw' Uw Bw r Bw' Uw' Bw' l' (M' Bw y)
+
{{Alg6|wca=(y' Bw' M) Bw Rw Bw' l Bw Rw' Uw Bw r Bw' Uw' Bw' l' (M' Bw y)
 
|sign=(y' b' m) b r b' 2L b r' u b 2R b' u' b' 2L' (m' b y)
 
|sign=(y' b' m) b r b' 2L b r' u b 2R b' u' b' 2L' (m' b y)
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(z Dw) Fw Rw Fw' l Fw Rw' B Dw Fw r Fw' Dw' B' Fw' l' (Dw' z')
+
{{Alg6|wca=(z Dw) Fw Rw Fw' l Fw Rw' B Dw Fw r Fw' Dw' B' Fw' l' (Dw' z')
 
|sign=(z d) f r f' 2L f r' B d f 2R f' d' B' f' 2L' (d' z')
 
|sign=(z d) f r f' 2L f r' B d f 2R f' d' B' f' 2L' (d' z')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(z Dw) B l' Fw Rw Fw' l Fw Rw' Dw Fw r Fw' Dw' Fw' B' (Dw' z')
+
{{Alg6|wca=(z Dw) B l' Fw Rw Fw' l Fw Rw' Dw Fw r Fw' Dw' Fw' B' (Dw' z')
 
|sign=(z d) B 2L' f r f' 2L f r' d f 2R f' d' f' B' (d' z')
 
|sign=(z d) B 2L' f r f' 2L f r' d f 2R f' d' f' B' (d' z')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(z Dw) B l Fw Dw Fw r' Fw' Dw' Rw Fw' l' Fw Rw' Fw' B' (Dw' z')
+
{{Alg6|wca=(z Dw) B l Fw Dw Fw r' Fw' Dw' Rw Fw' l' Fw Rw' Fw' B' (Dw' z')
 
|sign=(z d) B 2L f d f 2R' f' d' r f' 2L' f r' f' B' (d' z')
 
|sign=(z d) B 2L f d f 2R' f' d' r f' 2L' f r' f' B' (d' z')
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x l' U L U l' U' L' U' x U2 l' U2 l U2 r' U2 l r x2
+
{{Alg6|wca=x l' U L U l' U' L' U' x U2 l' U2 l U2 r' U2 l r x2
 
|sign=x 2L' U L U 2L' U' L' U' x U2 2L' U2 2L U2 2R' U2 2L 2R x2
 
|sign=x 2L' U L U 2L' U' L' U' x U2 2L' U2 2L U2 2R' U2 2L 2R x2
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x l' U L U l' U' L' U' M' U2 l' U2 l U2 r' U2 l2 x'
+
{{Alg6|wca=x l' U L U l' U' L' U' M' U2 l' U2 l U2 r' U2 l2 x'
 
|sign=x 2L' U L U 2L' U' L' U' m' U2 2L' U2 2L U2 2R' U2 2L2 x'
 
|sign=x 2L' U L U 2L' U' L' U' m' U2 2L' U2 2L U2 2R' U2 2L2 x'
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-588960
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-588960
 
}}
 
}}
{{Alg5|wca=x l U2 l U2 M U L U l U' L' U' l' U2 r U2 l2 x'
+
{{Alg6|wca=x l U2 l U2 M U L U l U' L' U' l' U2 r U2 l2 x'
 
|sign=x 2L U2 2L U2 m U L U 2L U' L' U' 2L' U2 2R U2 2L2 x'
 
|sign=x 2L U2 2L U2 m U L U 2L U' L' U' 2L' U2 2R U2 2L2 x'
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-6#post-845287
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-6#post-845287
 
}}
 
}}
{{Alg5|wca=Rw U2 l U2 3Lw U L' U l U' L U' l' U2 r U2 Lw2 x'
+
{{Alg6|wca=Rw U2 l U2 3Lw U L' U l U' L U' l' U2 r U2 Lw2 x'
 
|sign=r U2 2L U2 3l U L' U 2L U' L U' 2L' U2 2R U2 l2 x'
 
|sign=r U2 2L U2 3l U L' U 2L U' L U' 2L' U2 2R U2 l2 x'
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|length=(22,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-6#post-842827
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-6#post-842827
 
}}
 
}}
{{Alg5|wca=y' l U F2 U' l U F2 l F L F l F' L' F' l' U' l2 y
+
{{Alg6|wca=y' l U F2 U' l U F2 l F L F l F' L' F' l' U' l2 y
 
|sign=y' 2L U F2 U' 2L U F2 2L F L F 2L F' L' F' 2L' U' 2L2 y
 
|sign=y' 2L U F2 U' 2L U F2 2L F L F 2L F' L' F' 2L' U' 2L2 y
 
|length=(21,18)|name=|wide=N|author=Christopher Mowla
 
|length=(21,18)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x Lw' L' U L' U l' U' L U' M' U2 l' U2 l U2 r' U2 Lw2 x'
+
{{Alg6|wca=x Lw' L' U L' U l' U' L U' M' U2 l' U2 l U2 r' U2 Lw2 x'
 
|sign=x l' L' U L' U 2L' U' L U' m' U2 2L' U2 2L U2 2R' U2 l2 x'
 
|sign=x l' L' U L' U 2L' U' L U' m' U2 2L' U2 2L U2 2R' U2 l2 x'
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|length=(23,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-6#post-845287
 
|url=https://www.speedsolving.com/forum/threads/4x4-parity-algorithms.10037/page-6#post-845287
 
}}
 
}}
{{Alg5|wca=(x L2)(r F U2 F')4 r (L2 x')
+
{{Alg6|wca=(x L2)(r F U2 F')4 r (L2 x')
|sign=(x L2)(2R F U2 F')4 2R (L2 x')
+
|sign=(x L2) (2R F U2 F')4 2R (L2 x')
 
|length=(25,19)|name=|wide=N|author=Floyd Newberry
 
|length=(25,19)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=(x L2)(r' F U2 F')4 r' (L2 x')
+
{{Alg6|wca=(x L2)(r' F U2 F')4 r' (L2 x')
|sign=(x L2)(2R' F U2 F')4 2R' (L2 x')
+
|sign=(x L2) (2R' F U2 F')4 2R' (L2 x')
 
|length=(25,19)|name=|wide=N|author=Floyd Newberry
 
|length=(25,19)|name=|wide=N|author=Floyd Newberry
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
 
}}
 
}}
{{Alg5|wca=y' r U r' U' r' u' r u r' U' r' U r' u' U r U2 r Uw r2 y//Safe
+
{{Alg6|wca=y' r U r' U' r' u' r u r' U' r' U r' u' U r U2 r Uw r2 y //Safe
|sign=y' 2R U 2R' U' 2R' 2U' 2R 2U 2R' U' 2R' U 2R' 2U' U 2R U2 2R u 2R2 y//Safe
+
|sign=y' 2R U 2R' U' 2R' 2U' 2R 2U 2R' U' 2R' U 2R' 2U' U 2R U2 2R u 2R2 y //Safe
 
|length=(21,20)|name=|wide=N|author=Ben Whitmore
 
|length=(21,20)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=r' U' r U' r' D b2 r b2 r' U2 D' r' U' r U' r U r' U r2//Safe
+
{{Alg6|wca=r' U' r U' r' D b2 r b2 r' U2 D' r' U' r U' r U r' U r2 //Safe
|sign=2R' U' 2R U' 2R' D 2B2 2R 2B2 2R' U2 D' 2R' U' 2R U' 2R U 2R' U 2R2//Safe
+
|sign=2R' U' 2R U' 2R' D 2B2 2R 2B2 2R' U2 D' 2R' U' 2R U' 2R U 2R' U 2R2 //Safe
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
|length=(25,21)|name=|wide=N|author=|url=https://www.speedsolving.com/forum/threads/gods-algorithm-discovered-for-oll-parity-edge-flip-theory.26622/page-2#post-515118
 
}}
 
}}
{{Alg5|wca=y' x Lw' U' R' U' l2 U R U Lw' U2 Lw U' R' U' l U R U Lw' U2 Lw2 x' y
+
{{Alg6|wca=y' x Lw' U' R' U' l2 U R U Lw' U2 Lw U' R' U' l U R U Lw' U2 Lw2 x' y
 
|sign=y' x l' U' R' U' 2L2 U R U l' U2 l U' R' U' 2L U R U l' U2 l2 x' y
 
|sign=y' x l' U' R' U' 2L2 U R U l' U2 l U' R' U' 2L U R U l' U2 l2 x' y
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|length=(25,21)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x l2 U2 Lw U l U' Lw' U2 Lw' U2 Lw U2 Lw U l2 U' Lw' U2 Lw' U2 Lw' L2 x'
+
{{Alg6|wca=x l2 U2 Lw U l U' Lw' U2 Lw' U2 Lw U2 Lw U l2 U' Lw' U2 Lw' U2 Lw' L2 x'
 
|sign=x 2L2 U2 l U 2L U' l' U2 l' U2 l U2 l U 2L2 U' l' U2 l' U2 l' L2 x'
 
|sign=x 2L2 U2 l U 2L U' l' U2 l' U2 l U2 l U 2L2 U' l' U2 l' U2 l' L2 x'
 
|length=(30,22)|name=|wide=N|author=Christopher Mowla
 
|length=(30,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(y Rw' U2 r') Rw2 U2 Rw U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw (r U2 Rw y')
+
{{Alg6|wca=(y Rw' U2 r') Rw2 U2 Rw U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw (r U2 Rw y')
 
|sign=(y r' U2 2R') r2 U2 r U2 r U 2R U' r' U2 r' U2 r U2 r U 2R2 U' r' U2 r (2R U2 r y')
 
|sign=(y r' U2 2R') r2 U2 r U2 r U 2R U' r' U2 r' U2 r U2 r U 2R2 U' r' U2 r (2R U2 r y')
 
|length=(37,27)|name=|wide=N|author=Christopher Mowla
 
|length=(37,27)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
<b>Non-symmetrical algorithms</b>
+
<span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);"><b>Non-symmetrical algorithms</b></span>
{{Alg5|wca=Lw' Dw B2 Rw2 Fw r Fw' Rw2 B2 r' Dw' Lw Dw r Dw'
+
{{Alg6|wca=Lw' Dw B2 Rw2 Fw r Fw' Rw2 B2 r' Dw' Lw Dw r Dw'
 
|sign=l' d B2 r2 f 2R f' r2 B2 2R' d' l d 2R d'
 
|sign=l' d B2 r2 f 2R f' r2 B2 2R' d' l d 2R d'
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw'
+
{{Alg6|wca=r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw'
 
|sign=2R' u l u' 2R2 f2 l' f 2R' f' l f2 2R' u l' u'
 
|sign=2R' u l u' 2R2 f2 l' f 2R' f' l f2 2R' u l' u'
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=y' Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw' y
+
{{Alg6|wca=y' Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw' y
 
|sign=y' u' f 2L' f' u f 2L' u2 R u 2L' u' R' u2 2L2 f' y
 
|sign=y' u' f 2L' f' u f 2L' u2 R u 2L' u' R' u2 2L2 f' y
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=z x2 Rw' Uw l' Uw' Rw Uw l' Fw2 R Fw l' Fw' R' Fw2 l2 Uw' x2 z'
+
{{Alg6|wca=z x2 Rw' Uw l' Uw' Rw Uw l' Fw2 R Fw l' Fw' R' Fw2 l2 Uw' x2 z'
 
|sign=z x2 r' u 2L' u' r u 2L' f2 R f 2L' f' R' f2 2L2 u' x2 z'
 
|sign=z x2 r' u 2L' u' r u 2L' f2 R f 2L' f' R' f2 2L2 u' x2 z'
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|length=(19,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=z Uw' Rw Uw2 l' Uw r' Uw' l Uw2 R' Uw Bw2 Uw' r' Uw Bw2 z'
+
{{Alg6|wca=z Uw' Rw Uw2 l' Uw r' Uw' l Uw2 R' Uw Bw2 Uw' r' Uw Bw2 z'
 
|sign=z u' r u2 2L' u 2R' u' 2L u2 R' u b2 u' 2R' u b2 z'
 
|sign=z u' r u2 2L' u 2R' u' 2L u2 R' u b2 u' 2R' u b2 z'
 
|length=(20,16)|name=|wide=N|author=Christopher Mowla
 
|length=(20,16)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Uw Rw Bw' r F' R' r Uw' r' Uw r' R F Bw Rw' Uw'
+
{{Alg6|wca=r' Uw Rw Bw' r F' R' r Uw' r' Uw r' R F Bw Rw' Uw'
|sign=2R' u r b' 2R F' R' 2R u' 2R' u 2R' R F b r' u'  
+
|sign=2R' u r b' 2R F' R' 2R u' 2R' u 2R' R F b r' u'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' Uw Rw Bw' r R' F' r Uw' r' Uw r' F R Bw Rw' Uw'
+
{{Alg6|wca=r' Uw Rw Bw' r R' F' r Uw' r' Uw r' F R Bw Rw' Uw'
|sign=2R' u r b' 2R R' F' 2R u' 2R' u 2R' F R b r' u'  
+
|sign=2R' u r b' 2R R' F' 2R u' 2R' u 2R' F R b r' u'
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' Rw' Uw' r Uw Rw Bw' F' Rw R Uw' r Uw Rw' R' F r' Bw y
+
{{Alg6|wca=y' Rw' Uw' r Uw Rw Bw' F' Rw R Uw' r Uw Rw' R' F r' Bw y
 
|sign=y' r' u' 2R u r b' F' r R u' 2R u r' R' F 2R' b y
 
|sign=y' r' u' 2R u r b' F' r R u' 2R u r' R' F 2R' b y
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|length=(17,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=y' Rw' Uw' r Uw Rw Bw' R2 F' r Uw' r Uw r' F Rw' R' Bw y
+
{{Alg6|wca=y' Rw' Uw' r Uw Rw Bw' R2 F' r Uw' r Uw r' F Rw' R' Bw y
|sign=y' r' u' 2R u r b' R2 F' 2R u' 2R u 2R' F r' R' b y  
+
|sign=y' r' u' 2R u r b' R2 F' 2R u' 2R u 2R' F r' R' b y
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|length=(18,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' r' Fw Rw Uw' r2 x
+
{{Alg6|wca=x' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' r' Fw Rw Uw' r2 x
 
|sign=x' 2F' u r' f' 2R' f r u' 2F 2R' u r' f' 2R' f r u' 2R2 x
 
|sign=x' 2F' u r' f' 2R' f r u' 2F 2R' u r' f' 2R' f r u' 2R2 x
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|length=(19,18)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=z' r' Uw Bw Uw' Bw L Bw r Bw' L' Bw' Uw Bw' Lw Uw' r Uw Lw' Uw' z
+
{{Alg6|wca=z' r' Uw Bw Uw' Bw L Bw r Bw' L' Bw' Uw Bw' Lw Uw' r Uw Lw' Uw' z
 
|sign=z' 2R' u b u' b L b 2R b' L' b' u b' l u' 2R u l' u' z
 
|sign=z' 2R' u b u' b L b 2R b' L' b' u b' l u' 2R u l' u' z
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|length=(19,19)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
{{Alg5|wca=r Uw' Lw Uw r' Uw' Fw' Uw' B Rw2 B' l B Rw2 B' Uw Fw Lw' Uw
+
{{Alg6|wca=r Uw' Lw Uw r' Uw' Fw' Uw' B Rw2 B' l B Rw2 B' Uw Fw Lw' Uw
 
|sign=2R u' l u 2R' u' f' u' B r2 B' 2L B r2 B' u f l' u
 
|sign=2R u' l u 2R' u' f' u' B r2 B' 2L B r2 B' u f l' u
 
|length=(21,19)|name=|wide=N|author=Christopher Mowla
 
|length=(21,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
}}
+
}}
{{Alg5|wca=Rw2 U Rw' U Rw' U Rw U2 Rw U2 Rw' U Rw U' Rw' U' Rw' U2 Rw' U2 Rw U2 Rw' U Rw2 U2
+
{{Alg6|wca=Rw2 U Rw' U Rw' U Rw U2 Rw U2 Rw' U Rw U' Rw' U' Rw' U2 Rw' U2 Rw U2 Rw' U Rw2 U2
|sign=r2 U r' U r' U r U2 r U2 r' U r U' r' U' r' U2 r' U2 r U2 r' U r2 U2
+
|sign=r2 U r' U r' U r U2 r U2 r' U r U' r' U' r' U2 r' U2 r U2 r' U r2 U2
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
+
|length=(34,26)|name=|wide=Y|author=Bruce Norskog
 +
|url=
 +
}}
 +
{{Alg6|wca=Rw' U Rw' U' Rw2 U2 Rw' U2 Rw' U Rw U' Rw' U Rw2 U' Rw U2 Rw' U2 Rw U2 Rw2 U Rw' U' Rw U
 +
|sign=r' U r' U' r2 U2 r' U2 r' U r U' r' U r2 U' r U2 r' U2 r U2 r2 U r' U' r U
 +
|length=(36,28)|name=5x5x5 Alg
 +
|wide=Y|author=Ben Whitmore
 +
|url=
 +
}}
 +
{{br|b=1}}
 +
 
 +
=<span style="font-family:Georgia;color:rgb(0,200,0);">Non Dedge-Preserving Last Layer 4-Cycle Cases in Two Dedges</span>=
 +
*These are all of the other 4-cycles that can occur in two dedges in the last layer besides double parity and adjacent double parity.
 +
*These are additional cases which arise in the {{LinkColorI|p=K4|c=rgb(229,148,0)|t=K4 Method}} and other {{LinkColorI|p=direct solving|c=rgb(229,148,0)|t=direct solving methods}}.
 +
{{br|b=1}}
 +
==<span style="font-family:Georgia;color:rgb(0,200,0);">In opposite dedges</span>==
 +
===<span style="font-family:Georgia;color:rgb(0,200,0);">Checkerboard</span>===
 +
[[Image:Chkbrd.png|110px|]]
 +
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 +
{{br|b=1}}
 +
{{Alg6|wca=Rw2 U2 r E2 r' E2 r U2 Rw2
 +
|sign=r2 U2 2R e2 2R' e2 2R U2 r2
 +
|length=(15,9)|name=v1|wide=N|author=Tom Rokicki & Ed Trice
 +
|url=https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-12#post-975170
 +
}}
 +
{{Alg6|wca=Lw2 U2 l E2 l' E2 l U2 Lw2
 +
|sign=l2 U2 2L e2 2L' e2 2L U2 l2
 +
|length=(15,9)|name=v2|wide=N|author=Tom Rokicki & Ed Trice
 +
|url=https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-12#post-975170
 +
}}
 +
{{Alg6|wca=l f l U2 S' l S U2 l f' l
 +
|sign=2L 2F 2L U2 s' 2L s U2 2L 2F' 2L
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=https://www.speedsolving.com/threads/a-collection-of-algorithms.708/page-124#post-1428115
 +
}}
 +
{{Alg6|wca=l f' l U2 S l S' U2 l f l
 +
|sign=2L 2F' 2L U2 s 2L s' U2 2L 2F 2L
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=l b l U2 S l S' U2 l b' l
 +
|sign=2L 2B 2L U2 s 2L s' U2 2L 2B' 2L
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=l b' l U2 S' l S U2 l b l
 +
|sign=2L 2B' 2L U2 s' 2L s U2 2L 2B 2L
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=r f r U2 S' r S U2 r f' r
 +
|sign=2R 2F 2R U2 s' 2R s U2 2R 2F' 2R
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=r f' r U2 S r S' U2 r f r
 +
|sign=2R 2F' 2R U2 s 2R s' U2 2R 2F 2R
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=r b r U2 S r S' U2 r b' r
 +
|sign=2R 2B 2R U2 s 2R s' U2 2R 2B' 2R
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=r b' r U2 S' r S U2 r b r
 +
|sign=2R 2B' 2R U2 s' 2R s U2 2R 2B 2R
 +
|length=(13,11)|name=|wide=N|author=Tom Rokicki
 +
|url=
 +
}}
 +
{{Alg6|wca=(f2 u' r2 Uw2 S') r (S Uw2 r2 u f2)
 +
|sign=(2F2 2U' 2R2 u2 s') 2R (s u2 2R2 2U 2F2)
 +
|length=(17,11)|name=|wide=N|author=Christopher Mowla
 +
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 +
}}
 +
{{Alg6|wca=(f2 u r2 Uw2 S') r (S Uw2 r2 u' f2)
 +
|sign=(2F2 2U 2R2 u2 s') 2R (s u2 2R2 2U' 2F2)
 +
|length=(17,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw' U' Rw2 U2 Rw' U2 Rw' U Rw U' Rw' U Rw2 U' Rw U2 Rw' U2 Rw U2 Rw2 U Rw' U' Rw U
+
{{Alg6|wca=r2 U2 l' E2 r E2 l U2 S2 r2 S2
|sign=r' U r' U' r2 U2 r' U2 r' U r U' r' U r2 U' r U2 r' U2 r U2 r2 U r' U' r U
+
|sign=2R2 U2 2L' e2 2R e2 2L U2 s2 2R2 s2
|length=(36,28)|name=5x5x5 Alg
+
|length=(19,11)|name=|wide=N|author=Per Kristen Fredlund
|wide=Y|author=Ben Whitmore
+
|url=http://twistypuzzles.com/forum/viewtopic.php?p=407643#p407643
|url=
 
 
}}
 
}}
 
+
{{Alg6|wca=r2 S2 U2 l E2 r E2 l' U2 r2 S2
=Non Dedge-Preserving Last Layer 4-Cycle Cases in Two Dedges=
+
|sign=2R2 s2 U2 2L e2 2R e2 2L' U2 2R2 s2
*These are all of the other 4-cycles that can occur in two dedges in the last layer besides double parity and adjacent double parity.
+
|length=(19,11)|name=|wide=N|author=Per Kristen Fredlund
*These are additional cases which arise in the K4 Method and other direct-solving methods.
 
 
 
 
 
==In opposite dedges==
 
===Checkerboard===
 
[[Image:Chkbrd.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
 
 
 
 
{{Alg5|wca=Rw2 U2 r E2 r' E2 r U2 Rw2
 
|sign=r2 U2 2R e2 2R' e2 2R U2 r2
 
|length=(15,9)|name=v1|wide=N|author=Tom Rokicki & Ed Trice
 
|url=https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-12#post-975170
 
}}
 
{{Alg5|wca=Lw2 U2 l E2 l' E2 l U2 Lw2
 
|sign=l2 U2 2L e2 2L' e2 2L U2 l2
 
|length=(15,9)|name=v2|wide=N|author=Tom Rokicki & Ed Trice
 
|url=https://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-12#post-975170
 
}}
 
{{Alg5|wca=(f2 u' r2 Uw2 S') r (S Uw2 r2 u f2)
 
|sign=(2F2 2U' 2R2 u2 s') 2R (s u2 2R2 2U 2F2)
 
|length=(17,11)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
}}
 
{{Alg5|wca=(f2 u r2 Uw2 S') r (S Uw2 r2 u' f2)
 
|sign=(2F2 2U 2R2 u2 s') 2R (s u2 2R2 2U' 2F2)
 
|length=(17,11)|name=|wide=N|author=Christopher Mowla
 
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 (r S2)2 r' U2 l2 f2 M2 f2
+
{{Alg6|wca=r2 U2 (r S2)2 r' U2 l2 f2 M2 f2
 
|sign=2R2 U2 (2R s2)2 2R' U2 2L2 2F2 m2 2F2
 
|sign=2R2 U2 (2R s2)2 2R' U2 2L2 2F2 m2 2F2
 
|length=(21,12)|name=|wide=N|author=Christopher Mowla
 
|length=(21,12)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-38#post-616772
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-38#post-616772
 
}}
 
}}
{{Alg5|wca=r2 U2 (r S2)2 r' U2 l2 b2 M2 b2
+
{{Alg6|wca=r2 U2 (r S2)2 r' U2 l2 b2 M2 b2
 
|sign=2R2 U2 (2R s2)2 2R' U2 2L2 2B2 m2 2B2
 
|sign=2R2 U2 (2R s2)2 2R' U2 2L2 2B2 m2 2B2
 
|length=(21,12)|name=|wide=N|author=|url=
 
|length=(21,12)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=r S' L2 S (r U2)2 r S' L2 S r
+
{{Alg6|wca=r S' L2 S (r U2)2 r S' L2 S r
 
|sign=2R s' L2 s (2R U2)2 2R s' L2 s 2R
 
|sign=2R s' L2 s (2R U2)2 2R s' L2 s 2R
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r S R2 S' (r U2)2 r S R2 S' r
+
{{Alg6|wca=r S R2 S' (r U2)2 r S R2 S' r
 
|sign=2R s R2 s' (2R U2)2 2R s R2 s' 2R
 
|sign=2R s R2 s' (2R U2)2 2R s R2 s' 2R
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 Uw U S Lw2 u2) r (u2 Lw2 S' U' Uw' Rw2)
+
{{Alg6|wca=(Rw2 Uw U S Lw2 u2) r (u2 Lw2 S' U' Uw' Rw2)
 
|sign=(r2 u U s l2 2U2) 2R (2U2 l2 s' U' u' r2)
 
|sign=(r2 u U s l2 2U2) 2R (2U2 l2 s' U' u' r2)
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
 
}}
 
}}
{{Alg5|wca=(Rw2 Uw' U' S Lw2 u2) r (u2 Lw2 S' U Uw Rw2)
+
{{Alg6|wca=(Rw2 Uw' U' S Lw2 u2) r (u2 Lw2 S' U Uw Rw2)
 
|sign=(r2 u' U' s l2 2U2) 2R (2U2 l2 s' U u r2)
 
|sign=(r2 u' U' s l2 2U2) 2R (2U2 l2 s' U u r2)
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 S) (r' U2)4 r' (S' Rw2)
+
{{Alg6|wca=(Rw2 S) (r' U2)4 r' (S' Rw2)
 
|sign=(r2 s) (2R' U2)4 2R' (s' r2)
 
|sign=(r2 s) (2R' U2)4 2R' (s' r2)
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw2 S') (r' U2)4 r' (S Rw2)
+
{{Alg6|wca=(Rw2 S') (r' U2)4 r' (S Rw2)
 
|sign=(r2 s') (2R' U2)4 2R' (s r2)
 
|sign=(r2 s') (2R' U2)4 2R' (s r2)
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'
+
{{Alg6|wca=r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'
 
|sign=2R' U2 2R2 U2 2R U2 2R' U2 2R U2 2R2 U2 2R'
 
|sign=2R' U2 2R2 U2 2R U2 2R' U2 2R U2 2R2 U2 2R'
|length=(21,13)|name=Alg(v1a)
+
|length=(21,13)|name=Alg(v1a)|wide=Y|author=|url=
|wide=Y|author=|url=
 
 
}}
 
}}
{{Alg5|wca=Rw' U2 r2 U2 Rw U2 r' U2 Rw U2 r2 U2 Rw'
+
{{Alg6|wca=Rw' U2 r2 U2 Rw U2 r' U2 Rw U2 r2 U2 Rw'
 
|sign=r' U2 2R2 U2 r U2 2R' U2 r U2 2R2 U2 r'
 
|sign=r' U2 2R2 U2 r U2 2R' U2 r U2 2R2 U2 r'
 
|length=(21,13)|name=Alg(v1b)
 
|length=(21,13)|name=Alg(v1b)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=r' U2 Rw2 U2 r U2 r' U2 r U2 Rw2 U2 r'
+
{{Alg6|wca=r' U2 Rw2 U2 r U2 r' U2 r U2 Rw2 U2 r'
 
|sign=2R' U2 r2 U2 2R U2 2R' U2 2R U2 r2 U2 2R'
 
|sign=2R' U2 r2 U2 2R U2 2R' U2 2R U2 r2 U2 2R'
 
|length=(21,13)|name=Alg(v1c)
 
|length=(21,13)|name=Alg(v1c)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw' U2 r2 U2 r U2 r' U2 Rw U2 r2 U2 r'
+
{{Alg6|wca=Rw' U2 r2 U2 r U2 r' U2 Rw U2 r2 U2 r'
 
|sign=r' U2 2R2 U2 2R U2 2R' U2 r U2 2R2 U2 2R'
 
|sign=r' U2 2R2 U2 2R U2 2R' U2 r U2 2R2 U2 2R'
 
|length=(21,13)|name=Alg(v1d)
 
|length=(21,13)|name=Alg(v1d)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l'
+
{{Alg6|wca=l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l'
 
|sign=2L' U2 2L2 U2 2L U2 2L' U2 2L U2 2L2 U2 2L'
 
|sign=2L' U2 2L2 U2 2L U2 2L' U2 2L U2 2L2 U2 2L'
 
|length=(21,13)|name=Alg(v2a)
 
|length=(21,13)|name=Alg(v2a)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 l2 U2 Lw U2 l' U2 Lw U2 l2 U2 Lw'
+
{{Alg6|wca=Lw' U2 l2 U2 Lw U2 l' U2 Lw U2 l2 U2 Lw'
 
|sign=l' U2 2L2 U2 l U2 2L' U2 l U2 2L2 U2 l'
 
|sign=l' U2 2L2 U2 l U2 2L' U2 l U2 2L2 U2 l'
 
|length=(21,13)|name=Alg(v2b)
 
|length=(21,13)|name=Alg(v2b)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=l' U2 Lw2 U2 l U2 l' U2 l U2 Lw2 U2 l'
+
{{Alg6|wca=l' U2 Lw2 U2 l U2 l' U2 l U2 Lw2 U2 l'
 
|sign=2L' U2 l2 U2 2L U2 2L' U2 2L U2 l2 U2 2L'
 
|sign=2L' U2 l2 U2 2L U2 2L' U2 2L U2 l2 U2 2L'
 
|length=(21,13)|name=Alg(v2c)
 
|length=(21,13)|name=Alg(v2c)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 l2 U2 l U2 l' U2 Lw U2 l2 U2 l'
+
{{Alg6|wca=Lw' U2 l2 U2 l U2 l' U2 Lw U2 l2 U2 l'
 
|sign=l' U2 2L2 U2 2L U2 2L' U2 l U2 2L2 U2 2L'
 
|sign=l' U2 2L2 U2 2L U2 2L' U2 l U2 2L2 U2 2L'
 
|length=(21,13)|name=Alg(v2d)
 
|length=(21,13)|name=Alg(v2d)
 
|wide=Y|author=|url=
 
|wide=Y|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Bowtie/Hourglass===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Bowtie/Hourglass</span>===
 
[[Image:Hourglass.png|110px|]]
 
[[Image:Hourglass.png|110px|]]
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
+
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.  However, this is a special case where, instead of having to take the inverse of these algorithms to solve the inverse case, you may simply do a U2 turn (or y2 cube rotation) and then perform these same algorithms to solve the inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=r2 U2 r B2 r B2 E2 l' B2 l B2 D2 l' y2
{{Alg5|wca=r2 U2 r B2 r B2 E2 l' B2 l B2 D2 l' y2
 
 
|sign=2R2 U2 2R B2 2R B2 e2 2L' B2 2L B2 D2 2L' y2
 
|sign=2R2 U2 2R B2 2R B2 e2 2L' B2 2L B2 D2 2L' y2
 
|length=(21,13)|name=|wide=N|author=Oscar Roth Andersen
 
|length=(21,13)|name=|wide=N|author=Oscar Roth Andersen
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975788
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975788
 
}}
 
}}
{{Alg5|wca=r U2 r U2 F2 r F2 l' U2 M r' Uw2 r2 u2
+
{{Alg6|wca=r U2 r U2 F2 r F2 l' U2 M r' Uw2 r2 u2
 
|sign=2R U2 2R U2 F2 2R F2 2L' U2 m 2R' u2 2R2 2U2
 
|sign=2R U2 2R U2 F2 2R F2 2L' U2 m 2R' u2 2R2 2U2
 
|length=(22,14)|name=|wide=N|author=
 
|length=(22,14)|name=|wide=N|author=
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975829
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975829
 
}}
 
}}
{{Alg5|wca=r U2 r U2 M' U2 r U2 r' U2 M r' Uw2 r2 u2
+
{{Alg6|wca=r U2 r U2 M' U2 r U2 r' U2 M r' Uw2 r2 u2
 
|sign=2R U2 2R U2 m' U2 2R U2 2R' U2 m 2R' u2 2R2 2U2
 
|sign=2R U2 2R U2 m' U2 2R U2 2R' U2 m 2R' u2 2R2 2U2
 
|length=(23,15)|name=|wide=N|author=|url=
 
|length=(23,15)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2
+
{{Alg6|wca=r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2
 
|sign=2R2 U2 2L' U2 2L F2 U2 2R2 U2 2R F2 2R' F2 2R' F2
 
|sign=2R2 U2 2L' U2 2L F2 U2 2R2 U2 2R F2 2R' F2 2R' F2
 
|length=(25,15)|name=|wide=Y|author=|url=
 
|length=(25,15)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=(B' Rw U2 D' x) U2 r' U2 r2 (U2 r')2 (x' D U2 Rw' B)
+
{{Alg6|wca=(B' Rw U2 D' x) U2 r' U2 r2 (U2 r')2 (x' D U2 Rw' B)
 
|sign=(B' r U2 D' x) U2 2R' U2 2R2 (U2 2R')2 (x' D U2 r' B)
 
|sign=(B' r U2 D' x) U2 2R' U2 2R2 (U2 2R')2 (x' D U2 r' B)
 
|length=(23,16)|name=|wide=N|author=xyzzy
 
|length=(23,16)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2
+
{{Alg6|wca=r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2
 
|sign=2R' U2 2R U2 2L' U2 2R U2 2L F2 2R' F2 2R F2 2R2 F2
 
|sign=2R' U2 2R U2 2L' U2 2R U2 2L F2 2R' F2 2R F2 2R2 F2
 
|length=(25,16)|name=|wide=Y|author=|url=
 
|length=(25,16)|name=|wide=Y|author=|url=
 
}}
 
}}
{{Alg5|wca=(B' R Uw' u' r' f2 Rw2 E) f' (E' Rw2 f2 r u Uw R' B)
+
{{Alg6|wca=(B' R Uw' u' r' f2 Rw2 E) f' (E' Rw2 f2 r u Uw R' B)
 
|sign=(B' R u' 2U' 2R' 2F2 r2 e) 2F' (e' r2 2F2 2R 2U u R' B)
 
|sign=(B' R u' 2U' 2R' 2F2 r2 e) 2F' (e' r2 2F2 2R 2U u R' B)
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(B' R Uw' u' r f2 Rw2 E) f' (E' Rw2 f2 r' u Uw R' B)
+
{{Alg6|wca=(B' R Uw' u' r f2 Rw2 E) f' (E' Rw2 f2 r' u Uw R' B)
 
|sign=(B' R u' 2U' 2R 2F2 r2 e) 2F' (e' r2 2F2 2R' 2U u R' B)
 
|sign=(B' R u' 2U' 2R 2F2 r2 e) 2F' (e' r2 2F2 2R' 2U u R' B)
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|length=(21,17)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r'
+
{{Alg6|wca=r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r'
 
|sign=2R U2 m' U2 2R2 U2 2R' U2 2R U2 2R' U2 2R' U2 2L U2 2R'
 
|sign=2R U2 m' U2 2R2 U2 2R' U2 2R U2 2R' U2 2R' U2 2L U2 2R'
 
|length=(26,17)|name=|wide=N|author=|url=
 
|length=(26,17)|name=|wide=N|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
==In adjacent dedges==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">In adjacent dedges</span>==
===Checkboard===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Checkerboard</span>===
 
[[Image:Adjchkbd.png|110px|]]
 
[[Image:Adjchkbd.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=F2 Uw' F2 Rw2 Uw2 R2 z' S u F' B' Uw2 Rw2 Uw' F2
{{Alg5|wca=F2 Uw' F2 Rw2 Uw2 R2 z' S u F' B' Uw2 Rw2 Uw' F2
 
 
|sign=F2 u' F2 r2 u2 R2 z' s 2U F' B' u2 r2 u' F2
 
|sign=F2 u' F2 r2 u2 R2 z' s 2U F' B' u2 r2 u' F2
 
|length=(22,14)|name=seq3002|wide=N|author=Tom Rokicki
 
|length=(22,14)|name=seq3002|wide=N|author=Tom Rokicki
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975957
 
|url=http://www.speedsolving.com/forum/threads/announcing-new-4x4x4-brute-force-solver.46925/page-14#post-975957
 
}}
 
}}
{{Alg5|wca=(F U' F' Rw2 U2) r' E2 r E2 r' (U2 Rw2 F U F')
+
{{Alg6|wca=(F U' F' Rw2 U2) r' E2 r E2 r' (U2 Rw2 F U F')
 
|sign=(F U' F' r2 U2) 2R' e2 2R e2 2R' (U2 r2 F U F')
 
|sign=(F U' F' r2 U2) 2R' e2 2R e2 2R' (U2 r2 F U F')
 
|length=(21,15)|name=|wide=N|author=Tom Rokicki & Ed Trice
 
|length=(21,15)|name=|wide=N|author=Tom Rokicki & Ed Trice
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2)
+
{{Alg6|wca=(R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2)
 
|sign=(R2 u' 2U' 2R' 2F2 r2 e) 2F (e' r2 2F2 2R 2U u R2)
 
|sign=(R2 u' 2U' 2R' 2F2 r2 e) 2F (e' r2 2F2 2R 2U u R2)
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-705096
 
}}
 
}}
{{Alg5|wca=(R2 Uw' u' r f2 Rw2 E) f (E' Rw2 f2 r' u Uw R2)
+
{{Alg6|wca=(R2 Uw' u' r f2 Rw2 E) f (E' Rw2 f2 r' u Uw R2)
 
|sign=(R2 u' 2U' 2R 2F2 r2 e) 2F (e' r2 2F2 2R' 2U u R2)
 
|sign=(R2 u' 2U' 2R 2F2 r2 e) 2F (e' r2 2F2 2R' 2U u R2)
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Rw R U2 D' x)(r U2)2 r2 U2 r U2 (x' D U2 Rw' R')
+
{{Alg6|wca=(Rw R U2 D' x)(r U2)2 r2 U2 r U2 (x' D U2 Rw' R')
|sign=(r R U2 D' x)(2R U2)2 2R2 U2 2R U2 (x' D U2 r' R')
+
|sign=(r R U2 D' x) (2R U2)2 2R2 U2 2R U2 (x' D U2 r' R')
 
|length=(23,16)|name=|wide=N|author=xyzzy
 
|length=(23,16)|name=|wide=N|author=xyzzy
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-106#post-1296965
 
}}
 
}}
{{Alg5|wca=(Rw' F2 M2 F) U2 l U2 l2 U2 l U2 l (F' M2 F2 Rw)
+
{{Alg6|wca=(Rw' F2 M2 F) U2 l U2 l2 U2 l U2 l (F' M2 F2 Rw)
 
|sign=(r' F2 m2 F) U2 2L U2 2L2 U2 2L U2 2L (F' m2 F2 r)
 
|sign=(r' F2 m2 F) U2 2L U2 2L2 U2 2L U2 2L (F' m2 F2 r)
 
|length=(25,16)|name=|wide=N|author=Christopher Mowla
 
|length=(25,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-586243
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-586243
 
}}
 
}}
{{Alg5|wca=(Lw' U2 M2 U) M U2 l U2 l2 U2 l U2 r (U' M2 U2 Lw)
+
{{Alg6|wca=(Lw' U2 M2 U) M U2 l U2 l2 U2 l U2 r (U' M2 U2 Lw)
 
|sign=(l' U2 m2 U) m U2 2L U2 2L2 U2 2L U2 2R (U' m2 U2 l)
 
|sign=(l' U2 m2 U) m U2 2L U2 2L2 U2 2L U2 2R (U' m2 U2 l)
 
|length=(26,17)|name=|wide=N|author=Christopher Mowla
 
|length=(26,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
}}
 
}}
{{Alg5|wca=(R B) r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' (B' R')
+
{{Alg6|wca=(R B) r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' (B' R')
 
|sign=(R B) 2R U2 m' U2 2R2 U2 2R' U2 2R U2 2R' U2 2R' U2 2L U2 2R' (B' R')
 
|sign=(R B) 2R U2 m' U2 2R2 U2 2R' U2 2R U2 2R' U2 2R' U2 2L U2 2R' (B' R')
 
|length=(30,21)|name=|wide=N|author=|url=
 
|length=(30,21)|name=|wide=N|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Bowtie/Hourglass===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Bowtie/Hourglass</span>===
 
[[Image:Ahourglass.png|110px|]]
 
[[Image:Ahourglass.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=(R B) Rw2 U2 r' E2 r E2 r' U2 Rw2 (B' R')
{{Alg5|wca=(R B) Rw2 U2 r' E2 r E2 r' U2 Rw2 (B' R')
 
 
|sign=(R B) r2 U2 2R' e2 2R e2 2R' U2 r2 (B' R')
 
|sign=(R B) r2 U2 2R' e2 2R e2 2R' U2 r2 (B' R')
 
|length=(19,13)|name=|wide=N|author=Tom Rokicki & Ed Trice
 
|length=(19,13)|name=|wide=N|author=Tom Rokicki & Ed Trice
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R Fw f r u2 Rw2 S) u' (S' Rw2 u2 r' Fw' f' R')
+
{{Alg6|wca=(R Fw f r u2 Rw2 S) u' (S' Rw2 u2 r' Fw' f' R')
 
|sign=(R f 2F 2R 2U2 r2 s) 2U' (s' r2 2U2 2R' f' 2F' R')
 
|sign=(R f 2F 2R 2U2 r2 s) 2U' (s' r2 2U2 2R' f' 2F' R')
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(R Fw f r' u2 Rw2 S) u' (S' Rw2 u2 r Fw' f' R')
+
{{Alg6|wca=(R Fw f r' u2 Rw2 S) u' (S' Rw2 u2 r Fw' f' R')
 
|sign=(R f 2F 2R' 2U2 r2 s) 2U' (s' r2 2U2 2R f' 2F' R')
 
|sign=(R f 2F 2R' 2U2 r2 s) 2U' (s' r2 2U2 2R f' 2F' R')
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=F' Lw U D Lw2 Bw2 Rw' R' U' D B2 Lw2 Fw2 D2 Lw' F
+
{{Alg6|wca=F' Lw U D Lw2 Bw2 Rw' R' U' D B2 Lw2 Fw2 D2 Lw' F
 
|sign=F' l U D l2 b2 r' R' U' D B2 l2 f2 D2 l' F
 
|sign=F' l U D l2 b2 r' R' U' D B2 l2 f2 D2 l' F
 
|length=(21,15)|name=|wide=Y|author=Tom Rokicki
 
|length=(21,15)|name=|wide=Y|author=Tom Rokicki
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw)
+
{{Alg6|wca=(Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw)
 
|sign=(l' U2 m2 U' x) 2R' U2 2R' U2 2R2 U2 2R' U2 (x' U m2 U2 l)
 
|sign=(l' U2 m2 U' x) 2R' U2 2R' U2 2R2 U2 2R' U2 (x' U m2 U2 l)
 
|length=(25,16)|name=|wide=N|author=Christopher Mowla
 
|length=(25,16)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-586243
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-586243
 
}}
 
}}
{{Alg5|wca=R B r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r B' R'
+
{{Alg6|wca=R B r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r B' R'
 
|sign=R B 2R U2 2R2 U2 2R' U2 2R U2 2R' U2 2R2 U2 2R B' R'
 
|sign=R B 2R U2 2R2 U2 2R' U2 2R U2 2R' U2 2R2 U2 2R B' R'
 
|length=(25,17)|name=|wide=N|author=|url=
 
|length=(25,17)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(r U2 M2 U') M' U2 l' U2 l2 U2 l' U2 r' (U M2 U2 r')
+
{{Alg6|wca=(r U2 M2 U') M' U2 l' U2 l2 U2 l' U2 r' (U M2 U2 r')
 
|sign=(2R U2 m2 U') m' U2 2L' U2 2L2 U2 2L' U2 2R' (U m2 U2 2R')
 
|sign=(2R U2 m2 U') m' U2 2L' U2 2L2 U2 2L' U2 2R' (U m2 U2 2R')
 
|length=(26,17)|name=|wide=N|author=Christopher Mowla
 
|length=(26,17)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-652345
 
}}
 
}}
{{Alg5|wca=y2 Fw' r2 Uw2 L' Uw' U' R U F' R' F r' F' R F U' R' Uw U L Uw2 r' Fw Uw Fw' r' Fw Uw' y2
+
{{Alg6|wca=y2 Fw' r2 Uw2 L' Uw' U' R U F' R' F r' F' R F U' R' Uw U L Uw2 r' Fw Uw Fw' r' Fw Uw' y2
 
|sign=y2 f' 2R2 u2 L' u' U' R U F' R' F 2R' F' R F U' R' u U L u2 2R' f u f' 2R' f u' y2
 
|sign=y2 f' 2R2 u2 L' u' U' R U F' R' F 2R' F' R F U' R' u U L u2 2R' f u f' 2R' f u' y2
 
|length=(31,28)|name=|wide=N|author=Christopher Mowla
 
|length=(31,28)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
 
}}
 
}}
 +
{{br|b=1}}
  
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">Move count comparison of all last layer 2-cycles and 2 dedge 4-cycles</span>=
 
 
=Move count comparison of all last layer 2-cycles and 2 dedge 4-cycles=
 
 
*Since there is disagreement among cubers about whether lowest slice quarter turn moves (BQTM) or lowest slice half turn moves (BHTM) defines the "optimal algorithm", the table below categorizes all 2-cycle and 4-cycle cases (in two dedges) on the 4x4x4 by the average of the two.
 
*Since there is disagreement among cubers about whether lowest slice quarter turn moves (BQTM) or lowest slice half turn moves (BHTM) defines the "optimal algorithm", the table below categorizes all 2-cycle and 4-cycle cases (in two dedges) on the 4x4x4 by the average of the two.
 
 
*Each case's "Optimal Move Average" was found by taking the average of BQTM and BHTM from all algorithms on this page which solve it and choosing the smallest result.
 
*Each case's "Optimal Move Average" was found by taking the average of BQTM and BHTM from all algorithms on this page which solve it and choosing the smallest result.
 
+
*The table shows that the "worst case" is the <i>One Dedge Flip</i>, and that the "easiest case" is the <i>Checkerboard</i> case in two opposite dedges.
*The table shows that the "worst case" is <b>Adjacent Double Parity</b>, and that the "easiest case" is the <b>Checkerboard</b> case in two opposite dedges.
 
 
 
 
:*These results will change in the future if shorter algorithms are found for any of these cases.
 
:*These results will change in the future if shorter algorithms are found for any of these cases.
 
  
 
{|class="mw_metadata"
 
{|class="mw_metadata"
 
|+Arranged by Rank (Worst last layer cases are first.)
 
|+Arranged by Rank (Worst last layer cases are first.)
 
|-
 
|-
! Last Layer Case !! Minimum BQTM !! Minimum BHTM !! Optimal Move Average !! Rank
+
! <span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);">Last Layer Case</span> !! <span style="font-family:Georgia;font-size:120%;color:rgb(200,0,0);">Minimum BQTM</span> !! <span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);">Minimum BHTM</span> !! <span style="font-family:Georgia;font-size:120%;color:rgb(200,0,0);">Optimal Move Average</span> !! <span style="font-family:Georgia;font-size:120%;color:rgb(0,200,0);">Rank</span>
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/8/8c/Adj.dblparity.png Adjacent Double Parity 4-cycle] !! 23 !! 16 !! 19.5 !! 1
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/0/05/One_Dedge_Flip.png|c=rgb(229,148,0)|t=One Dedge Flip 2-cycle}} !! 18 !! 15 !! 18 !! 1
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/7/7b/Adjchkbd.png Adjacent Checkerboard 4-cycle] !! 21 !! 14 !! 18 !! 2
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/7/7b/Adjchkbd.png|c=rgb(229,148,0)|t=Adjacent Checkerboard 4-cycle}} !! 21 !! 14 !! 18 !! 1
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/0/05/One_Dedge_Flip.png One Dedge Flip 2-cycle] !! 18 !! 15 !! 18 !! 2
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/9/95/DblParity.png|c=rgb(229,148,0)|t=Double Parity 4-cycle}} !! 21 !! 14 !! 17.5 !! 2
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/9/95/DblParity.png Double Parity 4-cycle] !! 21 !! 14 !! 17.5 !! 3
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/1/11/Hourglass.png|c=rgb(229,148,0)|t=Bowtie/Hourglass 4-cycle}} !! 21 !! 13 !! 17 !! 3
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/1/11/Hourglass.png Bowtie/Hourglass 4-cycle] !! 21 !! 13 !! 17 !! 4
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/0/0a/Adj.case1.png|c=rgb(229,148,0)|t=Close Unoriented 2-cycle}}!! 17 !! 15 !! 17 !! 3
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/0/0a/Adj.case1.png Close Unoriented 2-cycle]!! 17 !! 15 !! 17 !! 4
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/2/2c/Adjcase2.png|c=rgb(229,148,0)|t=Far Unoriented 2-cycle}} !! 17 !! 15 !! 17 !! 3
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/2/2c/Adjcase2.png Far Unoriented 2-cycle] !! 17 !! 15 !! 17 !! 4
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/8/8c/Adj.dblparity.png|c=rgb(229,148,0)|t=Adjacent Double Parity 4-cycle}} !! 17 !! 16 !! 16.5 !! 4
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/6/6b/Ahourglass.png Adjacent Bowtie/Hourglass 4-cycle] !! 19 !! 13 !! 16 !! 5
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/6/6b/Ahourglass.png|c=rgb(229,148,0)|t=Adjacent Bowtie/Hourglass 4-cycle}} !! 19 !! 13 !! 16 !! 5
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/d/de/Adjcase3.png Oriented 2-cycle] !! 16 !! 15 !! 16 !! 5
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/d/de/Adjcase3.png|c=rgb(229,148,0)|t=Oriented 2-cycle}} !! 16 !! 15 !! 16 !! 5
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/9/96/Diag.opp.png Diagonal 2-cycle] !! 16 !! 14 !! 15.5 !! 6
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/9/96/Diag.opp.png|c=rgb(229,148,0)|t=Diagonal 2-cycle}} !! 16 !! 14 !! 15.5 !! 6
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/9/96/Adj2swap.png Opposite 2-cycle] !! 16 !! 12 !! 15.5 !! 6
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/9/96/Adj2swap.png|c=rgb(229,148,0)|t=Opposite 2-cycle}} !! 16 !! 12 !! 15.5 !! 6
 
|-
 
|-
! [https://www.speedsolving.com/wiki/images/5/50/Chkbrd.png Checkerboard 4-cycle] !! 15 !! 9 !! 12 !! 7
+
! {{LinkColorE|u=https://www.speedsolving.com/wiki/images/5/50/Chkbrd.png|c=rgb(229,148,0)|t=Checkerboard 4-cycle}} !! 15 !! 9 !! 12 !! 7
 
|}
 
|}
 +
{{br|b=1}}
  
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">Algorithms which do not preserve the centers</span>=
 
+
*These algorithms are for fixing the wing edges, but they do not preserve the centers.  Many of these algorithms can be used in solving methods such as the {{LinkColorI|p=Cage Method|c=rgb(229,148,0)|t=Cage Method}}.
=Algorithms which do not preserve the centers=
+
{{br|b=1}}
*These algorithms are for fixing the wing edges, but they do not preserve the centers.  Many of these algorithms can be used in solving methods such as the [[Cage Method]].
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">One dedge flip</span>==
 
 
 
 
==One dedge flip==
 
 
[[Image:COneDedge_Flip.png|110px|]]
 
[[Image:COneDedge_Flip.png|110px|]]
{{Alg5|wca=Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2
+
{{Alg6|wca=Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R' U2 B2 r2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R' U2 B2 r2
 
|length=(17,12)|name=|wide=N|author=Michael Gottlieb
 
|length=(17,12)|name=|wide=N|author=Michael Gottlieb
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=66059#p66059
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=66059#p66059
 
}}
 
}}
{{Alg5|wca=Rw2 U r' U' B2 U r U r' U2 B2 Rw2
+
{{Alg6|wca=Rw2 U r' U' B2 U r U r' U2 B2 Rw2
 
|sign=r2 U 2R' U' B2 U 2R U 2R' U2 B2 r2
 
|sign=r2 U 2R' U' B2 U 2R U 2R' U2 B2 r2
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 3Dw l U' R2 U l' U y r U2 F2 Rw2
+
{{Alg6|wca=Rw2 3Dw l U' R2 U l' U y r U2 F2 Rw2
 
|sign=r2 3d 2L U' R2 U 2L' U y 2R U2 F2 r2
 
|sign=r2 3d 2L U' R2 U 2L' U y 2R U2 F2 r2
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=Rw2 F r F' Uw2 B l' B l B2 Uw2 Rw2
+
{{Alg6|wca=Rw2 F r F' Uw2 B l' B l B2 Uw2 Rw2
 
|sign=r2 F 2R F' u2 B 2L' B 2L B2 u2 r2
 
|sign=r2 F 2R F' u2 B 2L' B 2L B2 u2 r2
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2
+
{{Alg6|wca=Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2
 
|sign=r2 U2 2R U2 2L' U2 2L U2 2R' F2 2R F2 r2
 
|sign=r2 U2 2R U2 2L' U2 2L U2 2R' F2 2R F2 r2
 
|length=(21,13)|name=|wide=N|author=|url=
 
|length=(21,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2
+
{{Alg6|wca=Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2
 
|sign=r2 U2 2R U2 2L' U2 2L U2 2R' B2 2L B2 r2
 
|sign=r2 U2 2R U2 2L' U2 2L U2 2R' B2 2L B2 r2
 
|length=(21,13)|name=|wide=N|author=|url=
 
|length=(21,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2
+
{{Alg6|wca=l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2
 
|sign=2L U2 2L' U2 l2 F2 2R' F2 r2 U2 2L' U2 2R x2
 
|sign=2L U2 2L' U2 l2 F2 2R' F2 r2 U2 2L' U2 2R x2
 
|length=(21,13)|name=|wide=N|author=|url=
 
|length=(21,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r
+
{{Alg6|wca=r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r
 
|sign=2R2 u b' u' 2R u r b 2R' b' r' b u' 2R
 
|sign=2R2 u b' u' 2R u r b 2R' b' r' b u' 2R
 
|length=(15,14)|name=|wide=N|author=Christopher Mowla
 
|length=(15,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r
+
{{Alg6|wca=r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r
 
|sign=2R2 U2 2R' U2 2R U2 2L' U2 2R U2 2R' U2 2L 2R
 
|sign=2R2 U2 2R' U2 2R U2 2L' U2 2R U2 2R' U2 2L 2R
 
|length=(21,14)|name=|wide=N|author=Lucas Garron
 
|length=(21,14)|name=|wide=N|author=Lucas Garron
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r
+
{{Alg6|wca=r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r
 
|sign=2R2 U2 2R U2 2L' U2 2L U2 2L' U2 2R U2 2L 2R
 
|sign=2R2 U2 2R U2 2L' U2 2L U2 2L' U2 2R U2 2L 2R
 
|length=(21,14)|name=|wide=N|author=Nicholas Ho
 
|length=(21,14)|name=|wide=N|author=Nicholas Ho
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' l' Uw Rw' Uw' l Uw y Lw Dw r' Dw' Lw' y' Rw Uw' Rw
+
{{Alg6|wca=Rw' l' Uw Rw' Uw' l Uw y Lw Dw r' Dw' Lw' y' Rw Uw' Rw
 
|sign=r' 2L' u r' u' 2L u y l d 2R' d' l' y' r u' r
 
|sign=r' 2L' u r' u' 2L u y l d 2R' d' l' y' r u' r
 
|length=(15,15)|name=|wide=N|author=Christopher Mowla
 
|length=(15,15)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=x r R' U' Rw U' r U Rw' r' U R U' r U r' x'
+
{{Alg6|wca=x r R' U' Rw U' r U Rw' r' U R U' r U r' x'
 
|sign=x 2R R' U' r U' 2R U r' 2R' U R U' 2R U 2R' x'
 
|sign=x 2R R' U' r U' 2R U r' 2R' U R U' 2R U 2R' x'
 
|length=(15,15)|name=|wide=N|author=|url=
 
|length=(15,15)|name=|wide=N|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Opposite double parity</span>==
==Opposite double parity==
 
 
[[Image:CDoubleParity.png|110px|]]
 
[[Image:CDoubleParity.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Most of these algorithms are exactly the same as the one dedge flip ones except that the extra quarter turn is inverted.
 
*Most of these algorithms are exactly the same as the one dedge flip ones except that the extra quarter turn is inverted.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=Rw' F' u F' D2 F u' F' l D2 F2 Rw
{{Alg5|wca=Rw' F' u F' D2 F u' F' l D2 F2 Rw
 
 
|sign=r' F' 2U F' D2 F 2U' F' 2L D2 F2 r
 
|sign=r' F' 2U F' D2 F 2U' F' 2L D2 F2 r
 
|length=(15,12)|name=|wide=N|author=Christopher Mowla
 
|length=(15,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U r' U' B2 U r U r U2 B2 Rw2
+
{{Alg6|wca=Rw2 U r' U' B2 U r U r U2 B2 Rw2
 
|sign=r2 U 2R' U' B2 U 2R U 2R U2 B2 r2
 
|sign=r2 U 2R' U' B2 U 2R U 2R U2 B2 r2
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U' r' U B2 U' r U' r U2 B2 Rw2
+
{{Alg6|wca=Rw2 U' r' U B2 U' r U' r U2 B2 Rw2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R U2 B2 r2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R U2 B2 r2
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 3Dw l U' R2 U l' U y r' U2 F2 Rw2
+
{{Alg6|wca=Rw2 3Dw l U' R2 U l' U y r' U2 F2 Rw2
 
|sign=r2 3d 2L U' R2 U 2L' U y 2R' U2 F2 r2
 
|sign=r2 3d 2L U' R2 U 2L' U y 2R' U2 F2 r2
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=x' Rw2 F2 r F2 r U2 l' U2 l U2 r' U2 Rw2 x
+
{{Alg6|wca=x' Rw2 F2 r F2 r U2 l' U2 l U2 r' U2 Rw2 x
 
|sign=x' r2 F2 2R F2 2R U2 2L' U2 2L U2 2R' U2 r2 x
 
|sign=x' r2 F2 2R F2 2R U2 2L' U2 2L U2 2R' U2 r2 x
 
|length=(21,13)|name=|wide=N|author=|url=
 
|length=(21,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l' y' Uw2 Rw2 Uw' l' Uw Rw2 Uw' l Uw' y U2 l U2 l'
+
{{Alg6|wca=l' y' Uw2 Rw2 Uw' l' Uw Rw2 Uw' l Uw' y U2 l U2 l'
 
|sign=2L' y' u2 r2 u' 2L' u r2 u' 2L u' y U2 2L U2 2L'
 
|sign=2L' y' u2 r2 u' 2L' u r2 u' 2L u' y U2 2L U2 2L'
 
|length=(18,14)|name=|wide=N|author=Christopher Mowla
 
|length=(18,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 b2 D' f' D B2 D' f U' f U D Bw2 Rw2
+
{{Alg6|wca=Rw2 b2 D' f' D B2 D' f U' f U D Bw2 Rw2
 
|sign=r2 2B2 D' 2F' D B2 D' 2F U' 2F U D b2 r2
 
|sign=r2 2B2 D' 2F' D B2 D' 2F U' 2F U D b2 r2
 
|length=(19,14)|name=|wide=N|author=Christopher Mowla
 
|length=(19,14)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2
+
{{Alg6|wca=l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2
 
|sign=2L 2R U2 2L U2 2R' U2 2R U2 2R' U2 2L' U2 2L2
 
|sign=2L 2R U2 2L U2 2R' U2 2R U2 2R' U2 2L' U2 2L2
 
|length=(21,14)|name=|wide=N|author=Nicholas Ho
 
|length=(21,14)|name=|wide=N|author=Nicholas Ho
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Adjacent double parity</span>==
==Adjacent double parity==
 
 
[[Image:Cadj.dblparity.png|110px|]]
 
[[Image:Cadj.dblparity.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=(r2 U' Rw U' R' U') r' (U R U Rw' U r2)
{{Alg5|wca=(r2 U' Rw U' R' U') r' (U R U Rw' U r2)
 
 
|sign=(2R2 U' r U' R' U') 2R' (U R U r' U 2R2)
 
|sign=(2R2 U' r U' R' U') 2R' (U R U r' U 2R2)
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
}}
 
}}
{{Alg5|wca=(r2 U F2 U' r' F2) r (F2 r U F2 U' r2)
+
{{Alg6|wca=(r2 U F2 U' r' F2) r (F2 r U F2 U' r2)
 
|sign=(2R2 U F2 U' 2R' F2) 2R (F2 2R U F2 U' 2R2)
 
|sign=(2R2 U F2 U' 2R' F2) 2R (F2 2R U F2 U' 2R2)
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|length=(19,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw
+
{{Alg6|wca=Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw
 
|sign=r' U r U F2 U' 2R' U F2 2R' U' R' U' r
 
|sign=r' U r U F2 U' 2R' U F2 2R' U' R' U' r
 
|length=(16,14)|name=|wide=N|author=Christopher Mowla
 
|length=(16,14)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-534006
 
}}
 
}}
{{Alg5|wca=(x Uw F U r' U R' U) r (U' R U' r U' F' Uw' x')
+
{{Alg6|wca=(x Uw F U r' U R' U) r (U' R U' r U' F' Uw' x')
 
|sign=(x u F U 2R' U R' U) 2R (U' R U' 2R U' F' u' x')
 
|sign=(x u F U 2R' U R' U) 2R (U' R U' 2R U' F' u' x')
 
|length=(15,15)|name=|wide=N|author=Christopher Mowla
 
|length=(15,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' r2 U' Rw U' l' U2 l' U2 l' U2 l2 U' Rw' U r2 x
+
{{Alg6|wca=x' r2 U' Rw U' l' U2 l' U2 l' U2 l2 U' Rw' U r2 x
 
|sign=x' 2R2 U' r U' 2L' U2 2L' U2 2L' U2 2L2 U' r' U 2R2 x
 
|sign=x' 2R2 U' r U' 2L' U2 2L' U2 2L' U2 2L2 U' r' U 2R2 x
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla
 
|length=(21,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Three flips</span>==
==Three flips==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Single parity</span>===
===Single parity===
 
 
[[Image:Collpo3flip.png|110px|]]
 
[[Image:Collpo3flip.png|110px|]]
{{Alg5|wca=M r' U B2 l2 B2 3Dw' Rw2 U2 r' U2 Rw2 y' M' r
+
{{Alg6|wca=M r' U B2 l2 B2 3Dw' Rw2 U2 r' U2 Rw2 y' M' r
 
|sign=m 2R' U B2 2L2 B2 3d' r2 U2 2R' U2 r2 y' m' 2R
 
|sign=m 2R' U B2 2L2 B2 3d' r2 U2 2R' U2 r2 y' m' 2R
 
|length=(21,14)|name=Pattern 1|wide=N|author=Per Kristen Fredlund
 
|length=(21,14)|name=Pattern 1|wide=N|author=Per Kristen Fredlund
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374737#p374737
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374737#p374737
 
}}
 
}}
{{Alg5|wca=(r2 F2 U) r U2 r' U2 r U2 r' U2 r (U' F2 r2)
+
{{Alg6|wca=(r2 F2 U) r U2 r' U2 r U2 r' U2 r (U' F2 r2)
 
|sign=(2R2 F2 U) 2R U2 2R' U2 2R U2 2R' U2 2R (U' F2 2R2)
 
|sign=(2R2 F2 U) 2R U2 2R' U2 2R U2 2R' U2 2R (U' F2 2R2)
 
|length=(23,15)|name=|wide=N|author=Christopher Mowla
 
|length=(23,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(r2 U2 F' M' U) r U2 r' U2 r U2 r' U2 r (U' M F U2 r2)
+
{{Alg6|wca=(r2 U2 F' M' U) r U2 r' U2 r U2 r' U2 r (U' M F U2 r2)
 
|sign=(2R2 U2 F' m' U) 2R U2 2R' U2 2R U2 2R' U2 2R (U' m F U2 2R2)
 
|sign=(2R2 U2 F' m' U) 2R U2 2R' U2 2R U2 2R' U2 2R (U' m F U2 2R2)
 
|length=(27,19)|name=|wide=N|author=Christopher Mowla
 
|length=(27,19)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Double parity</span>===
===Double parity===
 
 
[[Image:CageDp3flip.png|110px|]]
 
[[Image:CageDp3flip.png|110px|]]
{{Alg5|wca=y M r' U B2 l2 B2 3Dw' Rw2 U2 r U2 Rw2 y' M' r y'
+
{{Alg6|wca=y M r' U B2 l2 B2 3Dw' Rw2 U2 r U2 Rw2 y' M' r y'
 
|sign=y m 2R' U B2 2L2 B2 3d' r2 U2 2R U2 r2 y' m' 2R y'
 
|sign=y m 2R' U B2 2L2 B2 3d' r2 U2 2R U2 r2 y' m' 2R y'
 
|length=(21,14)|name=Pattern 1|wide=N|author=Per Kristen Fredlund
 
|length=(21,14)|name=Pattern 1|wide=N|author=Per Kristen Fredlund
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374737#p374737
 
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374737#p374737
 
}}
 
}}
{{Alg5|wca=(R2 D')(r' U' F' R' F R2 U') r' (U R2 F' R F U r)(r U2 r' U2)(D R2)
+
{{Alg6|wca=(R2 D')(r' U' F' R' F R2 U') r' (U R2 F' R F U r)(r U2 r' U2)(D R2)
 
|sign=(R2 D')(2R' U' F' R' F R2 U') 2R' (U R2 F' R F U 2R)(2R U2 2R' U2)(D R2)
 
|sign=(R2 D')(2R' U' F' R' F R2 U') 2R' (U R2 F' R F U 2R)(2R U2 2R' U2)(D R2)
 
|length=(29,22)|name=|wide=N|author=Christopher Mowla
 
|length=(29,22)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
==2-cycles in two adjacent dedges (in the M ring)==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">2-cycles in two adjacent dedges (in the M ring)</span>==
===Opposite===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Opposite</span>===
 
[[Image:Cadj.2swap.png|110px|]]
 
[[Image:Cadj.2swap.png|110px|]]
{{Alg5|wca=l U' l' U' F2 U l U' F2 U2
+
{{Alg6|wca=l U' l' U' F2 U l U' F2 U2
 
|sign=2L U' 2L' U' F2 U 2L U' F2 U2
 
|sign=2L U' 2L' U' F2 U 2L U' F2 U2
 
|length=(13,10)|name=|wide=N|author=|url=
 
|length=(13,10)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l U l' U F2 U' l U F2 U2
+
{{Alg6|wca=l U l' U F2 U' l U F2 U2
 
|sign=2L U 2L' U F2 U' 2L U F2 U2
 
|sign=2L U 2L' U F2 U' 2L U F2 U2
 
|length=(13,10)|name=|wide=N|author=|url=
 
|length=(13,10)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=z2 y' U2 R2 U l U' R2 U l' U y r z2
+
{{Alg6|wca=z2 y' U2 R2 U l U' R2 U l' U y r z2
 
|sign=z2 y' U2 R2 U 2L U' R2 U 2L' U y 2R z2
 
|sign=z2 y' U2 R2 U 2L U' R2 U 2L' U y 2R z2
 
|length=(13,10)|name=|wide=N|author=|url=
 
|length=(13,10)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l F2 r' U2 l U2 l' U2 r U2 F2
+
{{Alg6|wca=l F2 r' U2 l U2 l' U2 r U2 F2
 
|sign=2L F2 2R' U2 2L U2 2L' U2 2R U2 F2
 
|sign=2L F2 2R' U2 2L U2 2L' U2 2R U2 F2
 
|length=(17,11)|name=|wide=N|author=|url=
 
|length=(17,11)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=l' U Lw' U L U' l' U L' U' Lw l U'
+
{{Alg6|wca=l' U Lw' U L U' l' U L' U' Lw l U'
 
|sign=2L' U l' U L U' 2L' U L' U' l 2L U'
 
|sign=2L' U l' U L U' 2L' U L' U' l 2L U'
 
|length=(13,13)|name=|wide=N|author=|url=
 
|length=(13,13)|name=|wide=N|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Diagonal</span>===
===Diagonal===
 
 
[[Image:CDiag.opp.png|110px|]]
 
[[Image:CDiag.opp.png|110px|]]
 
*Some of these are nearly the same as the one dedge flip algorithms.
 
*Some of these are nearly the same as the one dedge flip algorithms.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=Lw' U' l U B2 U' l' U' l U2 B2 Lw
{{Alg5|wca=Lw' U' l U B2 U' l' U' l U2 B2 Lw
 
 
|sign=l' U' 2L U B2 U' 2L' U' 2L U2 B2 l
 
|sign=l' U' 2L U B2 U' 2L' U' 2L U2 B2 l
 
|length=(15,12)|name=|wide=N|author=Christopher Mowla
 
|length=(15,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' U l U' B2 U l' U l U2 B2 Lw
+
{{Alg6|wca=Lw' U l U' B2 U l' U l U2 B2 Lw
 
|sign=l' U 2L U' B2 U 2L' U 2L U2 B2 l
 
|sign=l' U 2L U' B2 U 2L' U 2L U2 B2 l
 
|length=(15,12)|name=|wide=N|author=Christopher Mowla
 
|length=(15,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' 3Dw' r' U L2 U' r U' y' l' U2 F2 Lw
+
{{Alg6|wca=Lw' 3Dw' r' U L2 U' r U' y' l' U2 F2 Lw
 
|sign=l' 3d' 2R' U L2 U' 2R U' y' 2L' U2 F2 l
 
|sign=l' 3d' 2R' U L2 U' 2R U' y' 2L' U2 F2 l
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|length=(17,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' U Rw' U r' U' Rw r U' R' U r' U' R x
+
{{Alg6|wca=x' U Rw' U r' U' Rw r U' R' U r' U' R x
 
|sign=x' U r' U 2R' U' r 2R U' R' U 2R' U' R x
 
|sign=x' U r' U 2R' U' r 2R U' R' U 2R' U' R x
 
|length=(13,13)|name=|wide=N|author=Marc Waterman
 
|length=(13,13)|name=|wide=N|author=Marc Waterman
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' R U Rw' U r' U' Rwr U' R' U r' U' x
+
{{Alg6|wca=x' R U Rw' U r' U' Rwr U' R' U r' U' x
 
|sign=x' R U r' U 2R' U' r2R U' R' U 2R' U' x
 
|sign=x' R U r' U 2R' U' r2R U' R' U 2R' U' x
 
|length=(13,13)|name=|wide=N|author=Marc Waterman
 
|length=(13,13)|name=|wide=N|author=Marc Waterman
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' x
+
{{Alg6|wca=x' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' x
 
|sign=x' 2R' u b' u' 2R u r b 2R' b' r' b u' x
 
|sign=x' 2R' u b' u' 2R u r b 2R' b' r' b u' x
 
|length=(13,13)|name=|wide=N|author=Christopher Mowla
 
|length=(13,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' 3Dw' r' U L2 U' r D' r' U D L2 y' Lw
+
{{Alg6|wca=Lw' 3Dw' r' U L2 U' r D' r' U D L2 y' Lw
 
|sign=l' 3d' 2R' U L2 U' 2R D' 2R' U D L2 y' l
 
|sign=l' 3d' 2R' U L2 U' 2R D' 2R' U D L2 y' l
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' U l U' B2 U l' U' B2 D2 r' D2 Lw
+
{{Alg6|wca=Lw' U l U' B2 U l' U' B2 D2 r' D2 Lw
 
|sign=l' U 2L U' B2 U 2L' U' B2 D2 2R' D2 l
 
|sign=l' U 2L U' B2 U 2L' U' B2 D2 2R' D2 l
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Lw' 3Dw' r' U L2 U' r U D2 y' r' D2 F2 Lw
+
{{Alg6|wca=Lw' 3Dw' r' U L2 U' r U D2 y' r' D2 F2 Lw
 
|sign=l' 3d' 2R' U L2 U' 2R U D2 y' 2R' D2 F2 l
 
|sign=l' 3d' 2R' U L2 U' 2R U D2 y' 2R' D2 F2 l
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|length=(17,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=(x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x)
+
{{Alg6|wca=(x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x)
 
|sign=(x') 2R' U2 2R U2 2L' U2 2L U2 2L' U2 2R U2 2L (x)
 
|sign=(x') 2R' U2 2R U2 2L' U2 2L U2 2L' U2 2R U2 2L (x)
 
|length=(19,13)|name=|wide=N|author=|url=
 
|length=(19,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 l' U2 r U2 r' U2 l F2 l' F2 Lw
+
{{Alg6|wca=Lw' U2 l' U2 r U2 r' U2 l F2 l' F2 Lw
 
|sign=l' U2 2L' U2 2R U2 2R' U2 2L F2 2L' F2 l
 
|sign=l' U2 2L' U2 2R U2 2R' U2 2L F2 2L' F2 l
 
|length=(19,13)|name=|wide=N|author=|url=
 
|length=(19,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=Lw' U2 l' U2 r U2 r' U2 l B2 r' B2 Lw
+
{{Alg6|wca=Lw' U2 l' U2 r U2 r' U2 l B2 r' B2 Lw
 
|sign=l' U2 2L' U2 2R U2 2R' U2 2L B2 2R' B2 l
 
|sign=l' U2 2L' U2 2R U2 2R' U2 2L B2 2R' B2 l
 
|length=(21,13)|name=|wide=N|author=|url=
 
|length=(21,13)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=M' l' U2 l' U2 l U2 r' U2 l U2 l' U2 l
+
{{Alg6|wca=M' l' U2 l' U2 l U2 r' U2 l U2 l' U2 l
 
|sign=m' 2L' U2 2L' U2 2L U2 2R' U2 2L U2 2L' U2 2L
 
|sign=m' 2L' U2 2L' U2 2L U2 2R' U2 2L U2 2L' U2 2L
 
|length=(20,14)|name=|wide=N|author=Nicholas Ho
 
|length=(20,14)|name=|wide=N|author=Nicholas Ho
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">2-cycles in two opposite dedges (in the M ring)</span>==
==2-cycles in two opposite dedges (in the M ring)==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Directly opposite</span>===
===Directly opposite===
 
 
[[Image:A2spnM.png‎‎|110px|]]
 
[[Image:A2spnM.png‎‎|110px|]]
{{Alg5|wca=y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw
+
{{Alg6|wca=y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw
 
|sign=y l' u' 2R f 2R f' 2R2 u l u' 2R d
 
|sign=y l' u' 2R f 2R f' 2R2 u l u' 2R d
 
|length=(13,12)|name=|wide=N|author=Christopher Mowla
 
|length=(13,12)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' r' U r' U r U2 r U r' U r' U'
+
{{Alg6|wca=r' U' r' U r' U r U2 r U r' U r' U'
 
|sign=2R' U' 2R' U 2R' U 2R U2 2R U 2R' U 2R' U'
 
|sign=2R' U' 2R' U 2R' U 2R U2 2R U 2R' U 2R' U'
 
|length=(15,14)|name=|wide=N|author=Ben Whitmore
 
|length=(15,14)|name=|wide=N|author=Ben Whitmore
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
 
}}
 
}}
{{Alg5|wca=U' Rw' U r' U' Rw r U' R' U r' U' R U2
+
{{Alg6|wca=U' Rw' U r' U' Rw r U' R' U r' U' R U2
 
|sign=U' r' U 2R' U' r 2R U' R' U 2R' U' R U2
 
|sign=U' r' U 2R' U' r 2R U' R' U 2R' U' R U2
 
|length=(15,14)|name=|wide=N|author=François Courtès
 
|length=(15,14)|name=|wide=N|author=François Courtès
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
===Opposite/Diagonal===
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Opposite/Diagonal</span>===
 
[[Image:OppdiagnM.PNG|110px|]]
 
[[Image:OppdiagnM.PNG|110px|]]
 
*These are the same as the one dedge flips but without first and last moves.
 
*These are the same as the one dedge flips but without first and last moves.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=U r' U' B2 U r U r' U2 B2
{{Alg5|wca=U r' U' B2 U r U r' U2 B2
 
 
|sign=U 2R' U' B2 U 2R U 2R' U2 B2
 
|sign=U 2R' U' B2 U 2R U 2R' U2 B2
 
|length=(13,10)|name=|wide=N|author=Christopher Mowla
 
|length=(13,10)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U' r' U B2 U' r U' r' U2 B2
+
{{Alg6|wca=U' r' U B2 U' r U' r' U2 B2
 
|sign=U' 2R' U B2 U' 2R U' 2R' U2 B2
 
|sign=U' 2R' U B2 U' 2R U' 2R' U2 B2
 
|length=(13,10)|name=|wide=N|author=Christopher Mowla
 
|length=(13,10)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=3Dw l U' R2 U l' D l U' D' R2 y
+
{{Alg6|wca=3Dw l U' R2 U l' D l U' D' R2 y
 
|sign=3d 2L U' R2 U 2L' D 2L U' D' R2 y
 
|sign=3d 2L U' R2 U 2L' D 2L U' D' R2 y
 
|length=(13,11)|name=|wide=N|author=Christopher Mowla
 
|length=(13,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=U' r' U B2 U' r U B2 D2 l D2
+
{{Alg6|wca=U' r' U B2 U' r U B2 D2 l D2
 
|sign=U' 2R' U B2 U' 2R U B2 D2 2L D2
 
|sign=U' 2R' U B2 U' 2R U B2 D2 2L D2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=3Dw l U' R2 U l' U' D2 y l D2 F2
+
{{Alg6|wca=3Dw l U' R2 U l' U' D2 y l D2 F2
 
|sign=3d 2L U' R2 U 2L' U' D2 y 2L D2 F2
 
|sign=3d 2L U' R2 U 2L' U' D2 y 2L D2 F2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=x' U2 l U2 r' U2 r U2 l' F2 r F2 x
+
{{Alg6|wca=x' U2 l U2 r' U2 r U2 l' F2 r F2 x
 
|sign=x' U2 2L U2 2R' U2 2R U2 2L' F2 2R F2 x
 
|sign=x' U2 2L U2 2R' U2 2R U2 2L' F2 2R F2 x
 
|length=(17,11)|name=|wide=N|author=|url=
 
|length=(17,11)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r U2 l' U2 l U2 r' F2 r F2
+
{{Alg6|wca=U2 r U2 l' U2 l U2 r' F2 r F2
 
|sign=U2 2R U2 2L' U2 2L U2 2R' F2 2R F2
 
|sign=U2 2R U2 2L' U2 2L U2 2R' F2 2R F2
 
|length=(17,11)|name=|wide=N|author=|url=
 
|length=(17,11)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=U2 r U2 l' U2 l U2 r' B2 l B2
+
{{Alg6|wca=U2 r U2 l' U2 l U2 r' B2 l B2
 
|sign=U2 2R U2 2L' U2 2L U2 2R' B2 2L B2
 
|sign=U2 2R U2 2L' U2 2L U2 2R' B2 2L B2
 
|length=(17,11)|name=|wide=N|author=|url=
 
|length=(17,11)|name=|wide=N|author=|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">4-cycles in opposite dedges</span>==
==4-cycles in opposite dedges==
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Checkerboard</span>===
===Checkboard===
 
 
[[Image:Cchkbrd.png|110px|]]
 
[[Image:Cchkbrd.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=Rw2 U2 r U2 Rw2
{{Alg5|wca=Rw2 U2 r U2 Rw2
 
 
|sign=r2 U2 2R U2 r2
 
|sign=r2 U2 2R U2 r2
 
|length=(9,5)|name=|wide=N|author=Marc Waterman
 
|length=(9,5)|name=|wide=N|author=Marc Waterman
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
===<span style="font-family:Georgia;color:rgb(0,200,0);">Bowtie/Hourglass</span>===
===Bowtie/Hourglass===
 
 
[[Image:Chrglass.png|110px|]]
 
[[Image:Chrglass.png|110px|]]
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
*Note: Since this is a 4-cycle case, it and its inverse case are not the same.  One can simply apply the inverse of this case's algorithms to get algorithms for its inverse case.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=(y L' U B' Rw2 U2) r' (U2 Rw2 B U' L y')
{{Alg5|wca=(y L' U B' Rw2 U2) r' (U2 Rw2 B U' L y')
 
 
|sign=(y L' U B' r2 U2) 2R' (U2 r2 B U' L y')
 
|sign=(y L' U B' r2 U2) 2R' (U2 r2 B U' L y')
 
|length=(15,11)|name=|wide=N|author=|url=
 
|length=(15,11)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=(y L F' U Rw2 F2) r (F2 Rw2 U' F L' y')
+
{{Alg6|wca=(y L F' U Rw2 F2) r (F2 Rw2 U' F L' y')
 
|sign=(y L F' U r2 F2) 2R (F2 r2 U' F L' y')
 
|sign=(y L F' U r2 F2) 2R (F2 r2 U' F L' y')
 
|length=(15,11)|name=|wide=N|author=|url=
 
|length=(15,11)|name=|wide=N|author=|url=
 
}}
 
}}
{{Alg5|wca=r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x
+
{{Alg6|wca=r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x
 
|sign=2R U2 2R' U2 x' U2 2R U2 2R2 U2 2R' U2 2R' x
 
|sign=2R U2 2R' U2 x' U2 2R U2 2R2 U2 2R' U2 2R' x
 
|length=(19,12)|name=|wide=N|author=Nicholas Ho
 
|length=(19,12)|name=|wide=N|author=Nicholas Ho
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r2 U2 r U2 x' D2 r' U2 r D2 r' U2 r' x
+
{{Alg6|wca=r2 U2 r U2 x' D2 r' U2 r D2 r' U2 r' x
 
|sign=2R2 U2 2R U2 x' D2 2R' U2 2R D2 2R' U2 2R' x
 
|sign=2R2 U2 2R U2 x' D2 2R' U2 2R D2 2R' U2 2R' x
 
|length=(19,12)|name=|wide=N|author=Kenneth Gustavsson
 
|length=(19,12)|name=|wide=N|author=Kenneth Gustavsson
 
|url=
 
|url=
 
}}
 
}}
 +
{{br|b=1}}
  
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">Algorithms which do not preserve F3L OR the centers</span>=
 
 
=Algorithms which do not preserve F3L OR the centers=
 
 
*These algorithms are least practical when it comes to use of parity algorithms, and therefore they are mentioned here for theoretical purposes only.  They have fewer moves than any other OLL parity algorithm forms.
 
*These algorithms are least practical when it comes to use of parity algorithms, and therefore they are mentioned here for theoretical purposes only.  They have fewer moves than any other OLL parity algorithm forms.
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Single parity</span>==
==Single parity==
+
{{Alg6|wca=Rw2 U r' U' B2 U r U r' B2 Rw2
{{Alg5|wca=Rw2 U r' U' B2 U r U r' B2 Rw2
 
 
|sign=r2 U 2R' U' B2 U 2R U 2R' B2 r2
 
|sign=r2 U 2R' U' B2 U 2R U 2R' B2 r2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U' r' U B2 U' r U' r' B2 Rw2
+
{{Alg6|wca=Rw2 U' r' U B2 U' r U' r' B2 Rw2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R' B2 r2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R' B2 r2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U f U' B2 U f' U l B2 Rw2
+
{{Alg6|wca=Rw2 U f U' B2 U f' U l B2 Rw2
 
|sign=r2 U 2F U' B2 U 2F' U 2L B2 r2
 
|sign=r2 U 2F U' B2 U 2F' U 2L B2 r2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=r' U' R U' r U2 r U2 r U' R' U' r'
+
{{Alg6|wca=r' U' R U' r U2 r U2 r U' R' U' r'
 
|sign=2R' U' R U' 2R U2 2R U2 2R U' R' U' 2R'
 
|sign=2R' U' R U' 2R U2 2R U2 2R U' R' U' 2R'
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' R U r' U2 r' U2 r' U R' U' r'
+
{{Alg6|wca=r' U' R U r' U2 r' U2 r' U R' U' r'
 
|sign=2R' U' R U 2R' U2 2R' U2 2R' U R' U' 2R'
 
|sign=2R' U' R U 2R' U2 2R' U2 2R' U R' U' 2R'
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|length=(15,13)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' R U r' F2 U2 r U2 F2 r' U R' U' r'
+
{{Alg6|wca=r' U' R U r' F2 U2 r U2 F2 r' U R' U' r'
 
|sign=2R' U' R U 2R' F2 U2 2R U2 F2 2R' U R' U' 2R'
 
|sign=2R' U' R U 2R' F2 U2 2R U2 F2 2R' U R' U' 2R'
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|length=(19,15)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Double parity</span>==
==Double parity==
+
{{Alg6|wca=r 3Dw r' 3Dw F2 3Dw' r 3Dw l' F2 l
{{Alg5|wca=r 3Dw r' 3Dw F2 3Dw' r 3Dw l' F2 l
 
 
|sign=2R 3d 2R' 3d F2 3d' 2R 3d 2L' F2 2L
 
|sign=2R 3d 2R' 3d F2 3d' 2R 3d 2L' F2 2L
 
|length=(13,11)|name=|wide=N|author=Christopher Mowla
 
|length=(13,11)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=Rw U R B R' l Fw2 r' Fw2 U' Rw2 x
+
{{Alg6|wca=Rw U R B R' l Fw2 r' Fw2 U' Rw2 x
 
|sign=r U R B R' 2L f2 2R' f2 U' r2 x
 
|sign=r U R B R' 2L f2 2R' f2 U' r2 x
 
|length=(14,11)|name=|wide=N|author=Bruce Norskog
 
|length=(14,11)|name=|wide=N|author=Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-536776
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-536776
 
}}
 
}}
{{Alg5|wca=Rw U R B l Fw2 r' Fw2 R' U' Rw2 x
+
{{Alg6|wca=Rw U R B l Fw2 r' Fw2 R' U' Rw2 x
 
|sign=r U R B 2L f2 2R' f2 R' U' r2 x
 
|sign=r U R B 2L f2 2R' f2 R' U' r2 x
 
|length=(14,11)|name=|wide=N|author=Bruce Norskog
 
|length=(14,11)|name=|wide=N|author=Bruce Norskog
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-536776
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-536776
 
}}
 
}}
{{Alg5|wca=Rw2 U r' U' B2 U r U r B2 Rw2
+
{{Alg6|wca=Rw2 U r' U' B2 U r U r B2 Rw2
 
|sign=r2 U 2R' U' B2 U 2R U 2R B2 r2
 
|sign=r2 U 2R' U' B2 U 2R U 2R B2 r2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U' r' U B2 U' r U' r B2 Rw2
+
{{Alg6|wca=Rw2 U' r' U B2 U' r U' r B2 Rw2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R B2 r2
 
|sign=r2 U' 2R' U B2 U' 2R U' 2R B2 r2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw2 U f U' B2 U f' U l' B2 Rw2
+
{{Alg6|wca=Rw2 U f U' B2 U f' U l' B2 Rw2
 
|sign=r2 U 2F U' B2 U 2F' U 2L' B2 r2
 
|sign=r2 U 2F U' B2 U 2F' U 2L' B2 r2
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|length=(15,11)|name=|wide=N|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/#post-527952
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2
+
{{Alg6|wca=Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2
 
|sign=r U2 r U2 r U2 r2 U' R U r2 U R U' r2
 
|sign=r U2 r U2 r U2 r2 U' R U r2 U R U' r2
 
|length=(21,15)|name=|wide=Y|author=Christopher Mowla
 
|length=(21,15)|name=|wide=Y|author=Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-604444
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-604444
 
}}
 
}}
{{Alg5|wca=Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw'
+
{{Alg6|wca=Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw'
 
|sign=r U2 r2 U' r' U2 r U2 r' U' r2 U' R2 U' r'
 
|sign=r U2 r2 U' r' U2 r U2 r' U' r2 U' R2 U' r'
 
|length=(21,15)|name=|wide=Y|author=Kåre Krig & Christopher Mowla
 
|length=(21,15)|name=|wide=Y|author=Kåre Krig & Christopher Mowla
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-604444
 
|url=https://www.speedsolving.com/forum/threads/new-4x4-parity-algs-using-r-rw-u.30127/#post-604444
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Either single parity or double parity</span>==
==Either single parity or double parity==
+
*The following list of algorithms can be considered either <i>single parity</i> or <i>double parity</i>.  Just exchange the last move Rw' with Lw', Rw with Lw, and so forth.
*The following list of algorithms can be considered either <b>single parity</b> or <b>double parity</b>.  Just exchange the last move Rw' with Lw', Rw with Lw, and so forth.
+
{{br|b=1}}
 
+
{{Alg6|wca=Rw' U' R' U' Rw F' R' F' Rw'
 
 
{{Alg5|wca=Rw' U' R' U' Rw F' R' F' Rw'
 
 
|sign=r' U' R' U' r F' R' F' r'
 
|sign=r' U' R' U' r F' R' F' r'
 
|length=(9,9)|name=|wide=Y|author=Christopher Mowla
 
|length=(9,9)|name=|wide=Y|author=Christopher Mowla
Line 9,148: Line 9,450:
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-809227
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-809227
 
}}
 
}}
{{Alg5|wca=Rw F R F Lw' B R B Lw
+
{{Alg6|wca=Rw F R F Lw' B R B Lw
 
|sign=r F R F l' B R B l
 
|sign=r F R F l' B R B l
 
|length=(9,9)|name=|wide=Y|author=David Gilday
 
|length=(9,9)|name=|wide=Y|author=David Gilday
Line 9,154: Line 9,456:
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-11#post-873559
 
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-11#post-873559
 
}}
 
}}
{{Alg5|wca=Rw' U' R U' Rw F' R F' Rw'
+
{{Alg6|wca=Rw' U' R U' Rw F' R F' Rw'
 
|sign=r' U' R U' r F' R F' r'
 
|sign=r' U' R U' r F' R F' r'
 
|length=(9,9)|name=|wide=Y|author=Christopher Mowla
 
|length=(9,9)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U' r' D' R D' Rw
+
{{Alg6|wca=Rw U' R U' r' D' R D' Rw
 
|sign=r U' R U' 2R' D' R D' r
 
|sign=r U' R U' 2R' D' R D' r
 
|length=(9,9)|name=|wide=N|author=Christopher Mowla
 
|length=(9,9)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R' U Rw U F2 U Rw'
+
{{Alg6|wca=Rw' U R' U Rw U F2 U Rw'
 
|sign=r' U R' U r U F2 U r'
 
|sign=r' U R' U r U F2 U r'
 
|length=(10,9)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,9)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R U' Rw' D' R2 D' Lw
+
{{Alg6|wca=Rw U' R U' Rw' D' R2 D' Lw
 
|sign=r U' R U' r' D' R2 D' l
 
|sign=r U' R U' r' D' R2 D' l
 
|length=(10,9)|name=|wide=Y|author=Christopher Mowla
 
|length=(10,9)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' F2 U' r B' R B' Lw'
+
{{Alg6|wca=Rw' U' F2 U' r B' R B' Lw'
 
|sign=r' U' F2 U' 2R B' R B' l'
 
|sign=r' U' F2 U' 2R B' R B' l'
 
|length=(10,9)|name=|wide=N|author=Christopher Mowla
 
|length=(10,9)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' L U' F2 Lw U' R U' Rw'
+
{{Alg6|wca=Rw U' L U' F2 Lw U' R U' Rw'
 
|sign=r U' L U' F2 l U' R U' r'
 
|sign=r U' L U' F2 l U' R U' r'
 
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
 
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
}}
 
}}
{{Alg5|wca=Rw U' L' U' F2 l U L U Rw'
+
{{Alg6|wca=Rw U' L' U' F2 l U L U Rw'
 
|sign=r U' L' U' F2 2L U L U r'
 
|sign=r U' L' U' F2 2L U L U r'
 
|length=(11,10)|name=|wide=N|author=Christopher Mowla
 
|length=(11,10)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' L' U' Rw F2 U L U Rw
+
{{Alg6|wca=Rw' U' L' U' Rw F2 U L U Rw
 
|sign=r' U' L' U' r F2 U L U r
 
|sign=r' U' L' U' r F2 U L U r
 
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
 
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U' L' U' B2 Rw' B R B Rw
+
{{Alg6|wca=Rw' U' L' U' B2 Rw' B R B Rw
 
|sign=r' U' L' U' B2 r' B R B r
 
|sign=r' U' L' U' B2 r' B R B r
 
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
 
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U R2 U Rw F2 U L' U Rw
+
{{Alg6|wca=Rw' U R2 U Rw F2 U L' U Rw
 
|sign=r' U R2 U r F2 U L' U r
 
|sign=r' U R2 U r F2 U L' U r
 
|length=(12,10)|name=|wide=Y|author=Christopher Mowla
 
|length=(12,10)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U F' U l U2 F' U2 F Rw'
+
{{Alg6|wca=Rw' U F' U l U2 F' U2 F Rw'
 
|sign=r' U F' U 2L U2 F' U2 F r'
 
|sign=r' U F' U 2L U2 F' U2 F r'
 
|length=(12,10)|name=|wide=N|author=Christopher Mowla
 
|length=(12,10)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw U' R' U' Rw' D' L D L' D' Lw
+
{{Alg6|wca=Rw U' R' U' Rw' D' L D L' D' Lw
 
|sign=r U' R' U' r' D' L D L' D' l
 
|sign=r U' R' U' r' D' L D L' D' l
 
|length=(11,11)|name=|wide=Y|author=Christopher Mowla
 
|length=(11,11)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw B U F' R b' M R E' R Bw
+
{{Alg6|wca=Rw B U F' R b' M R E' R Bw
 
|sign=r B U F' R 2B' m R e' R b
 
|sign=r B U F' R 2B' m R e' R b
 
|length=(11,11)|name=|wide=N|author=Bruce Norskog & Christopher Mowla
 
|length=(11,11)|name=|wide=N|author=Bruce Norskog & Christopher Mowla
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-757595
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-757595
 
}}
 
}}
{{Alg5|wca=Rw U R' U R r' U2 B' L' B' Rw'
+
{{Alg6|wca=Rw U R' U R r' U2 B' L' B' Rw'
 
|sign=r U R' U R 2R' U2 B' L' B' r'
 
|sign=r U R' U R 2R' U2 B' L' B' r'
 
|length=(12,11)|name=|wide=N|author=Christopher Mowla
 
|length=(12,11)|name=|wide=N|author=Christopher Mowla
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
}}
 
}}
{{Alg5|wca=l' B' u B' D2 B u' B' l D2 l'
+
{{Alg6|wca=l' B' u B' D2 B u' B' l D2 l'
 
|sign=2L' B' 2U B' D2 B 2U' B' 2L D2 2L'
 
|sign=2L' B' 2U B' D2 B 2U' B' 2L D2 2L'
 
|length=(13,11)|name=|wide=N|author=Christopher Mowla
 
|length=(13,11)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw F U' R U Rw' F U R F' U Rw
+
{{Alg6|wca=Rw F U' R U Rw' F U R F' U Rw
 
|sign=r F U' R U r' F U R F' U r
 
|sign=r F U' R U r' F U R F' U r
 
|length=(12,12)|name=|wide=Y|author=Christopher Mowla
 
|length=(12,12)|name=|wide=Y|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=Rw' U F' L F Rw F R B' E y B Rw'
+
{{Alg6|wca=Rw' U F' L F Rw F R B' E y B Rw'
 
|sign=r' U F' L F r F R B' e y B r'
 
|sign=r' U F' L F r F R B' e y B r'
 
|length=(12,12)|name=|wide=Y|author=Christopher Mowla
 
|length=(12,12)|name=|wide=Y|author=Christopher Mowla
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
}}
 
}}
{{Alg5|wca=Rw S' F L F' U b' U E M U Bw
+
{{Alg6|wca=Rw S' F L F' U b' U E M U Bw
 
|sign=r s' F L F' U 2B' U e m U b
 
|sign=r s' F L F' U 2B' U e m U b
 
|length=(12,12)|name=|wide=N|author=Bruce Norskog & Christopher Mowla
 
|length=(12,12)|name=|wide=N|author=Bruce Norskog & Christopher Mowla
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-757595
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-757595
 
}}
 
}}
{{Alg5|wca=Rw' U' F R' F' Rw F' U' F2 R U Rw'
+
{{Alg6|wca=Rw' U' F R' F' Rw F' U' F2 R U Rw'
 
|sign=r' U' F R' F' r F' U' F2 R U r'
 
|sign=r' U' F R' F' r F' U' F2 R U r'
 
|length=(13,12)|name=|wide=Y|author=Christopher Mowla
 
|length=(13,12)|name=|wide=Y|author=Christopher Mowla
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
|url=http://www.speedsolving.com/forum/threads/4x4x4-edge-parity-is-there-a-shorter-alg-that-doesnt-preserve-corners.26564/page-2#post-808368
 
}}
 
}}
 
+
{{br|b=1}}
 
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">2-cycles</span>==
==2-cycles==
+
*Although the following list of algorithms is not "OLL parity", where dedge preservation is important, they are the briefest 2-cycle algorithms yet to be found. They do not preserve F3L or the centers.
*Although the following list of algorithms is not "OLL parity", where dedge preservation is important, they are the briefest 2-cycle algorithms yet to be found. They do not preserve F3L or the centers.  
 
 
*These algorithms are nothing more than 2-cycle algorithms which don't preserve centers with beginning and ending outer layer turns omitted.
 
*These algorithms are nothing more than 2-cycle algorithms which don't preserve centers with beginning and ending outer layer turns omitted.
 
+
{{br|b=1}}
 
+
{{Alg6|wca=r' U' B2 U r U r'
{{Alg5|wca=r' U' B2 U r U r'
 
 
|sign=2R' U' B2 U 2R U 2R'
 
|sign=2R' U' B2 U 2R U 2R'
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U B2 U' r U' r'
+
{{Alg6|wca=r' U B2 U' r U' r'
 
|sign=2R' U B2 U' 2R U' 2R'
 
|sign=2R' U B2 U' 2R U' 2R'
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U L2 U' r D' r'
+
{{Alg6|wca=r' U L2 U' r D' r'
 
|sign=2R' U L2 U' 2R D' 2R'
 
|sign=2R' U L2 U' 2R D' 2R'
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
{{Alg5|wca=r' U' R2 U r D r'
+
{{Alg6|wca=r' U' R2 U r D r'
 
|sign=2R' U' R2 U 2R D 2R'
 
|sign=2R' U' R2 U 2R D 2R'
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|length=(8,7)|name=|wide=N|author=Christopher Mowla
 
|url=
 
|url=
 
}}
 
}}
 
+
{{br|b=1}}
 
+
<div style="color:rgb(229,148,0);">
 
+
=<span style="font-family:Georgia;color:rgb(0,200,0);">External Links</span>=
=External Links=
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">PLL parity algorithms</span>==
==PLL parity algorithms==
+
*[https://www.reddit.com/r/Cubers/comments/d1x3kp/10_ways_to_swap_two_corners_on_a_4x4x4/ 10 Ways to Swap Two Corners on a 4x4x4]
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
+
*[http://www.speedcubedb.com/a/4x4/PLLParity Speedcubedb PLL parity algs]
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/30854
+
*[https://web.archive.org/web/20191022195817/https://pdfmage.org/dl/33d2cf68-c11c-4334-ac4b-180e34b89fee.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf Re: 4*4 PLL Alg 5 moves cancelled (Yahoo Groups)]
 +
*[https://web.archive.org/web/20191022180641/https://pdfmage.org/dl/c1e593ff-c3f6-4fbb-b6e8-a6f298c9175f.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf Interesting 4*4 PLL Alg (Yahoo Groups)]
 
*http://frederickbadie.free.fr/444PLLparity.html
 
*http://frederickbadie.free.fr/444PLLparity.html
 
*https://www.speedsolving.com/forum/showthread.php?26357-PURE-Corner-swap-parity-algorithms
 
*https://www.speedsolving.com/forum/showthread.php?26357-PURE-Corner-swap-parity-algorithms
 
*https://www.speedsolving.com/forum/showthread.php?23182-full-4x4-pll
 
*https://www.speedsolving.com/forum/showthread.php?23182-full-4x4-pll
 
+
*https://www.speedcubingtips.eu/4x4x4-pll-et-parites/
==OLL parity algorithms==
+
{{br|b=1}}
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/35545
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">OLL parity algorithms</span>==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/29327
+
*[http://www.speedcubedb.com/a/4x4/OLLParity Speedcubedb OLL Parity algs]
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/28904
+
*[https://web.archive.org/web/20191022181706/https://pdfmage.org/dl/9b81d780-1a41-4545-b303-2f5f7e0bfc8f.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf Both 4x4x4 parities in one (Yahoo Groups)]
 +
*[https://web.archive.org/web/20191022185029/https://pdfmage.org/dl/7fa559ce-6a73-42fd-b55b-098b0a6096c7.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf Some tricks for 4x4x4 (Yahoo Groups)]
 +
*[https://web.archive.org/web/20191022182233/https://pdfmage.org/dl/cc327e46-f9a4-471f-98d4-3b05ea53644e.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf double parity 4x4 (Yahoo Groups)]
 
*http://www.speedsolving.com/forum/showthread.php?11311-4x4x4-OP-DP-algorithms-%28more-finger-friendly%29
 
*http://www.speedsolving.com/forum/showthread.php?11311-4x4x4-OP-DP-algorithms-%28more-finger-friendly%29
 
*http://www.speedsolving.com/forum/showthread.php?15614-Odd-parity-Algorithms-%28specifically-single-edge-quot-flip-quot-%29
 
*http://www.speedsolving.com/forum/showthread.php?15614-Odd-parity-Algorithms-%28specifically-single-edge-quot-flip-quot-%29
Line 9,303: Line 9,606:
 
*http://www.mementoslangues.fr/CubeDesign/4xCubes/DoubleMidgeFlip.pdf
 
*http://www.mementoslangues.fr/CubeDesign/4xCubes/DoubleMidgeFlip.pdf
 
*http://apelgam.se/Rubik/4x4parity/
 
*http://apelgam.se/Rubik/4x4parity/
 
+
*https://www.speedcubingtips.eu/4x4x4-oll-et-parites/
==Supercube parity algorithms==
+
{{br|b=1}}
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/21622
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Supercube parity algorithms</span>==
 +
*[https://web.archive.org/web/20191022190525/https://pdfmage.org/dl/1e261a42-8b3e-4e03-b347-92335667a2dc.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf 5x5x5 help needed (Yahoo Groups)]
 
*http://www.speedsolving.com/forum/showthread.php?4659-4x4-algorithm
 
*http://www.speedsolving.com/forum/showthread.php?4659-4x4-algorithm
 
*http://www.speedsolving.com/forum/showthread.php?37308-Is-a-SuperCube-Safe-Single-Dedge-Flip-Algorithm-Possible-in-lt-U-Rw-gt
 
*http://www.speedsolving.com/forum/showthread.php?37308-Is-a-SuperCube-Safe-Single-Dedge-Flip-Algorithm-Possible-in-lt-U-Rw-gt
 
*http://www.speedsolving.com/forum/showthread.php?26622-God-s-algorithm-discovered-for-OLL-parity-edge-flip-%28theory%29
 
*http://www.speedsolving.com/forum/showthread.php?26622-God-s-algorithm-discovered-for-OLL-parity-edge-flip-%28theory%29
 
+
{{br|b=1}}
==OLL parity algorithms which do not preserve F3L==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">OLL parity algorithms which do not preserve F3L</span>==
 
*http://www.speedsolving.com/forum/showthread.php?37962-Fixing-4x4x4-orientation-parity-earlier-than-usual
 
*http://www.speedsolving.com/forum/showthread.php?37962-Fixing-4x4x4-orientation-parity-earlier-than-usual
 
*http://www.speedsolving.com/forum/showthread.php?26564-4x4x4-edge-parity-is-there-a-shorter-alg-that-doesn-t-preserve-corners
 
*http://www.speedsolving.com/forum/showthread.php?26564-4x4x4-edge-parity-is-there-a-shorter-alg-that-doesn-t-preserve-corners
 
*http://www.speedsolving.com/forum/showthread.php?17839-WANTED-New-Dedge-Flip-Algorithm!
 
*http://www.speedsolving.com/forum/showthread.php?17839-WANTED-New-Dedge-Flip-Algorithm!
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=9502
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=9502
 
+
{{br|b=1}}
==K4 method parity algorithms==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">K4 method parity algorithms</span>==
 
*http://tomas.rokicki.com/ell4x4.html
 
*http://tomas.rokicki.com/ell4x4.html
 
*https://www.speedsolving.com/forum/showthread.php?708-A-Collection-of-Algorithms&p=811284&viewfull=1#post811284
 
*https://www.speedsolving.com/forum/showthread.php?708-A-Collection-of-Algorithms&p=811284&viewfull=1#post811284
 
+
{{br|b=1}}
==Cage method parity algorithms==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Cage method parity algorithms</span>==
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=6552
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=6552
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=7140
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=7140
 
+
{{br|b=1}}
==Comprehending and making your own parity algorithms==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Comprehending and making your own parity algorithms</span>==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/12909
+
*[https://web.archive.org/web/20191022182704/https://pdfmage.org/dl/ba673e7c-4bb9-43ec-842a-171b288f6390.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf 5x5x5 help! (Yahoo Groups)]
 
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=9720
 
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=9720
 
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=995
 
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=995
Line 9,331: Line 9,635:
 
*http://www.speedsolving.com/forum/showthread.php?22969-Methods-for-Forming-2-Cycle-Odd-Parity-Algorithms-for-Big-Cubes
 
*http://www.speedsolving.com/forum/showthread.php?22969-Methods-for-Forming-2-Cycle-Odd-Parity-Algorithms-for-Big-Cubes
 
*http://www.speedsolving.com/forum/showthread.php?21725-New-Two-Corner-Swap-Algorithm-Technique-for-Big-Even-Cubes-%28PLL-Parity%29
 
*http://www.speedsolving.com/forum/showthread.php?21725-New-Two-Corner-Swap-Algorithm-Technique-for-Big-Even-Cubes-%28PLL-Parity%29
 +
*[https://www.reddit.com/r/Cubers/comments/d1x3kp/10_ways_to_swap_two_corners_on_a_4x4x4/ 10 Ways to Swap Two Corners on a 4x4x4]
 
*http://www.speedsolving.com/forum/showthread.php?43745-4x4-fixing-one-edge-parity-without-algorithms
 
*http://www.speedsolving.com/forum/showthread.php?43745-4x4-fixing-one-edge-parity-without-algorithms
 
*https://www.speedsolving.com/forum/threads/help-in-solving-4%C3%974%C3%974-parities-intuitively.13572/
 
*https://www.speedsolving.com/forum/threads/help-in-solving-4%C3%974%C3%974-parities-intuitively.13572/
Line 9,336: Line 9,641:
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=31410
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=31410
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=32717
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=32717
 
+
{{br|b=1}}
==General parity theory==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">General parity theory</span>==
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=31472
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=31472
 
*http://hlavolam.maweb.eu/parity-problem
 
*http://hlavolam.maweb.eu/parity-problem
Line 9,348: Line 9,653:
 
*https://www.speedsolving.com/forum/showthread.php?21045-Difference-between-OLL-and-PLL-parity-on-4x4
 
*https://www.speedsolving.com/forum/showthread.php?21045-Difference-between-OLL-and-PLL-parity-on-4x4
 
*https://www.speedsolving.com/forum/showthread.php?52852-Can-all-parity-be-explained
 
*https://www.speedsolving.com/forum/showthread.php?52852-Can-all-parity-be-explained
 
+
{{br|b=1}}
==Preventing/Avoiding parity==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Preventing/Avoiding parity</span>==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/10755
+
*[https://web.archive.org/web/20191022182939/https://pdfmage.org/dl/5b95b875-8836-49b5-9508-a39930a30d2e.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf Challenge for those who enjoy the 4x4x4 (Yahoo Groups)]
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=7366
 
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=7366
 
*https://www.speedsolving.com/forum/showthread.php?892-avoiding-4x4-pairity-problems
 
*https://www.speedsolving.com/forum/showthread.php?892-avoiding-4x4-pairity-problems
Line 9,357: Line 9,662:
 
*https://www.speedsolving.com/forum/threads/avoiding-parity-problems-in-big-cubes.4894/
 
*https://www.speedsolving.com/forum/threads/avoiding-parity-problems-in-big-cubes.4894/
 
*https://www.speedsolving.com/forum/threads/parity-error-prediction-and-new-simulator.306/
 
*https://www.speedsolving.com/forum/threads/parity-error-prediction-and-new-simulator.306/
 
+
{{br|b=1}}
==Miscellaneous==
+
==<span style="font-family:Georgia;color:rgb(0,200,0);">Miscellaneous</span>==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/12612
+
<div "class="noprint">
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/10119
+
*[https://web.archive.org/web/20191022183329/https://pdfmage.org/dl/993319a5-c490-4b6d-bd5f-ca46d7d6888d.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf (No title) (Yahoo Groups)]
 +
*[https://web.archive.org/web/20191022183556/https://pdfmage.org/dl/431f5d26-4116-4694-9735-28f9cfc4602c.pdf/speed%20solving%20rubik's%20cube%20-%20all%20about%20speed%20solving%20the%20rubik's%20cube%20-%20yahoo%20groups.pdf The corner cycle alg is no longer "magical" (Yahoo Groups)]
 
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=9133
 
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=9133
*http://www.mementoslangues.fr (Go to "Cube Design")
+
*http://www.mementoslangues.fr/CubeDesign/
 +
</div>
 +
</ul></div>

Latest revision as of 09:42, 22 February 2024

  • Click on the speedsolving.com cube logo SS Cube Logo HD Tiny.png to the left the algorithms to see them executed with Lucas Garron's online cube simulator.
  • The Printable version of this page is now actually printable (and in color, if desired).