Speedsolving.com Wiki - User contributions [en]

Twisty Corners of Last Layer

2020-01-04T06:32:22Z

Oyyq99999: Undo revision 32640 by Oyyq99999 (talk)

{{Method Infobox
|name=TCLL (2x2x2)
|image=
|proposers=[[Robert Yau]]
[[Christopher Olson]]
|year=2013
|anames
|variants=[[LBL]]
[[CLL]]
|steps=2
|algs=128 (86 for only TCLL)
|moves=<15
|purpose=
* [[Speedsolving]]
}}
'''TCLL''' or '''Twisty Corners of Last Layer''' is an advanced 2x2 method proposed in 2013 by [[Robert Yau]] and [[Christopher Olson|Chris Olson]] based off a study into [http://www.speedsolving.com/forum/threads/rofl-method.43898/ RoFL] (ROtten First Layer) by [[Stefan Pochmann]]. It is efficient and is very good for those who can 1-look their 2x2 solves and cancel into algorithms. It can be divided into 3 subsets: regular [[CLL]], '''TCLL-''' (where the misoriented corner in DR faces to the right) and '''TCLL+''' (where the corner faces to the front). There are 43 algorithms for each TCLL set and 42 for the CLL.

==Steps==
#Solve a layer (one corner can be twisted in place)
#TCLL

==Pros==
*Can easily be 1-looked in almost all cases fairly easily.
*Lots of cancellations can be formed between the layer and the algorithm
*Building a layer with a twisted corner is much shorter than building a full layer
*Can have ridiculously easy solves

==Cons==
*It is not generally recommended to use TCLL as a stand alone method
*Beginners may find it difficult to 1-look solves and take advantage of the cancellations
* Approximately 2 Times more algorithms than CLL, EG-1 or EG-2

==Example Solves==
#R' F' R2 F R' U' F2 R' U'
#*x2 y' (Canceling moves instead of doing U2 R U2 R) U2 F R F' R U
#F' R U' R' U F2 R' U2 R2
#*y' L' U' L' F' L F U2 L' U2 L
#U R' F R' U2 R F' R U'
#*z2 U' (Canceling moves instead of doing R U' R') R U2 R' U2 R U2 R' U
#R' F U R F2 R U' R2 U
#*x L2 U2 R U R' U' R U2 R' F' R U R' F'
#U2 F2 U' F U' F' R' F' U2
#*x' y' U F2 R U2 R' U R' F R F' R U' R'
#U R2 F' U R U2 R F2 U2
#*x' U2 R y U' F R' F' R2 U R'
#U2 F' R' U' F2 U' R2 U R2
#*x2 U F' R F' R U R2 U' R U R'

==See Also==
*[[CLL]]
*[[EG]]

==External Links==
*[https://www.speedsolving.com/forum/threads/tcll-2x2-method.44438/ TCLL proposal thread]
*[https://cyotheking.squarespace.com/tcll-1/ Chris Olson's TCLL- page on his website]
*[https://cyotheking.squarespace.com/tcll/ Chris Olson's TCLL+ page on his website]
*[http://www.speedsolving.com/forum/threads/rofl-method.43898/ Stefan's RoFL Thread]
*[http://www.speedsolving.com/forum/threads/all-of-tcll-sub-1.44955/ Chris Olson Sub-1s all TCLL+]

[[Category:Acronyms]]
[[Category:2x2x2]]
[[Category:2x2x2 methods]]
[[Category:2x2x2 speedsolving methods]]
[[Category:2x2x2 substeps]]

Template:Regularcubics

2018-11-09T08:56:24Z

Oyyq99999:

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! colspan="5" | Regular cubic twisty puzzles
|-
| style="background-color:#c6efce;color:#006100;" | <center>[[0x0x0 Cube|0x0x0]]</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[1x1x1 Cube|1x1x1]]</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[2x2x2 Cube|2x2x2]] '''Pocket Cube'''</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[Rubik's Cube (puzzle type)|3x3x3]] '''Rubik's Cube'''</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[4x4x4 Cube|4x4x4]] '''Rubik's Revenge'''</center>
|-
| style="background-color:#c6efce;color:#006100;" | <center>[[5x5x5 Cube|5x5x5]] '''Professor's Cube'''</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[6x6x6 Cube|6x6x6]] '''V-Cube 6'''</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[7x7x7 Cube|7x7x7]] '''V-Cube 7'''</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[8x8x8 Cube|8x8x8]]</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[9x9x9 Cube|9x9x9]]</center>
|-
| style="background-color:#c6efce;color:#006100;" | <center>[[10x10x10 Cube|10x10x10]]</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[11x11x11 Cube|11x11x11]]</center>
| style="background-color:#dfdfff;color:#0131b7;" | <center>[[12x12x12 Cube|12x12x12]]</center>
| style="background-color:#c6efce;color:#006100;" | <center>[[13x13x13 Cube|13x13x13]] '''MoYu 13x13'''</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[14x14x14 Cube|14x14x14]]</center>
|-
| style="background-color:#c6efce;color:#0131b7;" | <center>[[15x15x15 Cube|15x15x15]] '''MoYu 15x15'''</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[16x16x16 Cube|16x16x16]]</center>
| style="background-color:#c6efce;color:#0131b7;" | <center>[[17x17x17 Cube|17x17x17]] '''Over The Top'''</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[18x18x18 Cube|18x18x18]]</center>
| style="background-color:#ffffdd;color:#8a7600;" | <center>[[19x19x19 Cube|19x19x19]] '''WuYa'''</center>
|-
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[20x20x20 Cube|20x20x20]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[21x21x21 Cube|21x21x21]]</center>
| style="background-color:#dfdfff;color:#0131b7;" | <center>[[22x22x22 Cube|22x22x22]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[23x23x23 Cube|23x23x23]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[24x24x24 Cube|24x24x24]]</center>
|-
| style="background-color:#ffffdd;color:#8a7600;" | <center>[[25x25x25 Cube|25x25x25]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[26x26x26 Cube|26x26x26]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[27x27x27 Cube|27x27x27]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[28x28x28 Cube|28x28x28]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[29x29x29 Cube|29x29x29]]</center>
|-
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[30x30x30 Cube|30x30x30]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[31x31x31 Cube|31x31x31]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[32x32x32 Cube|32x32x32]]</center>
| style="background-color:#dfdfff;color:#0131b7;" | <center>[[33x33x33 Cube|33x33x33]]</center>
| style="background-color:#ffc7ce;color:#9c0006;" | <center>[[34x34x34 Cube|34x34x34]]</center>
|-
! colspan="5" |
|-
| <center>Key:</center>
| style="background-color:#c6efce;color:#006100" | Mass-produced
| style="background-color:#dfdfff;color:#0131b7" | Exists, not manufactured
| style="background-color:#ffffdd;color:#8a7600" | Work in progress
| style="background-color:#ffc7ce;color:#9c0006" | <center>Not existent</center>
|}

Daniel Sheppard

2018-11-05T01:59:41Z

Oyyq99999: /* Beginnings (2008-2010) */

{{Infobox
|NAME=Daniel Sheppard
|IMAGE=Daniel Sheppard.jpg
|IMAGEYEAR=
|ALIASES=kinch2002
|COUNTRY=United Kingdom
|BIRTHDATE=7 February 1989
|AGE={{Age|1989|2|7}}
|JOBS=analyst
|YEARSACTIVE=2009-present
|ID=2009SHEP01
|FAMOUSFOR=Big cube BLD WRs, 2011 Clock World Champion
}}

'''Daniel Sheppard''' is a British speedcuber from Guildford, United Kingdom, mainly specializing in [[BLD|blindfolded solving]], but also in [[Clock]] and [[Fewest Moves]].

== Progression ==
=== Beginnings (2008-2010) ===
Daniel started cubing in 2008 while studying Mathematics at Oxford University and learned blindfold cubing from [[Macky|Macky's]] 3OP tutorial just before his first competition, UK Open 2009. Although his first National Record a few months later was in Pyraminx, he quickly realised that his natural ability lay in blindfold solving. In the following months he set many National Records in 4x4x4 blindfolded, 5x5x5 blindfolded and MultiBLD, as well as taking up Clock. 10 months after his first competition he had an official result in all events (single and average), which was a UWR for being the quickest to reach that milestone. At the [[European Championship 2010]] in Budapest, he won a silver medal in Clock. His result of 10/11 (with the last cube an M2 off) also won him a bronze medal in MultiBLD.

=== World stage (2011-present) ===
Since 2011, Daniel has been a world-level competitor in 4x4 and 5x5 blindfolded, as well as Fewest Moves and Clock. In July 2011 he set his first World Record in 4x4 blindfolded with a time of 3:26.11 at the Guildford Summer Open. At the [[World Championship 2011]] in Bangkok, he won 4 medals: bronzes in both Multi-BLD (behind [[Marcell Endrey|Marcell Endrey's]] WR) and 5x5x5 blindfolded, a tie for silver in Fewest Moves (29 moves), and Gold in Clock with a European Record average of 7.51 seconds in the final.

At the Irish Open in February 2012 he improved his own 4x4x4 Blindfolded World Record with a time of 3:17.41 and also came close in MultiBLD with 19/21, ranking him 4th in the world. At the Rapid Dash Open in April 2012 he broke the 5x5x5 Blindfolded World Record with a time of 7:05.68, although this was beaten 2 weeks later by [[Marcell Endrey]].

== Services and online presence ==
Daniel participated as an expert analyst in the investigation of [[Sebastián Pino Castillo]] and became a [[WCA delegate]] shortly thereafter.

Daniel is a frequent user of [[Speedsolving Forums]] and [[Rubik IRC Channel|#Rubik]], where he is known as kinch2002.

Daniel was instrumental in setting up the [[UK Cube Association]] and has been its president since 2012. Among his activities is organizing the annual [[UK Championships]].

== Achievements ==
=== Official milestones ===
Daniel was the first person to achieve the following.
* 4x4 blindfolded: sub-3:30

=== Titles ===

{{S-start}}

{{S-ach| ach=World Titles}}

{{S-title-bef| before=[[Koen Wermer]] | year=2009 }}
{{S-title| title=Rubik's Clock World Champion | year=2011 }}
{{S-title-aft | after=[[Deven Nadudvari]] | year=2013}}

{{S-end}}

== See also ==
* [[List of World Records/4BLD]]
* [[List of World Records/5BLD]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/member.php?3140-kinch2002 Daniel's Speedsolving.com profile]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?36431-5x5x5-Blindfolded-WR-7-05.68-Daniel-Sheppard 5x5x5 Blindfolded WR 7:05.68 Daniel Sheppard]

[[Category:Former world champions|Sheppard, Daniel]]
[[Category:Former world record holders|Sheppard, Daniel]]
[[Category:Clock solvers|Sheppard, Daniel]]
[[Category:Fewest Moves solvers|Sheppard, Daniel]]
[[Category:Speedcubers|Sheppard, Daniel]]

4x4x4 parity algorithms

2018-10-16T07:04:56Z

Oyyq99999: /* Some short/easy parity fixes */

=Introduction=
This page attempts to list move optimal [[algorithm]]s for every common form of parity encountered in popular [[4x4x4]] (Rubik's Revenge) solving methods.

Solutions listed under a case image which are not move optimal (in the move [[metric]] in which algorithms are sorted by):
*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 [[supercube]], or

*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].

==Reduction parity==
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 parity case, but there is one situation of which any cuber who uses the term "parity" for the 4x4x4 identifies as parity: the single [[dedge]] flip.

<center>[[Image:One_Dedge_Flip.png|80px|]]</center>

The most popular 2-cycle (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.

<center>[[Image:Adj2swap.png|80px|]]</center>

An equally well-known form of reduction parity (this term will be defined formally soon) besides the single dedge flip is switching two opposite dedges in the same face.

<center>[[Image:Opppllparity.png|80px|]]</center>

This parity situation can be transformed into 21 other last layer forms of what is commonly called PLL parity 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.
<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"
| 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.
|}

Combining some form of PLL parity and a single dedge flip creates one of the many cases of what's commonly called double parity. 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 double parity 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 "single parity" on this page)

or

*a case which additionally has an odd permutation of dedges and an even permutation of corners (or vice versa) (which will be called "double parity" on this page)

is called an OLL parity algorithm.

It is common convention among the speedcubing community to use algorithms which contain wide (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 single parity algorithms perform additional swaps besides flipping a single dedge due to the use of wide turns.

<center>[[Image:Non-Pure_Single_Dedge_Flip.png|80px|]]</center>

Such an algorithm is called a non-pure algorithm when compared to algorithms which just flip a single dedge, which are often called pure flips. However, the term pure is more formally associated with an algorithm being supercube safe--algorithms which do not permute (move) any centers in the [[supercube]] version of a given [[order]].

{| 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" |
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.
|}

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 pseudo 3x3x3 state (this means an even nxnxn 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 reduction parity.

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>
|}

{| 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" |
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 1/2×1/2 = (chance of PLL parity)×(chance of single parity) = a 1/4 chance of getting all possibilities, separately.

That is, for the reduction method (and its variants),
*PLL parity occurs by itself 25% of the time,

*single parity occurs 25% of the time,

*double parity occurs 25% of the time, and

*there is no reduction parity 25% of the time.
|}

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.

The key characteristics of 4x4x4 reduction parity algorithms are:

*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 preserve the coupling of the dedges, but they may move entire dedges.)

Additionally (with no exceptions),

*All OLL parity algorithms contain an odd number of inner slice quarter turns. (They are called odd parity algorithms.)

*All PLL parity algorithms contain an even number of inner slice quarter turns. (They are called even parity algorithms.)

==Other parity cases==
Besides containing case images and algorithms for reduction parity cases, this page also contains odd parity cases 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"
| 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]].
|}

Also included on this page are other last layer 2-cycle cases:

[[Image:Diag.opp.png|80px|]] [[Image:Adj.case1.png|80px|]]

and 4-cycle cases which are contained within two dedges .

[[Image:Chkbrd.png|80px|]] [[Image:Adjchkbd.png|80px|]]

{| 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" |
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.
|}

(All of these cases often occur in the [http://snk.digibase.ca/k4/7.htm ELL] stage of the [[K4]] Method.)

Algorithms for the [[Cage Method]], as well as algorithms for theoretical purposes and general 4x4x4 exploration are present as well.

==Some short/easy parity fixes==
Since all OLL parity algorithms contain an odd 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 even number of inner slice quarter turns. [https://www.youtube.com/watch?v=-6INPKC7sfo Here's one video tutorial] that illustrates the typical process.

{| 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" |
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].

(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]

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 induce an odd permutation 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 "algorithm bar") 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
}}

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.

(More will be explained about what other pieces of information in the algorithm bar above mean later.)
|}

Since this algorithm contains move repetition, 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; and 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"
| bgcolor="fbfb8b" |
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 block quarter turn moves (BQTM). We can count that this algorithm has 7 block half turn moves (BHTM) without breaking it up.

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 [[metric]]s 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.

*Algorithms with fewer BQTM are listed before other algorithms which have the same number of BHTM as they.
|}

The shortest (and well-known) nxnxn 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 nxnxn 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 nxnxn 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 double parity) 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')
|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
}}

==Additional notes about the algorithms==
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.

===Notation and animations===
*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], 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 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 algorithm bar), to see the algorithm animated in [https://www.youtube.com/watch?v=j-svGANFGXc SiGN notation] at alg.cubing.net.

===Move sets===
Two algorithms of similar length (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 move set (consist only of certain types of turns).

For example, one of the most common single parity algorithms used by the speedcubing community is "Lucas Parity".

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)]

Notice that it only contains the (and inverses of the) moves Rw, U2, x and Lw.

{| 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" |
Interesting Note:

[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).
|}

An alternate algorithm of the same move length in BHTM (but contains 5 fewer BQTM) is the following.

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)]

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.

{| 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" |
This page not only contains commonly practiced speedsolving algorithms: it also contains algorithms which illustrate the veracity of the 4x4x4 cube parity algorithm domain.
|}

===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 algorithm bars is either labelled:

*Y (short for "Yes"), if all of an algorithm's inner slice turns can be substituted with their corresponding wide turns to still preserve F3L (or if an algorithm does not contain any inner layer slices)

or

*N (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. 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.
|}

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") and 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
}}

{| 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" |
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 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

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 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.
**[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
|sign=2R2 U2 2R2 U2 2D2 2R2 2D2
|length=(14,7)|name=|wide=N|author=|url=
}}
{{Alg5|wca=U2 r2 U2 r2 Uw2 r2 Uw2
|sign=U2 2R2 U2 2R2 u2 2R2 u2
|length=(14,7)|name=|wide=N|author=Chris Hardwick
|url=http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixPermutationParity
}}
{{Alg5|wca=(Uw2 Rw2 U2) r2 (U2 Rw2 Uw2)
|sign=(u2 r2 U2) 2R2 (U2 r2 u2)
|length=(14,7)|name=SP01
|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
|sign=r2 (U2 2R U2 s2)2 r2//Safe
|length=(18,10)|name=|wide=Y|author=Walter Randelshofer
|url=http://twistypuzzles.com/forum/viewtopic.php?p=350303#p350303
}}
{{Alg5|wca=r2 U2 B2 l r U2 M' U2 r2 B2 U2//Safe
|sign=2R2 U2 B2 2L 2R U2 m' U2 2R2 B2 U2//Safe
|length=(19,11)|name=|wide=N|author=Stefan Pochmann|url=
}}
{{Alg5|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')
|length=(20,11)|name=v1
|wide=Y|author=|url=
}}
{{Alg5|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')
|length=(20,11)|name=v2
|wide=Y|author=|url=
}}
{{Alg5|wca=(Rw2 U2)(E r2 E' r)2 (U2 Rw2)//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=
}}
{{Alg5|wca=(Rw2 U2)(E' r2 E r)2 (U2 Rw2)//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=
}}
{{Alg5|wca=(Rw2 U2)(E r2 E' r')2 (U2 Rw2)//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=
}}
{{Alg5|wca=(Rw2 U2)(E' r2 E r')2 (U2 Rw2)//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=
}}
{{Alg5|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
|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
|sign=2R' F U' R F' U 2L 2R U' F R' U F' 2L'//Safe
|length=(14,14)|name=|wide=N|author=|url=
}}
{{Alg5|wca=(Rw2 U2)(r E2)6 (U2 Rw2)//Safe
|sign=(r2 U2)(2R e2)6 (U2 r2)//Safe
|length=(24,15)|name=|wide=N|author=Christopher Mowla|url=
}}
{{Alg5|wca=(Rw2 U2)(r' E2)6 (U2 Rw2)//Safe
|sign=(r2 U2)(2R' e2)6 (U2 r2)//Safe
|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
|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
|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
|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
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_m_u/index.html
}}

====Adjacent====
[[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)
|length=(18,10)|name=|wide=N|author=Chris Hardwick
|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)
|sign=(R2 D' x u2 r2 U2) 2R2 (U2 r2 u2 x' D R2)
|length=(20,11)|name=SP02
|wide=N|author=Stefan Pochmann
|url=http://frederickbadie.free.fr/444PLLparity.html
}}
{{Alg5|wca=(R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2)
|sign=(R2 D' r2 U2 F2) 2R2 (F2 U2 r2 D R2)
|length=(20,11)|name=FB02
|wide=N|author=Frédérick Badie
|url=http://frederickbadie.free.fr/444PLLparity.html
}}
{{Alg5|wca=(F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2)
|sign=(F2 U r2 U2 F2) 2R2 (F2 U2 r2 U' F2)
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
|url=
}}
{{Alg5|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)
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
|url=
}}
{{Alg5|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)
|length=(20,11)|name=|wide=N|author=Stefan Pochmann
|url=
}}
{{Alg5|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')
|length=(18,12)|name=|wide=N|author=Chris Hardwick
|url=
}}
{{Alg5|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')
|length=(20,13)|name=|wide=N|author=Stefan Pochmann
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(16,14)|name=Inverse[Alg.1]|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(16,14)|name=Alg.2|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(16,14)|name=Inverse[Alg.2]|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(16,14)|name=Alg.3|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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')
|length=(16,14)|name=Inverse[Alg.3]|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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')
|length=(16,14)|name=Alg.4|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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')
|length=(16,14)|name=Inverse[Alg.4]|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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')
|length=(19,14)|name=|wide=N|author=Chris Hardwick
|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')
|sign=(R U R') U 2R2 U2 2R2 u2 2R2 u2 U (R U' R')
|length=(19,14)|name=|wide=N|author=Chris Hardwick
|url=
}}
{{Alg5|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)
|length=(20,15)|name=|wide=N|author=xyzzy
|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')
|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
|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)
|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
|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)
|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
|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)
|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
|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
|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=
}}
{{Alg5|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)
|length=(22,17)|name=v1
|wide=N|author=Christopher Mowla
|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
|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
|wide=N|author=Christopher Mowla &Robert Yau
|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
|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
|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
|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
|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'
|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
|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)
|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
|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'
|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
|url=
}}

===Two dedges (unoriented)===
====Opposite====
[[Image:Uopppllparity.png|110px|]]
{{Alg5|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
|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
}}
{{Alg5|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
|length=(16,12)|name=Mirror[Alg.1]|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(16,12)|name=Inverse[Alg.1]|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(16,12)|name=Mirror[Inverse[Alg.1]|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(16,12)|name=Alg.2|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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
|length=(16,12)|name=Mirror[Alg.2]|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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
|length=(16,12)|name=Inverse[Alg.2]|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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
|length=(16,12)|name=Mirror[Inverse[Alg.2]|wide=N|author=Walter Randelshofer
|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')
|sign=(y R' U F') 2R2 U2 2R2 u2 2R2 2U2 (F U' R y')
|length=(18,12)|name=|wide=N|author=Chris Hardwick
|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
|sign=2R U2 2L D2 2L' U2 m U2 2R D2 2R' U2 2L'//Safe
|length=(19,13)|name=|wide=N|author=Kenneth Gustavsson
|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)
|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
|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')
|sign=(y R' U F' r2 F2 U2) 2R2 (U2 F2 r2 F U' R y')
|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
|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
|url=
}}
{{Alg5|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')
|length=(24,19)|name=|wide=N|author=Christopher Mowla
|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')
|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
|url=
}}

====Adjacent====
[[Image:Uoadjpllparity.png|110px|]]
{{Alg5|wca=(R B) r2 U2 r2 Uw2 r2 u2 (B' R')
|sign=(R B) 2R2 U2 2R2 u2 2R2 2U2 (B' R')
|length=(16,10)|name=|wide=N|author=Chris Hardwick
|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')
|sign=(R B r2 F2 U2) 2R2 (U2 F2 r2 B' R')
|length=(18,11)|name=|wide=N|author=Stefan Pochmann
|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')
|sign=(3l U r2 U2 F2) 2R2 (F2 U2 r2 U' 3l')
|length=(18,11)|name=|wide=N|author=Stefan Pochmann
|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
|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
|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
|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
|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
|sign=R' U2 B 2U2 B' U2 R U' R' B 2U2 B' R U
|length=(16,14)|name=|wide=N|author=Walter Randelshofer
|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
|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=
}}

{| 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" |
The four cases above clearly switch two [[dedge]]s, but they can also be interpreted as doing two separate 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.)

There are actually 58 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.
|}

===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
|length=(20,11)|name=CG03
|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|wca=f2 Uw2 r2 U' r2 f2 U r2 f2 Uw2 f2
|sign=2F2 u2 2R2 U' 2R2 2F2 U 2R2 2F2 u2 2F2
|length=(20,11)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(20,11)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(22,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(22,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(22,13)|name=PKF03
|wide=N|author=Per Kristen Fredlund
|url=http://frederickbadie.free.fr/444PLLparity.html
}}
{{Alg5|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
|length=(22,13)|name=PKF03
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31044
}}
{{Alg5|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
|length=(23,13)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,13)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,13)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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=
}}
{{Alg5|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=
}}
{{Alg5|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
|length=(20,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|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
}}
{{Alg5|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=
}}
{{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'
|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
|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'
|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
|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
|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
|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'
|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
|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'
|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
|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'
|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
|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'
|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
|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'
|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
|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'
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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'
|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
|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'
|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
|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
|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
|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
|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
|url=
}}

=====Ob=====
[[Image:Circ4cy.png|110px|]][[Image:Ob_Perm_Diagram.png|110px|]]
{{Alg5|wca=r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2
|sign=2R2 u2 2R2 2B2 U' 2R2 2B2 U 2B2 u2 2R2
|length=(20,11)|name=CG03
|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|wca=f2 Uw2 f2 r2 U' f2 r2 U r2 Uw2 f2
|sign=2F2 u2 2F2 2R2 U' 2F2 2R2 U 2R2 u2 2F2
|length=(20,11)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(20,11)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(22,13)|name=|wide=N|author=|url=
}}
{{Alg5|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'
|length=(22,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(22,13)|name=PKF03
|wide=N|author=Per Kristen Fredlund
|url=http://frederickbadie.free.fr/444PLLparity.html
}}
{{Alg5|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
|length=(22,13)|name=PKF03
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31044
}}
{{Alg5|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
|length=(23,13)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,13)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,13)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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=
}}
{{Alg5|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=
}}
{{Alg5|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=
}}
{{Alg5|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
}}
{{Alg5|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=
}}
{{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
|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
|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
|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
|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'
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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'
|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
|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'
|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
|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
|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
|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
|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
|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
|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
|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
|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
|url=
}}

====8 permutation====
[[Image:Zigzag4cycdedges.png|110px|]][[Image:8_Perm_Diagram.png|110px|]]

*Note: This is commonly called the "W" permutation.

{{Alg5|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
|length=(20,12)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(21,12)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(21,13)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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)
|length=(22,13)|name=PKF04
|wide=N|author=Per Kristen Fredlund
|url=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
|sign=R2 u2 B2 R2 u2 B2 R2 U R2 B2 R2 U B2 u2
|length=(26,14)|name=CG04
|wide=Y|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(22,14)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(26,14)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(28,15)|name=|wide=N|author=Doug
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30921
}}
{{Alg5|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
|length=(21,16)|name=SP04
|wide=N|author=Stefan Pochmann
|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
|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
|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
|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
|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
|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
|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'
|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
|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
|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
|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)
|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
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-909556
}}

===Four Dedges (unoriented)===
====O permutation====
=====Oa=====
[[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
|sign=F2 m F2 U' 2L2 U2 2R2 u2 2R2 U' u2 B2 m B2
|length=(23,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
|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
|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
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(27,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(27,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(26,20)|name=|wide=N|author=xyzzy
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
}}

=====Ob=====
[[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
|sign=B2 m' B2 u2 U 2R2 u2 2R2 U2 2L2 U F2 m' F2
|length=(23,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
|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
|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
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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
|length=(24,14)|name=|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(27,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(27,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(26,20)|name=|wide=N|author=xyzzy
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
}}

====8 permutation====
[[Image:W_Permutation_(unoriented).png|110px|]][[Image:8_Perm_Diagram_(4_unoriented).png|110px|]]

*Note: This is commonly called the "W" permutation.

{{Alg5|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
|url=
}}
{{Alg5|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
|length=(22,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=(M2 U')(r' E2 l 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
|url=
}}
{{Alg5|wca=(M2 U')(E2 r' E2 l)3 (U M2)//Safe
|sign=(m2 U')(e2 2R' e2 2L)3 (U m2)//Safe
|length=(24,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|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
}}
{{Alg5|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')
|length=(25,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(27,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(27,17)|name=|wide=N|author=Christopher Mowla
|url=
}}

==Two corner swaps==
===Adjacent===
[[Image:Adj2crnrsp.png|110px|]]
{{Alg5|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'
|length=(24,16)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,16)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(25,16)|name=PKF10
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050
}}
{{Alg5|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
|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
|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
|url=
}}
{{Alg5|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'
|length=(27,17)|name=|wide=N|author=Clément Gallet &Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(29,17)|name=|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31048
}}
{{Alg5|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'
|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
}}
{{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
|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
|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
|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=
}}
{{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
|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
|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
|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
|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
|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
|url=
}}
{{Alg5|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
|length=(81,81)|name=|wide=Y|author=Christopher Mowla
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374983#p374983
}}

===Opposite/diagonal===
[[Image:Diag2cornerswap.png|110px|]]
{{Alg5|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
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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
|length=(27,15)|name=v1
|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,15)|name=v2
|wide=N|author=Michael Fung
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31349
}}
{{Alg5|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'
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(27,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(29,16)|name=|wide=Y|author=Clément Gallet
|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
|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
|wide=N|author=reThinking the Cube
|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
|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
|wide=N|author=reThinking the Cube
|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
|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
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(28,17)|name=|wide=Y|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(32,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(25,19)|name=FB14
|wide=N|author=Frédérick Badie
|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
|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=
}}
{{Alg5|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
|length=(35,22)|name=|wide=Y|author=Christopher Mowla
|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
|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
|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
|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
|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')
|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
|url=
}}
{{Alg5|wca=F' (Rw U' L' U Rw' 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
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374983#p374983
}}

==Two corner swaps (only 2 supercube center piece exchange)==
===Adjacent===
[[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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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'
|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
|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
|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
|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
|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=
}}
{{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
|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
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771998
}}

===Opposite/diagonal===
[[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'
|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
|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'
|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
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-53#post-771998
}}

===Two X-center piece swap algorithms===
[[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.

{{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'
|length=(13,10)|name=|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(13,12)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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
|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
|url=
}}

==Two corner swap and a dedge 3-cycle==
===D permutation===
====Da====
[[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'
|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
|url=
}}
{{Alg5|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'
|length=(27,17)|name=FB07
|wide=N|author=Frédérick Badie
|url=
}}
{{Alg5|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
|length=(27,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(27,17)|name=|wide=N|author=Clément Gallet
|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
|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
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
}}

====Db====
[[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
|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
|url=
}}
{{Alg5|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
|length=(27,17)|name=FB07
|wide=N|author=Frédérick Badie
|url=
}}
{{Alg5|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
|length=(27,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,17)|name=|wide=N|author=Clément Gallet
|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
|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
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-104#post-1286760
}}

===K permutation===
====Ka====
[[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
|sign=U R U' L U2 R' U L 2L2 F2 l2 f2 2L2 f2
|length=(20,14)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,15)|name=|wide=Y|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,15)|name=PKF06
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050
}}
{{Alg5|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
|length=(24,15)|name=|wide=N|author=Clément Gallet
|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'
|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
|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)
|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
|url=
}}

====Kb====
[[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'
|sign=f2 2L2 f2 l2 F2 2L2 L' U' R U2 L' U R' U'
|length=(20,14)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,15)|name=|wide=Y|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,15)|name=PKF06
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31050
}}
{{Alg5|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
|length=(24,15)|name=|wide=N|author=Clément Gallet
|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
|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
|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'
|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
|url=
}}

===P permutation===
====Pa====
[[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
|sign=U' z' U2 B2 l2 U2 L' B2 l2' L B2 L U2 l2' L U2 z
|length=(23,15)|name=CG05
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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
|length=(27,16)|name=
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
}}
{{Alg5|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'
|length=(27,16)|name=PKF05
|wide=N|author=Per Kristen Fredlund
|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
|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
|url=
}}

====Pb====
[[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
|sign=z' U2 l2 L' U2 L' B2 l2' L' B2 L U2 l2' B2 U2 z U
|length=(23,15)|name=CG05
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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'
|length=(27,16)|name=
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
}}
{{Alg5|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
|length=(27,16)|name=PKF05
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31043
}}
{{Alg5|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'
|length=(27,20)|name=|wide=N|author=Stefan Lidström
|url=
}}

====Pc====
[[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'
|sign=z' U2 l2' L U2 L F2 l2' L F2 L' U2 l2 F2 U2 z U'
|length=(23,15)|name=CG05
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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'
|length=(27,16)|name=
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
}}
{{Alg5|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'
|length=(27,16)|name=PKF05
|wide=N|author=Per Kristen Fredlund
|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
|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
|url=
}}

====Pd====
[[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
|sign=U z' U2 F2 l2' U2 L F2 l2 L' F2 L' U2 l2 L' U2 z
|length=(23,15)|name=CG05
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
}}
{{Alg5|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
|length=(27,16)|name=
|wide=N|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31347
}}
{{Alg5|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
|length=(27,16)|name=PKF05
|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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'
|length=(25,20)|name=|wide=N|author=Stefan Lidström
|url=
}}

===Q permutation===
====Qa====
[[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
|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
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31343
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,18)|name=PKF11
|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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'
|length=(27,18)|name=
|wide=N|author=Per Kristen Fredlund
|url=
}}

====Qb====
[[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
|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
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31343
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(30,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,18)|name=PKF11
|wide=N|author=Per Kristen Fredlund
|url=
}}
{{Alg5|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
|length=(27,18)|name=
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31055
}}

==Two corner swap and a dedge 2 2-cycle==
===C permutation===
====Ca====
[[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
|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
|url=
}}
{{Alg5|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'
|length=(21,13)|name=AO09
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30880
}}
{{Alg5|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
|length=(21,13)|name=Inv of AO09
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30880
}}
{{Alg5|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
|length=(20,14)|name=|wide=N|author=Frédérick Badie &Clément Gallet
|url=
}}
{{Alg5|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'
|length=(25,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,15)|name=|wide=N|author=Frédérick Badie
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30854
}}
{{Alg5|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'
|length=(21,16)|name=|wide=N|author=Christopher Mowla
|url=
}}

====Cb====
[[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'
|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
|url=
}}
{{Alg5|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
|length=(21,13)|name=AO09
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30877
}}
{{Alg5|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
|length=(21,13)|name=Inv of AO09
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30877
}}
{{Alg5|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'
|length=(20,14)|name=|wide=N|author=Frédérick Badie &Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30994
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,15)|name=|wide=N|author=Frédérick Badie
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30854
}}
{{Alg5|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
|length=(21,16)|name=|wide=N|author=Christopher Mowla
|url=
}}

===I permutation===
[[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
|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
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31344
}}
{{Alg5|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
|length=(25,15)|name=CG08
|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(26,16)|name=|wide=N|author=Kenneth Gustavsson
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/30906
}}
{{Alg5|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
|length=(23,17)|name=AO08
|wide=N|author=Alexander Ooms
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31012
}}
{{Alg5|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
|length=(27,16)|name=|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31043
}}

===Theta (θ) permutation===
[[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'
|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
|url=
}}
{{Alg5|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
|length=(25,16)|name=CG12
|wide=Y|author=Clément Gallet
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31346
}}
{{Alg5|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
|length=(29,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,18)|name=|wide=N|author=Per Kristen Fredlund &Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,18)|name=PKF12
|wide=N|author=Per Kristen Fredlund
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31055
}}
{{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'
|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
|url=
}}

===Xi (Ξ) permutation===
[[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'
|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
|url=
}}
{{Alg5|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
|length=(28,18)|name=|wide=Y|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(26,19)|name=FB13
|wide=Y|author=Frédérick Badie
|url=
}}
{{Alg5|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
|length=(33,19)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,20)|name=|wide=N|author=Frédérick Badie &Clément Gallet
|url=
}}
{{Alg5|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
|length=(25,20)|name=|wide=N|author=xyzzy
|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'
|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
|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
|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
|url=https://www.speedsolving.com/forum/threads/a-collection-of-algorithms.708/page-63#post-915705
}}

==The shortest PLL parity fixes in BQTM==
*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.

{{Alg5|wca=Rw U D L2 U D S2 Rw
|sign=r U D L2 U D s2 r
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U D L2 U D S2 Rw'
|sign=r' U D L2 U D s2 r'
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' D' L2 U' D' S2 Rw
|sign=r U' D' L2 U' D' s2 r
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U' D' L2 U' D' S2 Rw'
|sign=r' U' D' L2 U' D' s2 r'
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U D R2 U D S2 Rw
|sign=r U D R2 U D s2 r
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U D R2 U D S2 Rw'
|sign=r' U D R2 U D s2 r'
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' D' R2 U' D' S2 Rw
|sign=r U' D' R2 U' D' s2 r
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U' D' R2 U' D' S2 Rw'
|sign=r' U' D' R2 U' D' s2 r'
|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
}}

{{Alg5|wca=Rw U D S2 U' D' S2 Rw'
|sign=r U D s2 U' D' s2 r'
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U D S2 U' D' S2 Rw
|sign=r' U D s2 U' D' s2 r
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' D' S2 U D S2 Rw'
|sign=r U' D' s2 U D s2 r'
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U' D' S2 U D S2 Rw
|sign=r' U' D' s2 U D s2 r
|length=(10,8)|name=|wide=Y|author=Christopher Mowla
|url=
}}

*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:

{{Alg5|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'
|length=(18,14)|name=|wide=N|author=Christopher Mowla
|url=
}}

*However, note that this is not the shortest solution to this 4x4x4 position, as the following is a shorter supercube safe algorithm.

{{Alg5|wca=(l E2 r' E2)3//Safe
|sign=(2L e2 2R' e2)3
|length=(18,12)|name=|wide=N|author=Christopher Mowla
|url=
}}

=Pure Flips (Single Parity)=
*All algorithms in this "pure flips" section are single parity algorithms.

==One dedge flip==
[[Image:One_Dedge_Flip.png|110px|]]

===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 single slice turn-based 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 unique algorithm path, as move transformations (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 cyclic shifting (a special type of conjugation).

:Take for example the first algorithm in the first cluster under Group 1 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 Group 3 of non-symmetrical algorithms.

::*This is why Group 3 is called "Group 3: Cyclic Shift of Group 1", for example.

*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, there are actually only two fundamentally unique (25,15) algorithm paths: 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].

{| 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" |
<center>Additional Terminology</center>

An algorithm is called symmetrical 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 nxnxn 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, non-symmetrical algorithms are algorithms which are solely the result of a composition of one or more separate 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 base (the base 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?" ([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]).
|}

====(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
|length=(25,15)|name=Alg.1(v1)
|wide=Y|author=Frédérick_Badie
|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
|sign=2L U2 2R' F2 2R F2 2L2 U2 2L' U2 2L U2 F2 2L2 F2
|length=(25,15)|name=Mirror[Alg.1(v1)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.1(v1)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.1(v1)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Mirror[Inverse[Alg.1(v1)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.1(v1)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.1(v1)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v1)]]]
|wide=Y|author=Frédérick_Badie
|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.1(v2)
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.1(v2)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.1(v2)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.1(v2)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Mirror[Inverse[Alg.1(v2)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.1(v2)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.1(v2)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v2)]]]
|wide=Y|author=Frédérick_Badie
|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.1(v3)
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.1(v3)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.1(v3)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.1(v3)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.1(v3)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.1(v3)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.1(v3)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v3)]]]
|wide=Y|author=Frédérick_Badie
|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.1(v4)
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.1(v4)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.1(v4)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.1(v4)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.1(v4)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.1(v4)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.1(v4)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v4)]]]
|wide=Y|author=Frédérick_Badie
|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.1(v5)
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.1(v5)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.1(v5)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.1(v5)]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.1(v5)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.1(v5)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.1(v5)]]
|wide=Y|author=Frédérick_Badie
|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.1(v5)]]]
|wide=Y|author=Frédérick_Badie
|url=
}}

=====Group 2: F2 move conjugation + rotation of Group 1=====
{{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
|length=(25,15)|name=Alg.2(v1)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.2(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.2(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.2(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.2(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.2(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.2(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v1)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.2(v2)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.2(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.2(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.2(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.2(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.2(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.2(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v2)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.2(v3)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.2(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.2(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.2(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.2(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.2(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.2(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v3)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.2(v4)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.2(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.2(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.2(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.2(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.2(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.2(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v4)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.2(v5)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.2(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.2(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.2(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.2(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.2(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.2(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.2(v5)]]]
|wide=Y|author=|url=
}}

=====Group 3: cyclic shift of Group 1=====
{{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
|length=(25,15)|name=Alg.3(v1)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.3(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.3(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.3(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.3(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.3(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.3(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v1)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.3(v2)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.3(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.3(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.3(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.3(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.3(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.3(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v2)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.3(v3)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.3(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.3(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.3(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.3(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.3(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.3(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v3)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.3(v4)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.3(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Alg.3(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.3(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.3(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.3(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Inverse[Rotation[Alg.3(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v4)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.3(v5)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.3(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.3(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.3(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Mirror[Inverse[Alg.3(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.3(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.3(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.3(v5)]]]
|wide=Y|author=|url=
}}

=====Group 4: B2 move conjugation of Group 3=====
{{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
|length=(25,15)|name=Alg.4(v1)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.4(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.4(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.4(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.4(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.4(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.4(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v1)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.4(v2)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.4(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.4(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.4(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.4(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.4(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.4(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v2)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.4(v3)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.4(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.4(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.4(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.4(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.4(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.4(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v3)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.4(v4)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.4(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.4(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.4(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.4(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.4(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.4(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v4)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.4(v5)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.4(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.4(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.4(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.4(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.4(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.4(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.4(v5)]]]
|wide=Y|author=|url=
}}

====Symmetrical algorithms====
=====Group 1=====
*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
|sign=2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2
|length=(25,15)|name=Alg.5(v1)
|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
|sign=2L2 B2 U2 2R' U2 2L U2 2L' U2 F2 2L' F2 2R B2 2L2
|length=(25,15)|name=Mirror[Alg.5(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v1)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v2)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v2)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v3)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v3)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v4)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v4)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v5)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v5)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v6)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v6)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v6)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v6)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v6)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v6)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v6)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v6)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v7)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v7)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v7)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v7)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v7)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v7)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v7)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v7)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.5(v8)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.5(v8)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.5(v8)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.5(v8)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.5(v8)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.5(v8)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.5(v8)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.5(v8)]]]
|wide=Y|author=|url=
}}

=====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.
{{Alg5|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
|length=(25,15)|name=Alg.6(v1)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v1)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v1)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v1)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v2)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v2)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v2)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v2)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v3)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v3)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v3)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v3)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v4)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v4)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v4)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v4)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v5)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v5)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v5)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v5)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v6)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v6)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v6)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v6)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v6)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v6)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v6)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v6)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v7)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v7)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v7)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v7)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v7)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v7)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v7)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v7)]]]
|wide=Y|author=|url=
}}

{{Alg5|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
|length=(25,15)|name=Alg.6(v8)
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Alg.6(v8)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Alg.6(v8)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Rotation[Alg.6(v8)]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Alg.6(v8)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Rotation[Alg.6(v8)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Inverse[Rotation[Alg.6(v8)]]
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,15)|name=Mirror[Inverse[Rotation[Alg.6(v8)]]]
|wide=Y|author=|url=
}}

===Shortest single slice quarter turn algorithms===
*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.

{| 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'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
|length=(21,18)|name=|wide=N|author=Christopher Mowla
|url=
}}

Update

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.)
{{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
|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
|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
|url=https://www.reddit.com/r/Cubers/comments/88gk96/daily_discussion_thread_mar_31_2018/dwkpl5r/
}}

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.
|}

*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.

*However, unlike the (25,15) solutions, this is by no means the complete set of all possible unique (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.

{{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'
|length=(23,16)|name=v1
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,16)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{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'
|length=(23,16)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,16)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,16)|name=cmowlaparity
|wide=Y|author=Christopher Mowla
|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
|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)
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,16)|name=v1
|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
}}
{{Alg5|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
|length=(23,16)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=v1
|wide=Y|author=Christopher Mowla
|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
|sign=r' U2 B 2R' B' U2 F2 r' U2 2R' U2 r B 2R F2 B' r
|length=(22,17)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,17)|name=v1
|wide=N|author=Christopher Mowla
|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
|sign=r' U2 B' 2R' B U2 F2 r' U2 2R' U2 r B' 2R F2 B r
|length=(22,17)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,17)|name=v1
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,17)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,17)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,17)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=v1
|wide=Y|author=Christopher Mowla
|url=
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|length=(23,18)|name=v1
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,18)|name=v2
|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,18)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,18)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}

===Shortest block quarter turn move algorithms===
*All of the algorithms in this section are wide turn based (they require--not just possess for easier execution--wide turns to create a single dedge flip).
*Most of these algorithms affect the centers of the supercube differently than the previously shown algorithms.

{| 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".

(Found in late January of 2018.)
{{Alg5|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
|length=(16,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
|}

Symmetrical algorithms
{{Alg5|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
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(19,18)|name=Challenger
|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
}}
{{Alg5|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
|length=(19,18)|name=Reverter
|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
}}
{{Alg5|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'
|length=(19,18)|name=Holy Grail
|wide=N|author=Christopher Mowla
|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)
|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
|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)
|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
|url=
}}
{{Alg5|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)
|length=(19,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(19,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(20,19)|name=|wide=N|author=Ben Whitmore
|url=
}}
{{Alg5|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
|length=(20,19)|name=|wide=N|author=Ben Whitmore
|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'
|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
|url=
}}
{{Alg5|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'
|length=(20,20)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(21,20)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,20)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(23,20)|name=|wide=N|author=Christopher Mowla
|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
|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
|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
|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
|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
|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
|url=
}}

Non-symmetrical algorithms
{{Alg5|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'
|length=(19,19)|name=|wide=N|author=Christopher Mowla
|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
|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
|url=
}}
{{Alg5|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
|length=(20,19)|name=|wide=N|author=Ben Whitmore
|url=
}}
{{Alg5|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
|length=(20,19)|name=|wide=N|author=Ben Whitmore
|url=
}}
{{Alg5|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
|length=(20,19)|name=|wide=N|author=Ben Whitmore
|url=
}}
{{Alg5|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'
|length=(21,21)|name=|wide=N|author=Christopher Mowla
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
}}

===Longer/faster algorithms===
*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 2 different face 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" |
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'
|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'
|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=
}}
{{Alg5|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
|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
|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=
}}

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'
|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=
}}

However, the majority of algorithms on this page are presented without 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).
|}

*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.

*All solutions ending in B2 may be conjugated with B2 to create a handful more of "unique" algorithms.

*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.)

*Even though it is very likely that algorithms related by transformations are listed next to each other, no official sorting by transformations was done.
*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.

{{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
|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
|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=
}}
{{Alg5|wca=r' U2 l F2 l' F2 l r F2 r F2 l' U2 F2 r2 F2
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|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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'
|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
|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=
}}
{{Alg5|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
|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'
|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=
}}
{{Alg5|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
|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'
|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=
}}

{{Alg5|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'
|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
|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=
}}
{{Alg5|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
|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'
|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=
}}
{{Alg5|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'
|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'
|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=
}}
{{Alg5|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'
|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'
|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=
}}
{{Alg5|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'
|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
|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=
}}
{{Alg5|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'
|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
|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=
}}
{{Alg5|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'
|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'
|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=
}}
{{Alg5|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'
|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
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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'
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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'
|length=(27,18)|name=|wide=Y|author=|url=
}}

{{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'
|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
|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'
|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
|url=
}}

===2-Gen and "Semi 2-gen" algorithms===
*2 Gen (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.

2-Gen
{{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
|length=(31,22)|name=|wide=N|author=Lucas Garron
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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'
|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
|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'
|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
|url=
}}
{{Alg5|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
|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
|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
|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
|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
|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
|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'
|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
|wide=Y|author=Ben Whitmore
|url=
}}

Semi 2-Gen
{{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'
|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
|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'
|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
|url=
}}

===4x4x4 supercube safe algorithms===
*All of the algorithms in this section "prove" that one can just switch two 4x4x4 supercube wing edges without affecting its centers.

{| 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" |
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.
|}

{{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
|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
|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
|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
|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
|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
|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
|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
}}
{{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
|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
|length=(42,29)|name=|wide=N|author=Ben Whitmore
|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
|sign=(r' U')(U' 2R2 U r (2R2 2U 2R2 2U') U' 2R' U r')3 (U r)//Safe
|length=(43,36)|name=|wide=N|author=Christopher Mowla
|url=http://twistypuzzles.com/forum/viewtopic.php?p=374338#p374338
}}

==Three dedge flips==
===In the last layer===
[[Image:Ollpo3flip.png|110px|]]
{{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
|length=(29,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(29,18)|name=|wide=N|author=Walter Randelshofer
|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'
|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=
}}
{{Alg5|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'
|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'
|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=
}}
{{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'
|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
|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'
|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
|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'
|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
|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'
|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
|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'
|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
|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'
|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
|url=
}}
{{Alg5|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
|length=(27,21)|name=v1
|wide=N|author=Kåre Krig
|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'
|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
|wide=N|author=Kåre Krig
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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'
|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
|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
|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
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_2R_3u/index.html
}}

===In the M layer===
[[Image:3SingleParityDedgeFlipInM.png|110px|]]
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Alg.1
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Alg.1]
|url=
}}
{{Alg5|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'
|length=(25,15)|name=|wide=N|author=|Inverse[Alg.1]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Rotation[Alg.1]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Alg.1]]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Rotation[Alg.1]]
|url=
}}
{{Alg5|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'
|length=(25,15)|name=|wide=N|author=|Inverse[Rotation[Alg.1]]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Rotation[Alg.1]]]
|url=
}}

{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Alg.2
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Alg.2]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Inverse[Alg.2]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Rotation[Alg.2]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Alg.2]]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Rotation[Alg.2]]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Inverse[Rotation[Alg.2]]
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=N|author=|Mirror[Inverse[Rotation[Alg.2]]]
|url=
}}

{{Alg5|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'
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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)
|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
|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)
|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
|url=
}}

===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.

{{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
|length=(31,20)|name=(ur)(rf)(fu)|wide=N|author=Walter Randelshofer
|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
|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
|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'
|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
|url=
}}

{{Alg5|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'
|length=(27,18)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
|url=
}}
{{Alg5|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'
|length=(27,19)|name=(ub)(rd)(fl)|wide=N|author=Walter Randelshofer
|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'
|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
|url=
}}

{{Alg5|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
|length=(29,18)|name=(ub)(rd)(fd)|wide=N|author=Walter Randelshofer
|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)
|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
|url=
}}

==Five dedge flips==
*There are many possible 5 dedge flip cases. All algorithms are labeled/named according to which dedges they flip.

{{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'
|length=(34,21)|name=(ur)(uf)(ul)(ub)(dr)|wide=N|author=Walter Randelshofer
|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
|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
|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'
|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
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
}}

{{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
|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
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
}}

==Seven dedge flips==
*There are many possible 7 dedge flip cases. All algorithms are labeled/named according to which dedges they flip.

{{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'
|length=(36,23)|name=(uf)(ul)(ub)(dr)(df)(dl)(db)|wide=N|author=André Boulouard
|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
|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
|url=
}}

==Nine dedge flips==
*There are several possible 9 dedge flip cases. All algorithms are labeled/named according to which dedges they flip.

{{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'
|length=(38,24)|name=(ur)(uf)(ul)(ub)(rf)(dr)(df)(dl)(db)|wide=N|author=André Boulouard
|url=
}}

==Eleven dedge flips==
[[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.

{{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
|length=(30,20)|name=|wide=N|author=Herbert Kociemba &Christopher Mowla
|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
|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
|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
|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
|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
|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
|url=
}}
{{Alg5|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
|length=(32,20)|name=|wide=N|author=Herbert Kociemba &Walter Randelshofer
|url=
}}
{{Alg5|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
|length=(32,20)|name=|wide=N|author=Herbert Kociemba &Walter Randelshofer
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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'
|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
|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
|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
|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'
|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
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-10#post-872801
}}

=Double Parity Cases Only Affecting Dedges=
==In the last layer==
===Opposite double parity===
[[Image: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.

{{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
|length=(21,14)|name=Alg.1|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.1]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.2|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.2]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.3|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.3]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.4|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.4]|wide=Y|author=
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.5]|wide=Y|author=Kenneth Gustavsson
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.6|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.6]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.7|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.7]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.8|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.8]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.9|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.9]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.10|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.10]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.11|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.11]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.12|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.12]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.13|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.13]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Alg.14|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(21,14)|name=Mirror[Alg.14]|wide=Y|author=
|url=
}}
{{Alg5|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
|length=(25,15)|name=|wide=Y|author=Frédérick Badie
|url=
}}
{{Alg5|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
|length=(21,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(27,16)|name=|wide=Y|author=Alexander Ooms
|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'
|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
|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
|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=
}}
{{Alg5|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
|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
|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
|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
|sign=r2 U B2 U' 2R' U B2 U' r 2R U B2 U 2R' U' B2 U' r
|length=(23,18)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,18)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,18)|name=v1
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,18)|name=v2
|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(29,18)|name=|wide=Y|author=|url=
}}
{{Alg5|wca=U2 x' r' (F2 U' l' U)5 r x
|sign=U2 x' 2R' (F2 U' 2L' U)5 2R x
|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/
}}
{{Alg5|wca=U2 x' r' (F2 U' l U)5 r x
|sign=U2 x' 2R' (F2 U' 2L U)5 2R x
|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/
}}
{{Alg5|wca=U2 x' r' (U' l' U F2)5 r x
|sign=U2 x' 2R' (U' 2L' U F2)5 2R x
|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/
}}
{{Alg5|wca=U2 x' r' (U' l U F2)5 r x
|sign=U2 x' 2R' (U' 2L U F2)5 2R x
|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/
}}
{{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')
|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
|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')
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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)
|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
|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
|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
|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)
|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
|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'
|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
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
}}

===Adjacent double parity===
[[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.

{{Alg5|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)
|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
}}
{{Alg5|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')
|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
}}
{{Alg5|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
|length=(23,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(23,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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)
|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
}}
{{Alg5|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
|length=(24,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(25,18)|name=|wide=N|author=Kenneth Gustavsson
|url=
}}
{{Alg5|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'
|length=(25,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(25,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|length=(25,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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'
|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'
|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
|url=
}}
{{Alg5|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'
|length=(27,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(27,18)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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')
|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
}}
{{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')
|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
|url=
}}
{{Alg5|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)
|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
}}
{{Alg5|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'
|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
}}
{{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')
|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
|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')
|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
|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)
|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
|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)
|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
|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')
|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
|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')
|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
|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
|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
|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
|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
|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')
|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)
|wide=N|author=Christopher Mowla
|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')
|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)
|wide=N|author=Christopher Mowla
|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
|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
|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
|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
|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'))
|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
|wide=N|author=Christopher Mowla
|url=
}}

===Three flips===
[[Image:Dp3flip.png|110px|]]
*Note that there are several possible dedge flip double parity 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.

{{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
|length=(29,17)|name=|wide=N|author=Clément Gallet
|url=
}}
{{Alg5|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
|length=(24,19)|name=|wide=N|author=Christopher Mowla
|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'
|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=
}}
{{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)
|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
|url=
}}

==In the M layer==
[[Image:MLyrparity.png|100px|]]
*Note that none of these algorithms affect the cube in the same manner as their inverses.

{{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'
|length=(19,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(20,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,15)|name=reParity(v2)
|wide=N|author=reThinking the Cube
|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)
|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
|url=
}}

=OLL parity algorithms which don't preserve the last layer=
[[Image:ImpurededgeFlip.PNG|110px|]]
*Some of the algorithms in this category are the most widely used speedsolving algorithms.
*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.

==Single parity==
===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 [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 [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.
**Most of these algorithms need to be adjusted to work on the 5x5x5.

{| 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'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!

{{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
|length=(23,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
|}

{{Alg5|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
|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
|sign=r' U2 r U2 r' F2 r2 U2 r U2 r' U2 F2 r2 F2
|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
|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=
}}
{{Alg5|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
|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
|sign=r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2
|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'
|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=
}}
{{Alg5|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
|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
|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=
}}

{{Alg5|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'
|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
|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=
}}
{{Alg5|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
|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'
|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=
}}

{{Alg5|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
|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
|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=
}}
{{Alg5|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'
|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
|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=
}}
{{Alg5|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'
|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
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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
|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=
}}

{{Alg5|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
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}

{{Alg5|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'
|length=(25,17)|name=lucasparity
|wide=Y|author=Lucas Garron & Stefan Pochmann
|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'
|sign=r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'
|length=(25,17)|name=lucasparity
|wide=Y|author=Lucas Garron & Stefan Pochmann
|url=
}}
{{Alg5|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'
|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'
|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=
}}

{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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
|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=
}}
{{Alg5|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
|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
|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=
}}

{{Alg5|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'
|length=(25,18)|name=|wide=Y|author=Christopher Mowla
|url=
}}

{{Alg5|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'
|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
}}
{{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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|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
|url=
}}

===3 flip===
{| 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" |
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.

The shortest of such conjugations is (B' R'),

{{Alg5|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)
|length=(27,21)|name=|wide=Y|author=Lucas Garron
|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.

On the other hand, the algorithms provided in this section are algorithms which flip 3 dedges without using this conjugation technique
|}

{{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
|length=(25,21)|name=|wide=Y|author=Christopher Mowla
|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
|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
|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
|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
|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
|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
|url=
}}

==Double parity==
===1 flip===
{{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
|length=(25,16)|name=v1
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,16)|name=v2
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,16)|name=v1
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,16)|name=v2
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,16)|name=v1
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,16)|name=v2
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(25,16)|name=v1
|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,16)|name=v2
|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
|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
|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(23,19)|name=v2
|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(26,20)|name=|wide=Y|author=Kåre Krig
|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
|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
|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'
|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
|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'
|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
|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
|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
|url=https://benwh.000webhostapp.com/twisty_puzzles/4x4/4x4_r_U/index.html
}}

===3 flip===
{{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
|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
|url=
}}

=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.)
*Unlike algorithms which preserve the first three layers, which are at minimum 14 block half turns (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.

==Corner permuters==
[[Image:CrnersParity.png‎|110px|]]
*Most of these algorithms are also just front right F3L slot destroyers.

Single Parity
{{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'
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|length=(21,17)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
|url=
}}
{{Alg5|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'
|length=(21,17)|name=|wide=N|author=Christopher Mowla & Bruce Norskog
|url=
}}
{{Alg5|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
|length=(21,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(22,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(22,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(24,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(24,19)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(24,19)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(24,19)|name=|wide=N|author=Kåre Krig
|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')
|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
|url=
}}

==Front-right F3L slot destroyers==
[[Image:FRF3Lslot.png|110px|]]

Single Parity
{{Alg5|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
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|length=(24,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(24,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(24,19)|name=|wide=N|author=Kåre Krig
|url=
}}

Double Parity
{{Alg5|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
|length=(21,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(24,18)|name=|wide=N|author=Kåre Krig
|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)
|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
|url=
}}

==Petrus==
[[Image:Pparity.png|110px|]]
*These algorithms "just" scramble two adjacent faces' worth of pieces.

Single Parity
{{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
|length=(17,13)|name=v1
|wide=Y|author=Bruce Norskog
|url=
}}
{{Alg5|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'
|length=(17,13)|name=v2
|wide=Y|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-722738
}}
{{Alg5|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'
|length=(17,13)|name=v3
|wide=Y|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-722738
}}
{{Alg5|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
|length=(17,13)|name=v4
|wide=Y|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-722738
}}
{{Alg5|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'
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(21,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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
|length=(21,17)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(21,17)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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'
|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
}}
{{Alg5|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
|length=(25,17)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(21,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(22,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(23,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(23,18)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(23,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(24,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(24,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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'
|length=(24,18)|name=|wide=Y|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(22,19)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(22,19)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(22,19)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(23,19)|name=|wide=N|author=Kåre Krig
|url=
}}
{{Alg5|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
|length=(23,19)|name=|wide=N|author=Kåre Krig
|url=
}}

Double Parity
{{Alg5|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'
|length=(20,14)|name=v1
|wide=Y|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-722738
}}
{{Alg5|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'
|length=(20,14)|name=v2
|wide=Y|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-722738
}}
{{Alg5|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'
|length=(20,14)|name=v1
|wide=Y|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-722738
}}
{{Alg5|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'
|length=(20,14)|name=v2
|wide=Y|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-722738
}}
{{Alg5|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
|length=(21,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(24,19)|name=|wide=Y|author=Stefan Pochmann
|url=https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/13698
}}

==X-Cross preservers==
[[Image:MoreT1F3Lslot.png|110px|]]

Single Parity
{{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'
|length=(21,15)|name=|wide=Y|author=Bruce Norskog & Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(22,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(20,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(22,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,19)|name=|wide=Y|author=Christopher Mowla
|url=
}}

==Random pseudo-3x3x3 positions==
[[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].

*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].

Single Parity
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Bruce Norskog
|url=
}}
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Bruce Norskog
|url=
}}
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Bruce Norskog
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(20,16)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{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'
|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
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-12#post-874531
}}

Double Parity
{{Alg5|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
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
|url=
}}
{{Alg5|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
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
|url=
}}
{{Alg5|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
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
|url=
}}
{{Alg5|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
|length=(19,13)|name=|wide=Y|author=Bruce Norskog
|url=
}}
{{Alg5|wca=Rw U2 Lw' U2 x' (Rw' U2 Lw U2)2 Lw'
|sign=r U2 l' U2 x' (r' U2 l U2)2 l'
|length=(19,13)|name=reParity
|wide=Y|author=reThinking the Cube
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|length=(20,14)|name=|wide=Y|author=xyzzy
|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
|sign=r2 U2 r' U2 r' U2 r' U2 D r' B U2 B' r
|length=(20,14)|name=|wide=Y|author=xyzzy
|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
|sign=r' U F2 U' r F2 B' r F2 r F2 r F2 r2
|length=(20,14)|name=|wide=Y|author=xyzzy
|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
|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
|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
|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
|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'
|sign=r U2 r' U2 D' r D F2 r F2 r F2 r' D' r'
|length=(20,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r' U2 r' U2 r' U2 r2 B R D' r B' U2 B r'
|length=(20,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r2 U2 r U2 r U2 r U2 D L' r F U2 F' r'
|length=(21,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r2 U2 r U2 r U2 r D L' U2 r F U2 F' r'
|length=(21,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 U2 r' F2 r2 U F R' L U F' r U2 F2 r
|length=(21,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 U2 r' F2 r2 U' F R' L U' F r U2 F2 r
|length=(21,15)|name=|wide=Y|author=xyzzy
|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
|sign=r U2 F2 r F2 r2 U L2 B' L B U r' F2 r2
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r U2 F2 r F2 r2 U B' L' B L2 U r' F2 r2
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r U2 F2 r F2 r2 U' R2 B R' B' U' r' F2 r2
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r U2 F2 r F2 r2 U' B R B' R2 U' r' F2 r2
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r D' B2 D r' D' r' U2 r' B2 U2 r U2 B2 r2
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 U2 B2 r B2 U2 r' B2 r' F' r' F U2 F' r
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 F2 r' D L2 B L' B' D r2 F2 r F2 D2 r
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 F2 r' D B L B' L2 D r2 F2 r F2 D2 r
|length=(22,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r2 F2 r' D2 B2 r' D B R' D F2 B' r2 B2 r'
|length=(22,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r2 F2 r' D2 B2 r' D' B' L D' F2 B r2 B2 r'
|length=(22,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r2 F2 r' D2 B2 r' F D' L F' D' F2 r2 B2 r'
|length=(22,15)|name=|wide=Y|author=xyzzy
|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'
|sign=r2 F2 r' D2 B2 r' F' D R' F D F2 r2 B2 r'
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 F2 r' D' R2 B' R B D' r2 F2 r F2 D2 r
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|sign=r2 F2 r' D' B' R' B R2 D' r2 F2 r F2 D2 r
|length=(22,15)|name=|wide=Y|author=xyzzy
|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
|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
|url=https://www.speedsolving.com/forum/threads/what-is-gods-number-on-a-4x4-rubiks-cube.35965/page-12#post-874531
}}

=Non Dedge-Preserving Last Layer 2-Cycle Cases=
*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.

==In opposite dedges==
===Opposite===
[[Image:Adj2swap.png|110px|]]

Symmetrical algorithms
{{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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(20,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|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'
|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
|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
|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
|url=
}}
{{Alg5|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'
|length=(17,16)|name=|wide=N|author=Christopher Mowla
|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'
|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
|url=
}}
{{Alg5|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
|length=(18,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(25,21)|name=|wide=Y|author=Floyd Newberry
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
}}
{{Alg5|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)
|length=(25,21)|name=|wide=Y|author=Floyd Newberry
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
}}

Non-symmetrical algorithms
{{Alg5|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'
|length=(23,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(21,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(21,17)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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
|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'
|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
|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
|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
|url=
}}

===Diagonal===
[[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.
*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.)

{| 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,
{{Alg5|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)
|length=(25,15)|name=|wide=N|author=Christopher Mowla
|url=
}}

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)
|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
|url=
}}

In fact, the combination of the first algorithm above with the inverse of the second,

(Rw2 F2 U2 r 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 r (r) U2 F2 Rw2 = (Rw2 F2 U2) r2 (U2 F2 Rw2) = Stefan Pochmann's nxnxn cube PLL parity algorithm.

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.
|}

Symmetrical algorithms
{{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'
|length=(16,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(16,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(16,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(26,17)|name=|wide=N|author=|url=
}}
{{Alg5|wca=F (l' F' U2 F)4 l' F'
|sign=F (2L' F' U2 F)4 2L' F'
|length=(23,19)|name=|wide=Y|author=Floyd Newberry
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
}}
{{Alg5|wca=F (l F' U2 F)4 l F'
|sign=F (2L F' U2 F)4 2L F'
|length=(23,19)|name=|wide=Y|author=Floyd Newberry
|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
|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
}}
{{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
|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
|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
|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
|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
|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
|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
|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
|url=
}}

Non-symmetrical algorithms
{{Alg5|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
|length=(21,14)|name=|wide=Y|author=Kenneth Gustavsson
|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=Nicholas Ho
|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=Nicholas Ho
|url=
}}
{{Alg5|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
|length=(25,14)|name=|wide=Y|author=|url=
}}
{{Alg5|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
|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'
|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
|url=
}}
{{Alg5|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'
|length=(16,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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'
|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
|url=
}}
{{Alg5|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
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|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
|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
|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
|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
|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'
|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
|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'
|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
|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'
|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
|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
|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
|url=https://www.speedsolving.com/forum/threads/is-a-supercube-safe-single-dedge-flip-algorithm-possible-in-u-rw.37308/
}}

==In adjacent dedges==
===Close unoriented===
[[Image:Adj.case1.png|110px|]]

Symmetrical algorithms
{{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'
|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
}}
{{Alg5|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
|length=(23,15)|name=|wide=N|author=reThinking the Cube
|url=
}}
{{Alg5|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
|length=(21,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(24,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(25,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(18,18)|name=|wide=N|author=Christopher Mowla
|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
|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
}}
{{Alg5|wca=(L U2)(r' F U2 F')4 r' (U2 L')
|sign=(L U2)(2R' F U2 F')4 2R' (U2 L')
|length=(27,21)|name=|wide=N|author=Floyd Newberry
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
}}
{{Alg5|wca=(L U2)(r F U2 F')4 r (U2 L')
|sign=(L U2)(2R F U2 F')4 2R (U2 L')
|length=(27,21)|name=|wide=N|author=Floyd Newberry
|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
|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
|url=
}}

Non-symmetrical algorithms
{{Alg5|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
|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/
}}
{{Alg5|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
|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/
}}
{{Alg5|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
|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/
}}
{{Alg5|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
|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/
}}
{{Alg5|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
|length=(23,21)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(24,21)|name=|wide=N|author=Christopher Mowla
|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
|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
|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
|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
|url=
}}

===Far unoriented===
[[Image:Adjcase2.png|110px|]]

Symmetrical algorithms
{{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'
|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
}}
{{Alg5|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')
|length=(23,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(18,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(18,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(18,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(18,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(18,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(24,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(23,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=R (l' B U2 B')4 l' R'
|sign=R (2L' B U2 B')4 2L' R'
|length=(23,19)|name=|wide=N|author=Floyd Newberry
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
}}
{{Alg5|wca=R (l B U2 B')4 l R'
|sign=R (2L B U2 B')4 2L R'
|length=(23,19)|name=|wide=N|author=Floyd Newberry
|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
|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
|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
|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
}}
{{Alg5|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'
|length=(27,22)|name=|wide=N|author=Christopher Mowla
|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'
|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
|url=
}}

Non-symmetrical algorithms
{{Alg5|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
|length=(27,19)|name=|wide=N|author=Christopher Mowla
|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
|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
|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
|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
|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
|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
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
}}

===Oriented===
[[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.

Symmetrical algorithms
{{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
|length=(17,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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)
|length=(19,15)|name=1st 15 Mover
|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-641481
}}
{{Alg5|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'
|length=(16,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(16,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,16)|name=|wide=N|author=Christopher Mowla
|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)
|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
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|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
}}
{{Alg5|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)
|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')
|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
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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'
|length=(22,17)|name=|wide=N|author=Christopher Mowla
|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'
|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
|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
|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
|url=
}}
{{Alg5|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'
|length=(23,18)|name=|wide=N|author=Christopher Mowla
|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')
|sign=(x L2)(2R F U2 F')4 2R (L2 x')
|length=(25,19)|name=|wide=N|author=Floyd Newberry
|url=http://twistypuzzles.com/forum/viewtopic.php?p=373920#p373920
}}
{{Alg5|wca=(x L2)(r' F U2 F')4 r' (L2 x')
|sign=(x L2)(2R' F U2 F')4 2R' (L2 x')
|length=(25,19)|name=|wide=N|author=Floyd Newberry
|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
|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
|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
|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
}}
{{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
|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
|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'
|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
|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')
|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
|url=
}}

Non-symmetrical algorithms
{{Alg5|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'
|length=(19,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|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
}}
{{Alg5|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'
|length=(20,16)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(18,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(21,19)|name=|wide=N|author=Christopher Mowla
|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
|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
|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
|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=
}}

=Non Dedge-Preserving Last Layer 4-Cycle Cases in Two Dedges=
*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 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=
}}
{{Alg5|wca=r2 U2 (r S2)2 r' U2 l2 f2 M2 f2
|sign=2R2 U2 (2R s2)2 2R' U2 2L2 2F2 m2 2F2
|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
}}
{{Alg5|wca=r2 U2 (r S2)2 r' U2 l2 b2 M2 b2
|sign=2R2 U2 (2R s2)2 2R' U2 2L2 2B2 m2 2B2
|length=(21,12)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|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
}}
{{Alg5|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)
|length=(19,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=(Rw2 S) (r' U2)4 r' (S' Rw2)
|sign=(r2 s) (2R' U2)4 2R' (s' r2)
|length=(19,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=(Rw2 S') (r' U2)4 r' (S Rw2)
|sign=(r2 s') (2R' U2)4 2R' (s r2)
|length=(19,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v1a)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v1b)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v1c)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v1d)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v2a)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v2b)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v2c)
|wide=Y|author=|url=
}}
{{Alg5|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'
|length=(21,13)|name=Alg(v2d)
|wide=Y|author=|url=
}}

===Bowtie/Hourglass===
[[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.

{{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
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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
|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
|sign=2R2 U2 2L' U2 2L F2 U2 2R2 U2 2R F2 2R' F2 2R' F2
|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)
|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
|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
|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=
}}
{{Alg5|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)
|length=(21,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(21,17)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(26,17)|name=|wide=N|author=|url=
}}

==In adjacent dedges==
===Checkboard===
[[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.

{{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
|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
}}
{{Alg5|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')
|length=(21,15)|name=|wide=N|author=Tom Rokicki & Ed Trice
|url=
}}
{{Alg5|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)
|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
}}
{{Alg5|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)
|length=(21,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(23,16)|name=|wide=N|author=xyzzy
|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)
|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
|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)
|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
|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')
|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=
}}

===Bowtie/Hourglass===
[[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.

{{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')
|length=(19,13)|name=|wide=N|author=Tom Rokicki & Ed Trice
|url=
}}
{{Alg5|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')
|length=(19,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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')
|length=(19,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,15)|name=|wide=Y|author=Tom Rokicki
|url=
}}
{{Alg5|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)
|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
}}
{{Alg5|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'
|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')
|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
|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
|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
|url=https://www.speedsolving.com/forum/threads/methods-for-forming-2-cycle-odd-parity-algorithms-for-big-cubes.22969/page-2#post-717206
}}

=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.

*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 Adjacent Double Parity, and that the "easiest case" is the Checkerboard case in two opposite dedges.

:*These results will change in the future if shorter algorithms are found for any of these cases.

{|class="mw_metadata"
|+Arranged by Rank (Worst last layer cases are first.)
|-
! Last Layer Case !! Minimum BQTM !! Minimum BHTM !! Optimal Move Average !! Rank
|-
! [https://www.speedsolving.com/wiki/images/8/8c/Adj.dblparity.png Adjacent Double Parity 4-cycle] !! 23 !! 16 !! 19.5 !! 1
|-
! [https://www.speedsolving.com/wiki/images/7/7b/Adjchkbd.png Adjacent Checkerboard 4-cycle] !! 21 !! 14 !! 18 !! 2
|-
! [https://www.speedsolving.com/wiki/images/0/05/One_Dedge_Flip.png One Dedge Flip 2-cycle] !! 18 !! 15 !! 18 !! 2
|-
! [https://www.speedsolving.com/wiki/images/9/95/DblParity.png Double Parity 4-cycle] !! 21 !! 14 !! 17.5 !! 3
|-
! [https://www.speedsolving.com/wiki/images/1/11/Hourglass.png Bowtie/Hourglass 4-cycle] !! 21 !! 13 !! 17 !! 4
|-
! [https://www.speedsolving.com/wiki/images/0/0a/Adj.case1.png Close Unoriented 2-cycle]!! 17 !! 15 !! 17 !! 4
|-
! [https://www.speedsolving.com/wiki/images/2/2c/Adjcase2.png Far Unoriented 2-cycle] !! 17 !! 15 !! 17 !! 4
|-
! [https://www.speedsolving.com/wiki/images/6/6b/Ahourglass.png 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
|-
! [https://www.speedsolving.com/wiki/images/9/96/Diag.opp.png 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
|-
! [https://www.speedsolving.com/wiki/images/5/50/Chkbrd.png Checkerboard 4-cycle] !! 15 !! 9 !! 12 !! 7
|}

=Algorithms which do not preserve the centers=
*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]].

==One dedge flip==
[[Image:COneDedge_Flip.png|110px|]]
{{Alg5|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
|length=(17,12)|name=|wide=N|author=Michael Gottlieb
|url=http://twistypuzzles.com/forum/viewtopic.php?p=66059#p66059
}}
{{Alg5|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
|length=(17,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|length=(17,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(21,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(21,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(15,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,14)|name=|wide=N|author=Lucas Garron
|url=
}}
{{Alg5|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
|length=(21,14)|name=|wide=N|author=Nicholas Ho
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|length=(15,15)|name=|wide=N|author=|url=
}}

==Opposite double parity==
[[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.
*Most of these algorithms are exactly the same as the one dedge flip ones except that the extra quarter turn is inverted.

{{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
|length=(15,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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
|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'
|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
|url=
}}
{{Alg5|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
|length=(19,14)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,14)|name=|wide=N|author=Nicholas Ho
|url=
}}

==Adjacent double parity==
[[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.

{{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)
|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
}}
{{Alg5|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)
|length=(19,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|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
}}
{{Alg5|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')
|length=(15,15)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(21,15)|name=|wide=N|author=Christopher Mowla
|url=
}}

==Three flips==
===Single parity===
[[Image:Collpo3flip.png|110px|]]
{{Alg5|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
|length=(21,14)|name=Pattern 1|wide=N|author=Per Kristen Fredlund
|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)
|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
|url=
}}
{{Alg5|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)
|length=(27,19)|name=|wide=N|author=Christopher Mowla
|url=
}}

===Double parity===
[[Image:CageDp3flip.png|110px|]]
{{Alg5|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'
|length=(21,14)|name=Pattern 1|wide=N|author=Per Kristen Fredlund
|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)
|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
|url=
}}

==2-cycles in two adjacent dedges (in the M ring)==
===Opposite===
[[Image:Cadj.2swap.png|110px|]]
{{Alg5|wca=l U' l' U' F2 U l U' F2 U2
|sign=2L U' 2L' U' F2 U 2L U' F2 U2
|length=(13,10)|name=|wide=N|author=|url=
}}
{{Alg5|wca=l U l' U F2 U' l U F2 U2
|sign=2L U 2L' U F2 U' 2L U F2 U2
|length=(13,10)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(13,10)|name=|wide=N|author=|url=
}}
{{Alg5|wca=l F2 r' U2 l U2 l' U2 r U2 F2
|sign=2L F2 2R' U2 2L U2 2L' U2 2R U2 F2
|length=(17,11)|name=|wide=N|author=|url=
}}
{{Alg5|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'
|length=(13,13)|name=|wide=N|author=|url=
}}

===Diagonal===
[[Image:CDiag.opp.png|110px|]]
*Some of these are nearly the same as the one dedge flip algorithms.

{{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
|length=(15,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{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
|length=(15,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(13,13)|name=|wide=N|author=Marc Waterman
|url=
}}
{{Alg5|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
|length=(13,13)|name=|wide=N|author=Marc Waterman
|url=
}}
{{Alg5|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
|length=(13,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(15,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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)
|length=(19,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(19,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(21,13)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(20,14)|name=|wide=N|author=Nicholas Ho
|url=
}}

==2-cycles in two opposite dedges (in the M ring)==
===Directly opposite===
[[Image:A2spnM.png‎‎|110px|]]
{{Alg5|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
|length=(13,12)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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/
}}
{{Alg5|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
|length=(15,14)|name=|wide=N|author=François Courtès
|url=
}}

===Opposite/Diagonal===
[[Image:OppdiagnM.PNG|110px|]]
*These are the same as the one dedge flips but without first and last moves.

{{Alg5|wca=U r' U' B2 U r U r' U2 B2
|sign=U 2R' U' B2 U 2R U 2R' U2 B2
|length=(13,10)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=U' r' U B2 U' r U' r' U2 B2
|sign=U' 2R' U B2 U' 2R U' 2R' U2 B2
|length=(13,10)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(13,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=U' r' U B2 U' r U B2 D2 l D2
|sign=U' 2R' U B2 U' 2R U B2 D2 2L D2
|length=(15,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(15,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(17,11)|name=|wide=N|author=|url=
}}
{{Alg5|wca=U2 r U2 l' U2 l U2 r' F2 r F2
|sign=U2 2R U2 2L' U2 2L U2 2R' F2 2R F2
|length=(17,11)|name=|wide=N|author=|url=
}}
{{Alg5|wca=U2 r U2 l' U2 l U2 r' B2 l B2
|sign=U2 2R U2 2L' U2 2L U2 2R' B2 2L B2
|length=(17,11)|name=|wide=N|author=|url=
}}

==4-cycles in opposite dedges==
===Checkboard===
[[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.

{{Alg5|wca=Rw2 U2 r U2 Rw2
|sign=r2 U2 2R U2 r2
|length=(9,5)|name=|wide=N|author=Marc Waterman
|url=
}}

===Bowtie/Hourglass===
[[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.

{{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')
|length=(15,11)|name=|wide=N|author=|url=
}}
{{Alg5|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')
|length=(15,11)|name=|wide=N|author=|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=N|author=Nicholas Ho
|url=
}}
{{Alg5|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
|length=(19,12)|name=|wide=N|author=Kenneth Gustavsson
|url=
}}

=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.

==Single parity==
{{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
|length=(15,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{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
|length=(15,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw2 U f U' B2 U f' U l B2 Rw2
|sign=r2 U 2F U' B2 U 2F' U 2L B2 r2
|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
}}
{{Alg5|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'
|length=(15,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(15,13)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|length=(19,15)|name=|wide=N|author=Christopher Mowla
|url=
}}

==Double parity==
{{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
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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
|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
}}
{{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
|length=(15,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{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
|length=(15,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw2 U f U' B2 U f' U l' B2 Rw2
|sign=r2 U 2F U' B2 U 2F' U 2L' B2 r2
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|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
}}

==Either single parity or double parity==
*The following list of algorithms can be considered either single parity or double parity. Just exchange the last move Rw' with Lw', Rw with Lw, and so forth.

{{Alg5|wca=Rw' U' R' U' Rw F' R' F' Rw'
|sign=r' U' R' U' r F' R' F' r'
|length=(9,9)|name=|wide=Y|author=Christopher Mowla
|v1
|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
|sign=r F R F l' B R B l
|length=(9,9)|name=|wide=Y|author=David Gilday
|v2
|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'
|sign=r' U' R U' r F' R F' r'
|length=(9,9)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' R U' r' D' R D' Rw
|sign=r U' R U' 2R' D' R D' r
|length=(9,9)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U R' U Rw U F2 U Rw'
|sign=r' U R' U r U F2 U r'
|length=(10,9)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' R U' Rw' D' R2 D' Lw
|sign=r U' R U' r' D' R2 D' l
|length=(10,9)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U' F2 U' r B' R B' Lw'
|sign=r' U' F2 U' 2R B' R B' l'
|length=(10,9)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' L U' F2 Lw U' R U' Rw'
|sign=r U' L U' F2 l U' R U' r'
|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
}}
{{Alg5|wca=Rw U' L' U' F2 l U L U Rw'
|sign=r U' L' U' F2 2L U L U r'
|length=(11,10)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U' L' U' Rw F2 U L U Rw
|sign=r' U' L' U' r F2 U L U r
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U' L' U' B2 Rw' B R B Rw
|sign=r' U' L' U' B2 r' B R B r
|length=(11,10)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U R2 U Rw F2 U L' U Rw
|sign=r' U R2 U r F2 U L' U r
|length=(12,10)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw' U F' U l U2 F' U2 F Rw'
|sign=r' U F' U 2L U2 F' U2 F r'
|length=(12,10)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw U' R' U' Rw' D' L D L' D' Lw
|sign=r U' R' U' r' D' L D L' D' l
|length=(11,11)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|wca=Rw B U F' R b' M R E' R Bw
|sign=r B U F' R 2B' m R e' R b
|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
}}
{{Alg5|wca=Rw U R' U R r' U2 B' L' B' Rw'
|sign=r U R' U R 2R' U2 B' L' B' r'
|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
}}
{{Alg5|wca=l' B' u B' D2 B u' B' l D2 l'
|sign=2L' B' 2U B' D2 B 2U' B' 2L D2 2L'
|length=(13,11)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|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
|length=(12,12)|name=|wide=Y|author=Christopher Mowla
|url=
}}
{{Alg5|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'
|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
}}
{{Alg5|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
|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
}}
{{Alg5|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'
|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
}}

==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.
*These algorithms are nothing more than 2-cycle algorithms which don't preserve centers with beginning and ending outer layer turns omitted.

{{Alg5|wca=r' U' B2 U r U r'
|sign=2R' U' B2 U 2R U 2R'
|length=(8,7)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=r' U B2 U' r U' r'
|sign=2R' U B2 U' 2R U' 2R'
|length=(8,7)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=r' U L2 U' r D' r'
|sign=2R' U L2 U' 2R D' 2R'
|length=(8,7)|name=|wide=N|author=Christopher Mowla
|url=
}}
{{Alg5|wca=r' U' R2 U r D r'
|sign=2R' U' R2 U 2R D 2R'
|length=(8,7)|name=|wide=N|author=Christopher Mowla
|url=
}}

=External Links=
==PLL parity algorithms==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/31340
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/30854
*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?23182-full-4x4-pll

==OLL parity algorithms==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/35545
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/29327
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/28904
*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?2727-4x4-Orientation-parity
*http://www.speedsolving.com/forum/showthread.php?30127-New-4x4-parity-algs-using-R-Rw-U
*https://www.speedsolving.com/forum/showthread.php?10037-4x4-Parity-Algorithms
*https://www.speedsolving.com/forum/showthread.php?27783-4x4-pure-double-parity
*http://www.speedsolving.com/forum/showthread.php?11409-4x4-Optimal-Solver-v2
*http://www.twistypuzzles.com/forum/viewtopic.php?f=8&t=8829
*http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
*http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixBothParities
*http://www.mementoslangues.fr/CubeDesign/4xCubes/DoubleMidgeFlip.pdf
*http://apelgam.se/Rubik/4x4parity/

==Supercube parity algorithms==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/21622
*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?26622-God-s-algorithm-discovered-for-OLL-parity-edge-flip-%28theory%29

==OLL parity algorithms which do not preserve F3L==
*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?17839-WANTED-New-Dedge-Flip-Algorithm!
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=9502

==K4 method parity algorithms==
*http://tomas.rokicki.com/ell4x4.html
*https://www.speedsolving.com/forum/showthread.php?708-A-Collection-of-Algorithms&p=811284&viewfull=1#post811284

==Cage method parity algorithms==
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=6552
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=7140

==Comprehending and making your own parity algorithms==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/12909
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=9720
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=995
*https://www.speedsolving.com/forum/showthread.php?15643-Can-we-really-solve-big-cubes&p=239619
*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?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/
*http://www.speedsolving.com/forum/showthread.php?26477-Contructing-Algorithms-%28not-a-how-to-sorry%29
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=31410
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=32717

==General parity theory==
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=31472
*http://hlavolam.maweb.eu/parity-problem
*https://www.speedsolving.com/forum/showthread.php?41972-Parity-Errors/
*https://www.speedsolving.com/forum/showthread.php?9996-understand-parity
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=26759
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=22201
*http://twistypuzzles.com/forum/viewtopic.php?f=8&t=12841
*https://www.youtube.com/watch?v=wmOyuROOANI
*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

==Preventing/Avoiding parity==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/10755
*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?15880-Can-odd-parity-be-detected-in-a-big-cube-prior-to-being-solved
*https://www.speedsolving.com/forum/showthread.php?19965-Avoiding-parity-errors-in-4x4x4
*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/

==Miscellaneous==
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/topics/12612
*https://groups.yahoo.com/neo/groups/speedsolvingrubikscube/conversations/messages/10119
*http://twistypuzzles.com/forum/viewtopic.php?f=1&t=9133
*http://www.mementoslangues.fr (Go to "Cube Design")

2GLL

2018-10-16T00:35:14Z

Oyyq99999: 12*6+10+4

{{Substep Infobox
|name=2GLL
|image=ZBLL.png
|proposers=[[Zbigniew Zborowski]], [[Ron van Bruchem]], [[Timothy Sun]], [[Lars Petrus]]
|year=2005?
|anames=Step 6+7 ([[Petrus method]])
|subgroup=
|algs=86
|moves=13.15
|purpose=
* [[Speedsolving]]
|previous=[[LL:EO cube state]]
|next=[[Solved cube state]]
}}

'''2GLL''' (short for ''2-Generator Last Layer'') is a subset of [[ZBLL]], which orients and permutes [[LL]] corners while permuting the edges and has 493 cases. 2GLL consists of the 85 cases (including solved) that orient the corners and permute the edges, i.e. exactly the ZBLL cases that can be solved by a [[2-gen]]erator algorithm (using say only U and R).

2GLL is very useful when used with a system that permutes LL corners and orients LL edges before reaching the last layer. One [[CFOP]]-derived system that achieves this is to do the [[cross]], three [[F2L]] pairs, [[ELS]], and lastly [[CPLS]]. One can also use specialized algorithms to control edge orientation during F2L. While these are good ways to branch off from [[CFOP]], most cubers agree that 2GLL works better with methods that, like [[ZZ]] or [[Petrus]], naturally orient the edges before the final F2L slot. 2GLL may also be used after F2L and [[CPEOLL]] which orients edges and permutes corners.

==Learning Approach==
Like ZBLL and [[COLL]], 2GLL cases can be divided into eight subsets, typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and [[EPLL]]. Each 2GLL case is typically recognized by its [[COLL]] followed by the edge cycle (see [[EPLL]]). There are up to 12 cases per COLL, or less due to symmetry.

==Recognition==
1. Recognize the corner orientation case (one of 7).

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines.
Since a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference. If it helps you to recognize better this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

Step 1 should be fairly easy to recognize, as there are only seven possible cases. If you have used another [[LL]] technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy.
Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in:
- If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms.
- If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then
- For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following:
--"Is this cycle going clockwise or anti-clockwise?"
--"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following:
--"Where does the FU sticker need to be in respect to the corner permutation?"
--"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following:
R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a [[Headlights]] case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now!
Next, note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts.
Next, note that this is a clockwise U perm - one that does not cycle RU.
That's it.
Right then, you should be able to apply your alg, AUF, slam your cube down, and stop the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

Before looking too far into 2GLL, it would probably be best to check out [[CPLS]] first.

== See also ==

* [[ZB Method]]
* [[ZBLS]]
* [[ZZ-a]]
* [[VH Method]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=ZBLL-T ZBLL Algorithms] (complete set)
* [[ZBLL]]

== External links ==
* [http://www.speedsolving.com/forum/showpost.php?p=445774&postcount=207 Stachu's 2GLL list] - complete
* [http://www.speedsolving.com/forum/showthread.php?p=454801#post454801 SpeedSolving.com thread]
* [http://lar5.com/cube/xMain.html Lars Petrus' 2GLL algorithms]
* [http://boca.bee.pl/cat.php?l=pl&cat=th&m=zz&ch=d BOCA 2GLL algs]

[[Category:3x3x3 last layer substeps]]
[[Category:Acronyms]]

Kaijun Lin

2018-03-05T04:24:48Z

Oyyq99999:

{{Infobox
|NAME=Kaijun Lin (林恺俊)
|IMAGE=Kaijun_Lin.jpg
|IMAGEYEAR=?
|ALIASES=
|COUNTRY=China
|JOBS=Student
|BIRTHDATE=
|AGE=
|YEARSACTIVE=2013-Present
|ID=2013LINK01
|FAMOUSFOR=Blindfolded solving
}}

'''Kaijun Lin (林恺俊)''' is a Chinese speedcuber. He has set many [[3BLD]], [[4BLD]], [[5BLD]] and [[MBLD]] [[AsR]]s and has set many 3BLD, 4BLD and 5BLD world records.

Lin currently holds the 1:34.66 4x4 blindfolded single world record and the 3:46.56 5x5 blindfolded single world record.

He currently uses Roux as his main method, averaging sub-8 with it.

==Achievements==
{{S-start}}

{{S-ach| ach=Continental Titles}}

{{S-title-bef| before=[[Yuhei Takagi]] | year=2014 }}
{{S-title| title=4x4x4 Blindfolded Asian Champion | year=2016 }}
{{S-inc }}

{{S-title-bef| before=[[Tomoaki Okayama]] | year=2014 }}
{{S-title| title=5x5x5 Blindfolded Asian Champion | year=2016 }}
{{S-inc }}

{{S-end}}

[[Category:Speedcubers|Lin, Kaijun]]
[[Category:Blindfold cubers|Lin, Kaijun]]
[[Category:Roux users|Lin, Kaijun]]

Tairan Zhong

2018-03-03T17:22:40Z

Oyyq99999: /* Records */

{{Infobox
|NAME=Tairan Zhong (钟泰然)
|IMAGE=Tairanzhong.jpg
|IMAGEYEAR=
|ALIASES=
|COUNTRY=China
|BIRTHDATE=
|AGE=
|JOBS=
|YEARSACTIVE=2013-present
|ID=2013ZHON04
|FAMOUSFOR=[[Clock]] WRs
}}

'''Tairan Zhong''' (钟泰然) is a Chinese [[speedcuber]] specializing in [[Rubik's Clock]]. He is one of the fastest Clock solvers in the world.

== Achievements ==
=== Titles ===
{{S-start}}

{{S-ach| ach=National Titles}}

{{S-title-bef| before=[[Shengliang Cai]] | year=2016}}
{{S-title| title=Clock Chinese Champion | year=2017}}
{{S-inc}}

{{S-end}}

=== Records ===
Tairan Zhong has set 3 world records in [[Clock]] for [[average]]; he is the first person in the world who gets a sub-5 average(4.95) in competition. He has also set 9 [[AsR]]s in Clock; 5 for [[single]], and 4 for average.

== See Also ==
* [[Evan Liu]]
* [[Nathaniel Berg]]
* [[Rubik's Clock]]

Danyang Chen

2018-01-30T08:45:43Z

Oyyq99999:

{{Infobox
|NAME=Danyang Chen
|IMAGE=DanyangChen.jpg
|IMAGEYEAR=
|ALIASES=
|COUNTRY=China
|BIRTHDATE=
|AGE=
|JOBS=
|YEARSACTIVE=2007-2011; 2017-present
|ID=2007DANY01
|FAMOUSFOR=[[BLD]] WR
}}

'''Danyang Chen''' (陈丹阳) was a [[China|Chinese]] speedcuber. He set the 3x3x3 blindfolded world record of 1:10 in 2007. He is a WCA delegate in China.

[[Category:Former world record holders|Chen, Danyang]]
[[Category:Blindfold cubers|Chen, Danyang]]
[[Category:Speedcubers|Chen, Danyang]]
[[Category:Cubers|Chen, Danyang]]

Category:Fewest Moves techniques

2017-10-16T08:01:26Z

Oyyq99999: /* External links */

This page introduces some tips and techniques to help you solve the cube in as [[Fewest Moves|few moves]] as possible.

The best results can be obtained when all techniques are controlled. It is strongly advised not to follow a strict pattern, for example a [[3x3x3 speedsolving methods|speedsolving method]]. However some algorithms learned from a speedsolving method will give some advantages in some cases. The most useful [[Fewest Moves Methods|methods]] are [[Heise]], [[Petrus]], [[Fridrich]], [[Roux]] and [[ZBLL]].

== Block Building ==
{{Main Article|Article=Block Building}}
Best start for an FMC is block building technique. Try to build a [[2x2x2 block]] then a [[2x2x3 block]]. After the 2x2x2 block you have 3 sides to extend it to a 2x2x3. Explore all of them. After the 2x2x3 block...

== Pair Insertion ==
When [[insertion|inserting]] Fridrich-pairs in F2L don't get stuck with you speedcubing methods but try some alternatives and check each of them for...

== Inverse Scramble ==
If you can't find a good start to your scramble, you can try inverting the scramble. That means the scramble R F' D2 U becomes U' D2 F R'. Find a good solution based on the inverted scramble, then invert the solution. The inverted solution will solve the original scramble. It looks strange to solve like this, but gives you more chances to find a good start.

== Pseudoblocks or Pre-scramble-moves==
Like [[Heise Method]] you can build pseudo blocks, which are adjacent 1x2x2 blocks or c/e pairs that are not adjacent but need an extra turn to get those blocks at the right color-centre. Solving with pseudo blocks can be very difficult and requires a lot of experience. As an alternative you can replace a pseudo block by a pre-scramble-move to give more oversight over your solve.

== NISS ==
The Normal-inverse-scramble-switch (NISS) technique was introduced in 2009 by Guus Razoux Schultz in the speedsolving forum here: http://www.speedsolving.com/forum/showthread.php?13599-The-FMC-thread/page19&p=258791#post258791
On this forum you can find several good explanations of how it works. Mike Hughey made it pretty understandable with the following description:

''Generally, you use premoves to modify a scramble so you can solve it more easily. The most common approach for this is to solve a "pseudo-block" of some sort, where for instance you might put in a corner-edge pair of the wrong color into a 2x2x2 or 2x2x3 block. Then you find the moves necessary to put that corner-edge pair (or whatever) into it's proper location in the solved cube. If you then apply those moves to the solved cube prior to applying the scramble, you'll find that the pseudo-block becomes an actual block. Then you can add those moves to the end of your final solution and it will be solved.''

''Guus's solution you mention is using "NISS" - his "normal-inverse-scramble-switch" method, where you solve part of the cube with the normal scramble, then when you get stuck, you switch to the inverse scramble and use it, then when you get stuck again, you switch back to the normal scramble, and so on. I love NISS - it's really fun to do! Anyway, when you switch from normal to inverse scrambles, the moves you used at the beginning of the normal scramble solve become premoves to the inverse scramble (and vice-versa). It takes trying it to see how it really works, and it's really quite ingenious.''

''The best way to understand these is to look at some of the solves that others have done (like the ones in the weekly competitions) and understand how they work. Examples are much more useful than descriptions - this isn't a particularly good description, but maybe it gives you an idea of what's going on. ''

''A pre-scramble move is a move you apply before the scramble and which allows you to find more possible solutions. Of course you must not forget to add the premove at the end of your solution.''

== Inserted Moves (single) ==
Sometimes after a promising start you can't find a good continuation. Say you have solved a 2x2x2 block, but after that there's nothing good. By stepping through the solution you might see that at one place there's no 2x2x2-pieces on U, at that place you can try to insert U, U' or U2 and see if a better continuation is possible.

== Inserted Algorithms/Commutators ==
A very powerful technique in FMC is to solve everything except 3-5 corners and then insert 8 move [[commutators]] that cycle three corners earlier in the solution. Since there many corner configurations that can be solved in 8 moves often one will cancel moves, and thus one corner cycle will add less than 8 moves to the total solution length. Edge cycles are not used as often since FMC is judged in [[HTM]] and edge cycles often involve slice moves that are counted as two moves. Some people use stickers to more easily track the unsolved pieces through the solution.

== Freestyle Solving ==
If you see some opportunity to solve a lot of blocks without any (known) pattern you could try to solve it. When leaving a maximum of 4 edges and 4 corners try to conjugate them to 1 face during a solve. Then use pre-scramble-moves or a second cube to solve that face / LL

== LL-algorithms ==
Sometimes you solve a lot of LL blocks using a very short LL algorithm, 8 or 9 moves maximum. Try to learn short LL algorithms in such a way that you know what it does to corners and edges. Start with the length-6 LL-alg, then the three 7-move LL-algs, the five 8-move LL-algs, and so on. You are really an expert when learning all LL-algs up to 10 moves.

A step up from this is to start the alg part from the [[last slot]], [[LPELL]] is one such method.

== Other Tips ==

* Do not use moves that turn the cube!

* Use fixed colors for up & front to enhance recognition!

* Better still, look at the centre of the face you are turning, it tells which side it is ("White" = U and so on), then orientation does not matter anymore.

* Write down promising moves, do not wait till the very end!

* Create a backup solve!

* Learn to scramble fast, it can save a lot of time during a 1-hour solve.

* Bring stickers (for insertions) and extra cubes during a competition.

== See also ==

* [[Fewest Moves]]
* [[Commutators]]
* [[Niklas]]
* [[God's Algorithm]]
* [[Fewest Moves methods]]
* [[Puzzle theory]]

== External links ==

* [http://www.ryanheise.com/cube/fundamental_techniques.html Ryan Heise's page on intuitive solving techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?t=1566 Fewest Moves: Tips and Techniques]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?p=221756 The FMC thread]
* Speedsolving.com [http://www.speedsolving.com/forum/showthread.php?13599-The-FMC-thread&p=723818&viewfull=1#post723818 6 to 10-move LL algorithms]
* Online tool: [https://fewestmov.es/ Insertion Finder]

[[Category:Fewest Moves Methods]]

__NOTOC__

Twisty Corners of Last Layer

2017-08-11T03:16:41Z

Oyyq99999:

{{Method Infobox
|name=TCLL (2x2x2)
|image=
|proposers=[[Robert Yau]]
[[Christopher Olson]]
|year=2013
|anames
|variants=[[LBL]]
[[CLL]]
|steps=2
|algs=126 (86 for only TCLL)
|moves=<15
|purpose=
* [[Speedsolving]]
}}
'''TCLL''' or '''Twisty Corners of Last Layer''' is an advanced 2x2 method proposed in 2013 by [[Robert Yau]] and [[Christopher Olson|Chris Olson]] based off a study into [http://www.speedsolving.com/forum/threads/rofl-method.43898/ RoFL] (ROtten First Layer) by [[Stefan Pochmann]]. It is efficient and is very good for those who can 1-look their 2x2 solves and cancel into algorithms. It can be divided into 3 subsets: regular [[CLL]], '''TCLL-''' (where the misoriented corner in DR faces to the right) and '''TCLL+''' (where the corner faces to the front). There are 43 algorithms for each TCLL set and 40 for the CLL.

==Steps==
#Solve a layer (one corner can be twisted in place)
#TCLL

==Pros==
*Can easily be 1-looked in almost all cases fairly easily.
*Lots of cancellations can be formed between the layer and the algorithm
*Building a layer with a twisted corner is much shorter than building a full layer
*Can have ridiculously easy solves

==Cons==
*It is not generally recommended to use TCLL as a stand alone method
*Beginners may find it difficult to 1-look solves and take advantage of the cancellations
*Approximately 2 Times more algorithms than CLL, EG-1 or EG-2

==Example Solves==
#R' F' R2 F R' U' F2 R' U'
#*x2 y' (Canceling moves instead of doing U2 R U2 R) U2 F R F' R U
#F' R U' R' U F2 R' U2 R2
#*y' L' U' L' F' L F U2 L' U2 L
#U R' F R' U2 R F' R U'
#*z2 U' (Canceling moves instead of doing R U' R') R U2 R' U2 R U2 R' U
#R' F U R F2 R U' R2 U
#*x L2 U2 R U R' U' R U2 R' F' R U R' F'
#U2 F2 U' F U' F' R' F' U2
#*x' y' U F2 R U2 R' U R' F R F' R U' R'
#U R2 F' U R U2 R F2 U2
#*x' U2 R y U' F R' F' R2 U R'
#U2 F' R' U' F2 U' R2 U R2
#*x2 U F' R F' R U R2 U' R U R'

==See Also==
*[[CLL]]
*[[EG]]

==External Links==
*[https://www.speedsolving.com/forum/threads/tcll-2x2-method.44438/ TCLL proposal thread]
*[https://cyotheking.squarespace.com/tcll-1/ Chris Olson's TCLL- page on his website]
*[https://cyotheking.squarespace.com/tcll/ Chris Olson's TCLL+ page on his website]
*[http://www.speedsolving.com/forum/threads/rofl-method.43898/ Stefan's RoFL Thread]
*[http://www.speedsolving.com/forum/threads/all-of-tcll-sub-1.44955/ Chris Olson Sub-1s all TCLL+]

[[Category:Acronyms]]
[[Category:2x2x2 substeps]]
[[Category:2x2x2 methods]]

Beyer-Hardwick Method

2017-07-07T07:31:16Z

Oyyq99999:

{{Method Infobox
|name= Beyer-Hardwick
|image=
|proposers=[[Chris Hardwick]] , [[Daniel Beyer]]
|year= ~2009
|a names=
|variants= Algorithms
|steps= 2
|algs= 0-818 (Intuitive) (378 for corners 440 for edges)
|moves=???
|purpose=
* [[Blindsolving]]
* [[FMC]]
}}

'''B'''eyer-'''H'''ardwick Method. An advanced blindsolving method based on the use of 3-cycle algorithms. The fundamental idea behind the BH method is to use pre-memorized, move optimal, commutator 3-cycles for all possible 3-cycles starting from a fixed buffer location. For pieces where orientation is defined, the position and orientation of pieces are solved simultaneously. The use of commutators allows the BH method to be used for solving any sized cube blindfolded.

== BH Corners ==
These are the different types of commutators you will "see" while learning BH.

''' Pure Commutators (8 moves)'''
- are the purest and smallest form of commutators and all other commutators are just setups into them hence called Pure Commutators (except Cyclic Shifts and Per Specials). They follow this formula: ABA'B' or [A, B] for short.

A is always a 3 move insert
B is the interchange move and always 1 move and opposite from the middle move of A. Ex [R U R', D] U is the middle move of the A move that means the B move must be some form of D move

To recognize 1 corner is in 1 layer and the remaining 2 are in a different layer. The 2 corners in one layer must be interchangeable and there must be a 3 move insert between 1 corner in 1 layer and 1 corner in the different layer.

There are only 3 A moves:
R U R'
R U' R'
R U2 R'
All Pure Comms are composed from these 3 A moves meaning there's only 18 algs and everything else is just mirror/inverse/rotation from the 18 algs.

''' A9 (9 moves)'''
- are conjugated Pure Comms with a cancellation resulting in 9 moves instead of 10. They follow this formula: SABA'B'S' or [S: [A, B] ]where S is the setup move.

Ex. [R: RUR', D] becomes R R U R' D R U' R' D' R' or simply R2 U R' D R U' R' D' R'.

All setup moves or S moves must cancel with A. There are no B9s or a corner commutator with a S move that cancels with the B move. If you find 1 then that just means it's a Pure Comm. Edge commutators though have B9s.

To recognize them they're the same as Pure Comms but they don't have a 3 move insert. But that's not always the case so just use elimination to figure it out. The first rule always applies so if you see that then it's a A9.

''' Orthogonals (10 moves) '''
- are conjugated Pure Comms with no cancellations resulting in 10 moves instead of 9. They follow the same formula [S: [A, B]] as well but the S move doesn't cancel with A nor B.

To recognize them you must know 2 terms:

Opposites - when 2 corners can't go to each other's places with 1 quarter turn. Ex. UBL is opposite to DBR
Note: We're only talking permutation-wise. Meaning UBL being opposite to BDR is as the same as saying UBL is opposite to DBR.

AnI or nI (Adj Non-interchangeable or Non-interchangeable - nI is a better term since saying AnI sometimes doesn't make sense. Put it simply a sticker is not interchangeable with another if you can't do it 1 move.

To recognize all 3 corners are opposites and nI to each other. (See what I mean? Saying AnI here doesn't make sense when alll the corners are opposite)

To do them just do ANY quarter turn S move and it will setup into a Pure Comm and undo the S move.

''' Cyclic Shifts (11 moves)'''
- they don't come from Pure Comms and follow a different formula: [A: B] [C: B] or A B A' C B C'

A is always 2 moves which are comprised of 2 adjacent layers (Ex. F and R) and one is going clockwise and another going counterclockwise

B is always a half turn and is not a opposite layer to either A or C
Ex. A is R F so B must not be any form of B or L move

C is the reverse of A (not inverse)
Ex. A is R F so C must be F R

Ex. [R F: U2] [F R: U2]

To recognize all 3 corners are on the same layer and are nI.

To do them figure out the middle piece of the cycle. Ex. UBL -> LFU -> BRU The middle piece is UBL and must go to LFU. Do [R F: U2] to swap them and now the next piece must go to BRU so do [F R: U2] to swap them and then you're done.

If you don't understand any of these it's all right since all Cyclic Shifts are the same meaning just by learning the one alg above you just need to mirror/inverse/rotate to solve any Cyclic Shift.

'''Column Cases (11 moves)'''
- they're just 11 movers that can be done in 2 ways: a setup into an A9 with no cancellation or a setup into a Cyclic Shift with a cancellation.

To recognize there are 2 corners interchangeable by a half turn and the remaining corner is nI to them.

'''Per Specials (12 moves)'''
- a special type of commutators that follow the same [A, B] formula but the A part is a 5 move insert and B is just a half turn. There's 6 of them and they're all the same meaning you just need to learn 1 alg and just mirror/inverse/rotate it.

Ex. [L U2 R' U2 L, U2]

To recognize all 3 corners are opposite and mutually interchangeable. Ex. UBL -> DFL -> DBR

== BH Edges ==
These are the types of edge commutators you'll "see" while learning BH edges.

'''Half Slice-Planes (4 moves)''' - A special type of commutator that makes its interchanges on the same outer layer.

Formula: [A, B] where a A is the interchange and B is the setup to the interchange.

'''Slice-Planes (SP5, SP7, SP9) (5, 7, 9 moves''' - Slice-Planes are conjugated Half Slice-Planes commutators.

'''Pure Commutators (8 moves)''' - Same as BH Pure Comms.

'''A9/B9 (9 moves)''' - Same as BH A9s except B9s exists.

'''Orthogonals (10 moves)''' - Same as BH Orthogonals.

== Learning Approach ==

Learning BH is a large task whether you'll opt for more speed-optimised algs some where down the line for some cases knowing the basic structure of a commutator [A, B] will help whether you'll look up a list or create the algs yourself since shortening an alg to [A, B] is alot easier to learn.

Creating the algs on your own is sometimes suggested as it will help you remember them more since you created them but looking up a list and not creating the algs yourself is fine but don't rely it on too much since that person's list is probably speed-optimised for them so if an alg is too hard to do try and make one for your self.

Note that BH or any form of commutators are intuitive meaning you don't need to generate the alg, YOU make them.

Whether you make them or not there's 2 routes to learning them: On the fly or learn the entire list before applying it on the cube.

Just like how F2L can be solved on the fly as long you know how to recognize certain cases or have a good sense for commutators you can actually not list every single case amd learn them rather you can do it while solving with no prior knowledge about a certain case just like you don't know every single F2L case but you can still do them.

== Recognition ==

'''BH Corners'''

1. '''Pure Commutators''' 
- 2 corners in one layer and another corner in a different layer. (Ex. 2 corners at U and and the 3rd corner at D) 
- The 2 corners in one layer are interchangeable 
- There's a 3 move insert 

2. '''A9''' 
- Exactly like a Pure Commutator but with no 3 move insert (Not applicable to all A9s) 
- Use elimination. (Ex. If it's not a Pure Comm with no 3 move insert then check if it's one of the other BH Corner Cases, if not then it's an A9) 

3.'''Orthogonals''' 
- All 3 corners are opposite and are all AnI to each other 

4. ''' Cyclic Shifts ''' 
- All 3 corners are in the same layer are are all AnI to each other 

5. ''' Columns ''' 
- Like a Pure Comm with no 3 move insert but the interchange corners are interchangeable with a half turn (Don't be confused with A9s) 

6. ''' Per Specials ''' 
- All 3 corners are opposite 
- All 3 corners are mutually interchangeable 

== External links ==
* [http://www.speedcubing.com/chris/bhcorners.html BH method for corners - Hardwick]
* [http://www.speedcubing.com/chris/bhedges.html BH method for 3x3 edges - Hardwick]
* [http://skarrie.se/edges/ BH method for 3x3 edges - Skarrie]
* [https://spreadsheets.google.com/pub?key=0AuQyS2mqoMAMdGxaamlSVFo5d0NhNkxUbWp0UGlLdXc&single=true&gid=0&output=html BH method for corners - Riffz]
* [https://docs.google.com/spreadsheet/pub?key=0AvKFSRYPmkKRdHY0QTVxQlRmV216SHJLRHlpWHBTakE&output=html BH method for corners - Jalocha]
* [http://www.speedsolving.com/forum/showthread.php?36014-The-edge-cycles-I-use-for-BLD&p=726087#post726087 edge cycles - lucarubik]
* [http://www.speedsolving.com/forum/showthread.php?36145-The-corner-cycles-I-use-for-BLD&p=728708#post728708 corner cycles - lucarubik]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=11909 Thoughts about the BH method]* [http://www.speedsolving.com/forum
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12268 Brian Yu's tutorial for BH corners]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?p=310411 Chris Hardwick's explanation of BH 3x3 edges]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?p=1601#post1601 Beginner BH ideas for big cube edges]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?p=1643#post1643 Intermediate/Advanced BH ideas for big cube edges]

[[Category:Blindsolving methods]]

{{Stub}}

Beyer-Hardwick Method

2017-07-07T07:29:18Z

Oyyq99999:

{{Method Infobox
|name= Beyer-Hardwick
|image=
|proposers=[[Chris Hardwick]] , [[Daniel Beyer]]
|year= ~2009
|a names=
|variants= Algorithms
|steps= 2
|algs= 0-819 (Intuitive) (378 for corners 440 for edges)
|moves=???
|purpose=
* [[Blindsolving]]
* [[FMC]]
}}

'''B'''eyer-'''H'''ardwick Method. An advanced blindsolving method based on the use of 3-cycle algorithms. The fundamental idea behind the BH method is to use pre-memorized, move optimal, commutator 3-cycles for all possible 3-cycles starting from a fixed buffer location. For pieces where orientation is defined, the position and orientation of pieces are solved simultaneously. The use of commutators allows the BH method to be used for solving any sized cube blindfolded.

== BH Corners ==
These are the different types of commutators you will "see" while learning BH.

''' Pure Commutators (8 moves)'''
- are the purest and smallest form of commutators and all other commutators are just setups into them hence called Pure Commutators (except Cyclic Shifts and Per Specials). They follow this formula: ABA'B' or [A, B] for short.

A is always a 3 move insert
B is the interchange move and always 1 move and opposite from the middle move of A. Ex [R U R', D] U is the middle move of the A move that means the B move must be some form of D move

To recognize 1 corner is in 1 layer and the remaining 2 are in a different layer. The 2 corners in one layer must be interchangeable and there must be a 3 move insert between 1 corner in 1 layer and 1 corner in the different layer.

There are only 3 A moves:
R U R'
R U' R'
R U2 R'
All Pure Comms are composed from these 3 A moves meaning there's only 18 algs and everything else is just mirror/inverse/rotation from the 18 algs.

''' A9 (9 moves)'''
- are conjugated Pure Comms with a cancellation resulting in 9 moves instead of 10. They follow this formula: SABA'B'S' or [S: [A, B] ]where S is the setup move.

Ex. [R: RUR', D] becomes R R U R' D R U' R' D' R' or simply R2 U R' D R U' R' D' R'.

All setup moves or S moves must cancel with A. There are no B9s or a corner commutator with a S move that cancels with the B move. If you find 1 then that just means it's a Pure Comm. Edge commutators though have B9s.

To recognize them they're the same as Pure Comms but they don't have a 3 move insert. But that's not always the case so just use elimination to figure it out. The first rule always applies so if you see that then it's a A9.

''' Orthogonals (10 moves) '''
- are conjugated Pure Comms with no cancellations resulting in 10 moves instead of 9. They follow the same formula [S: [A, B]] as well but the S move doesn't cancel with A nor B.

To recognize them you must know 2 terms:

Opposites - when 2 corners can't go to each other's places with 1 quarter turn. Ex. UBL is opposite to DBR
Note: We're only talking permutation-wise. Meaning UBL being opposite to BDR is as the same as saying UBL is opposite to DBR.

AnI or nI (Adj Non-interchangeable or Non-interchangeable - nI is a better term since saying AnI sometimes doesn't make sense. Put it simply a sticker is not interchangeable with another if you can't do it 1 move.

To recognize all 3 corners are opposites and nI to each other. (See what I mean? Saying AnI here doesn't make sense when alll the corners are opposite)

To do them just do ANY quarter turn S move and it will setup into a Pure Comm and undo the S move.

''' Cyclic Shifts (11 moves)'''
- they don't come from Pure Comms and follow a different formula: [A: B] [C: B] or A B A' C B C'

A is always 2 moves which are comprised of 2 adjacent layers (Ex. F and R) and one is going clockwise and another going counterclockwise

B is always a half turn and is not a opposite layer to either A or C
Ex. A is R F so B must not be any form of B or L move

C is the reverse of A (not inverse)
Ex. A is R F so C must be F R

Ex. [R F: U2] [F R: U2]

To recognize all 3 corners are on the same layer and are nI.

To do them figure out the middle piece of the cycle. Ex. UBL -> LFU -> BRU The middle piece is UBL and must go to LFU. Do [R F: U2] to swap them and now the next piece must go to BRU so do [F R: U2] to swap them and then you're done.

If you don't understand any of these it's all right since all Cyclic Shifts are the same meaning just by learning the one alg above you just need to mirror/inverse/rotate to solve any Cyclic Shift.

'''Column Cases (11 moves)'''
- they're just 11 movers that can be done in 2 ways: a setup into an A9 with no cancellation or a setup into a Cyclic Shift with a cancellation.

To recognize there are 2 corners interchangeable by a half turn and the remaining corner is nI to them.

'''Per Specials (12 moves)'''
- a special type of commutators that follow the same [A, B] formula but the A part is a 5 move insert and B is just a half turn. There's 6 of them and they're all the same meaning you just need to learn 1 alg and just mirror/inverse/rotate it.

Ex. [L U2 R' U2 L, U2]

To recognize all 3 corners are opposite and mutually interchangeable. Ex. UBL -> DFL -> DBR

== BH Edges ==
These are the types of edge commutators you'll "see" while learning BH edges.

'''Half Slice-Planes (4 moves)''' - A special type of commutator that makes its interchanges on the same outer layer.

Formula: [A, B] where a A is the interchange and B is the setup to the interchange.

'''Slice-Planes (SP5, SP7, SP9) (5, 7, 9 moves''' - Slice-Planes are conjugated Half Slice-Planes commutators.

'''Pure Commutators (8 moves)''' - Same as BH Pure Comms.

'''A9/B9 (9 moves)''' - Same as BH A9s except B9s exists.

'''Orthogonals (10 moves)''' - Same as BH Orthogonals.

== Learning Approach ==

Learning BH is a large task whether you'll opt for more speed-optimised algs some where down the line for some cases knowing the basic structure of a commutator [A, B] will help whether you'll look up a list or create the algs yourself since shortening an alg to [A, B] is alot easier to learn.

Creating the algs on your own is sometimes suggested as it will help you remember them more since you created them but looking up a list and not creating the algs yourself is fine but don't rely it on too much since that person's list is probably speed-optimised for them so if an alg is too hard to do try and make one for your self.

Note that BH or any form of commutators are intuitive meaning you don't need to generate the alg, YOU make them.

Whether you make them or not there's 2 routes to learning them: On the fly or learn the entire list before applying it on the cube.

Just like how F2L can be solved on the fly as long you know how to recognize certain cases or have a good sense for commutators you can actually not list every single case amd learn them rather you can do it while solving with no prior knowledge about a certain case just like you don't know every single F2L case but you can still do them.

== Recognition ==

'''BH Corners'''

1. '''Pure Commutators''' 
- 2 corners in one layer and another corner in a different layer. (Ex. 2 corners at U and and the 3rd corner at D) 
- The 2 corners in one layer are interchangeable 
- There's a 3 move insert 

2. '''A9''' 
- Exactly like a Pure Commutator but with no 3 move insert (Not applicable to all A9s) 
- Use elimination. (Ex. If it's not a Pure Comm with no 3 move insert then check if it's one of the other BH Corner Cases, if not then it's an A9) 

3.'''Orthogonals''' 
- All 3 corners are opposite and are all AnI to each other 

4. ''' Cyclic Shifts ''' 
- All 3 corners are in the same layer are are all AnI to each other 

5. ''' Columns ''' 
- Like a Pure Comm with no 3 move insert but the interchange corners are interchangeable with a half turn (Don't be confused with A9s) 

6. ''' Per Specials ''' 
- All 3 corners are opposite 
- All 3 corners are mutually interchangeable 

== External links ==
* [http://www.speedcubing.com/chris/bhcorners.html BH method for corners - Hardwick]
* [http://www.speedcubing.com/chris/bhedges.html BH method for 3x3 edges - Hardwick]
* [http://skarrie.se/edges/ BH method for 3x3 edges - Skarrie]
* [https://spreadsheets.google.com/pub?key=0AuQyS2mqoMAMdGxaamlSVFo5d0NhNkxUbWp0UGlLdXc&single=true&gid=0&output=html BH method for corners - Riffz]
* [https://docs.google.com/spreadsheet/pub?key=0AvKFSRYPmkKRdHY0QTVxQlRmV216SHJLRHlpWHBTakE&output=html BH method for corners - Jalocha]
* [http://www.speedsolving.com/forum/showthread.php?36014-The-edge-cycles-I-use-for-BLD&p=726087#post726087 edge cycles - lucarubik]
* [http://www.speedsolving.com/forum/showthread.php?36145-The-corner-cycles-I-use-for-BLD&p=728708#post728708 corner cycles - lucarubik]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=11909 Thoughts about the BH method]* [http://www.speedsolving.com/forum
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=12268 Brian Yu's tutorial for BH corners]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?p=310411 Chris Hardwick's explanation of BH 3x3 edges]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?p=1601#post1601 Beginner BH ideas for big cube edges]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?p=1643#post1643 Intermediate/Advanced BH ideas for big cube edges]

[[Category:Blindsolving methods]]

{{Stub}}

Category:Pyraminx methods

2017-07-04T07:48:11Z

Oyyq99999: /* Turning speed */

:''[[:Category:Pyraminx methods]]''

This page describes different methods to speedsolve the [[Pyraminx]].

When speedsolving the Pyraminx the method used does not matter as much as it does on other puzzles - an intermediate method is almost always good enough to get fast times. This is a very quick puzzle which isn't hard to solve efficiently, so the most important things to practice are [[Pyraminx methods#Lookahead|lookahead]] and [[Pyraminx methods#Turning speed|turning speed]].

Some of the descriptions here use an extended notation, see [[Pyraminx notation]] for an explanation of the system.

==Beginner Methods==

This method is recommended mainly to people who just want to solve the Pyraminx, although the puzzle isn't hard to figure out yourself. You can still go from a total beginner to under 30 seconds in about an hour with this method:

* Step 1: Orient the four corners and their tips. They don't move, so this shouldn't require any thought.
* Step 2: Use R' L R L' and L R' L' R to place the edges. These algorithms will move exactly three edges around, so just keep trying until you are done.

==Intermediate Methods==

Intermediate methods can easily give you an average of less than 10 seconds. It doesn't matter when the tips are solved, so they are not included in the listed steps.

===Keyhole===

* Step 1: Solve two edges around a center.
* Step 2: Use the extra edge slot, the "keyhole", to solve the centers of the last layer (the layer opposite that center).
* Step 3: Solve the edge that belongs in the keyhole. Algorithms can be found [[Pyraminx algorithms#Last edge on first tip:|here]].
* Step 4: Solves the edges of the last layer. Algorithms can be found [[Pyraminx algorithms#Edges of Last Layer: (ELL)|here]].

===Layer By Layer===

* Step 1: Sove three of the centers. They will share a color; try to simultaneously place as many of the edges of that layer as you can.
* Step 2: Finish the layer by inserting the remaining edges with RUR'-type insertions. Sometimes there are special tricks you can do in this step if you end up with edges that are already in the layer but in the wrong place or misoriented.
* Step 3: Solve the last layer in one step. There are 5 possible algorithms which can be found [[Pyraminx algorithms#Last Layer algorithms:|here]].

===Johan's method===

*Step 1: Solve the center pieces.
*Step 2: Solve 2 opposite edges.
*Step 3: Use commutators to permute the last 4 edges.
*Step 4: Orient last edges.

==Advanced Methods==

There are some advanced methods for the Pyraminx, and although they are not necessary to get very fast times, they could provide a boost to the serious solver. They are more efficient than intermediate methods but require more memorization or have harder recognition, and thus will take much more time to master. Also, just like in the beginner and intermediate methods, it doesn't matter when you solve the tips, so they are not included in the listed steps

===L4E===
L4E stands for Last 4 Edges. It is named after the alg set used in the final step, which is also called L4E.
* Step 1: Solve all of the centers and two adjacent edges. With practice this can be 1-looked in inspection.
* Step 2: Finish the last 4 edges in one step. There are 95 algs for this, but this step can also be done intuitively.

===1-Flip===

* Step 1: Solve two edges around a center, and put the third one in backwards.
* Step 2: Solve the centers and the flipped edge in one step.
* Step 3: Solve the edges of the last layer. Algorithms can be found [[Pyraminx algorithms#Edges of Last Layer: (ELL)|here]].

===Oka===
* Step 1: Solve one edge around a center, and insert another edge oriented correctly, but in the wrong spot.
* Step 2: Use the extra edge slot, just like in Keyhole, to solve the centers.
* Step 3: Solve the incorrectly flipped edge and the keyhole in one step.
* Step 4: Solve the edges of the last layer. Algorithms can be found [[Pyraminx algorithms#Edges of Last Layer: (ELL)|here]].

===Nutella===
* Step 1: Solve one edge around a center, and insert the two others in their opposite positions and orientatation.
* Step 2: Solve the centers and those two edges with one algorithm.
* Step 3: Solve the edges of the last layer. Algorithms can be found [[Pyraminx algorithms#Edges of Last Layer: (ELL)|here]].

===WO===
WO stands for Wedel-Odder, which was named after the creators of the method.
* Step 1: Solve all the three edges around a single center, forming a "top".
* Step 2: Use one algorithm to solve the centers while preserving the top.
* Step 3: Solve the edges of the last layer. Algorithms can be found [[Pyraminx algorithms#Edges of Last Layer: (ELL)|here]].

===Petrus===

* Step 1: Create a 'block' by matching one edge to the two adjacent corners.
* Step 2: Orient the remaining edges, [[Petrus]]-style, so that they can all be solved using only U and R turns.
* Step 3: Finish all of the edges using only U and R turns.

===FP===
FP stands for Fan's Pyraminx Method or Face-Permute. The idea is similar to Ortega/Varasano for the 2x2x2 cube.

* Step 1: Make one face. Nothing has to be permuted properly. This can be done in about 3-7 moves usually. It should be possible to easily see this from inspection. The EP of the bottom layer can be determined, making the recognition of the 2nd step extremely easy.
* Step 2: Permute everything. This can be done in about 6-8 moves usually. There are 20 algorithms for this step.

===FFL===
FFL stands for Flipped First Layer, and is an type of Layer-by-Layer Pyraminx method. It can be considered a sort-of "opposite" to the FP method, as you focus only on the permutation of the edges rather than the orientation of them.

There are 3 subsets of the FFL method: 1FFL, 2FFL, and 3FFL; where one, two, or all edges are disoriented respectively.

* Step 1: Solve one layer ignoring orientation of the edges. They must be permuted correctly, however.
* Step 2: Orient the first layer and solve the last 3 edges in one algorithm. There are about 18 algorithms total.

== Tips and Tricks ==
=== Lookahead ===
=== Turning speed ===
'''Re-grips:''' A good way to increase your turning speed is to optimise your algorithms so you can execute them using as few re-grips as possible,

:'''Example:''' Take the two-edge flip alg, a common case for most methods, normally it is notated something like R' L R L' U L' U' L but using the [[Pyraminx_notation#Extensions_to_the_Notation|extended notation]] that allows face twists as well as tip turns it can be notated and executed like R' L R r' R L' R' r and it gives only one re-grip and no rotations.

'''Triggers:''' Another way to increase the speed is to use [[trigger]]s. (L R') is possibly the easiest trigger you can do: turn L about 30% of the turn and then place your right thumb on top of the edge that now shows its corner sticking out of the F-face. Push the edge using the thumb down to the face compleating th L turn and from there keep pushing until also the R' is done. After some practice you can actually do the whole trigger witout pre-turning the L tip, just place you thumb at the proper place on the edge and go away, two turns in one!

To do the four turn 3-cycle LL edges (L R') (L' R) then do the first part as above and the second trigger (L' R) in the same manner but now do 30% L' and then the right thumb under the edge that comes out of the D-face and then push all the way up.

'''Alternative style:'''
An alternative style is to hold the whole pyraminx in one hand (left) and only use that hand for U layer triggers. Do everything else with the other hand as you would with a 3x3x3 cube.

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=20494 Pyraminx method names]
* YouTube: [http://www.youtube.com/watch?v=74zFmYtSfew How to solve a Pyraminx] (Corners First Method)
* YouTube: [http://www.youtube.com/watch?v=Oio3ZmPDv0g How to Solve a Tetraminx or Pyraminx] (Beginners Method)
* [http://www.cubewhiz.com/pyraminx.php Bob Burton Method] (Beginners Method)
* Last 4 Edges Algorithms: [http://www.mzrg.com/rubik/solving/pyraminx/index.html Solution to the Pyraminx]
* FFL Algorithms: [http://sites.google.com/site/philcuber/pyraminx FFL Pyraminx Algs]
*FP algoorithms: [https://docs.google.com/document/d/1RGjDVLQuxvb96nZqz0-HTngVcXwSsZOTXXBIlhkDCI4/edit?usp=sharing]
[[Category:Pyraminx]]

Twisty Corners of Last Layer

2017-05-04T09:33:32Z

Oyyq99999: /* Example Solves */

{{Method Infobox
|name=TCLL (2x2x2)
|image=
|proposers=[[Robert Yau]]
[[Christopher Olson]]
|year=2013
|anames
|variants=[[LBL]]
[[CLL]]
|steps=2
|algs=128 (86 for only TCLL)
|moves=<15
|purpose=
* [[Speedsolving]]
}}
'''TCLL''' or '''Twisty Corners of Last Layer''' is an advanced 2x2 method proposed in 2013 by [[Robert Yau]] and [[Christopher Olson|Chris Olson]] based off a study into [http://www.speedsolving.com/forum/threads/rofl-method.43898/ RoFL] (ROtten First Layer) by [[Stefan Pochmann]]. It is efficient and is very good for those who can 1-look their 2x2 solves and cancel into algorithms. It can be divided into 3 subsets: regular [[CLL]], '''TCLL-''' (where the misoriented corner in DR faces to the right) and '''TCLL+''' (where the corner faces to the front). There are 43 algorithms for each TCLL set and 42 for the CLL.

==Steps==
#Solve a layer (one corner can be twisted in place)
#TCLL

==Pros==
*Can easily be 1-looked in almost all cases fairly easily.
*Lots of cancellations can be formed between the layer and the algorithm
*Building a layer with a twisted corner is much shorter than building a full layer
*Can have ridiculously easy solves

==Cons==
*It is not generally recommended to use TCLL as a stand alone method
*Beginners may find it difficult to 1-look solves and take advantage of the cancellations

==Example Solves==
#R' F' R2 F R' U' F2 R' U'
#*x2 y' (Canceling moves instead of doing U2 R U2 R) U2 F R F' R U
#U R' F R' U2 R F' R U'
#*z2 U' (Canceling moves instead of doing R U' R') R U2 R' U2 R U2 R' U
Solves by Chris Olson.

==See Also==
*[[CLL]]
*[[EG]]

==External Links==
*[https://www.speedsolving.com/forum/threads/tcll-2x2-method.44438/ TCLL proposal thread]
*[https://cyotheking.squarespace.com/tcll-1/ Chris Olsen's TCLL- page on his website]
*[https://cyotheking.squarespace.com/tcll/ Chris Olsen's TCLL+ page on his website]
*[http://www.speedsolving.com/forum/threads/rofl-method.43898/ Stefan's RoFL Thread]
*[http://www.speedsolving.com/forum/threads/all-of-tcll-sub-1.44955/ Chris Olson Sub-1s all TCLL+]

[[Category:Acronyms]]
[[Category:2x2x2 substeps]]
[[Category:2x2x2 methods]]

2-Look PLL

2016-12-20T08:51:06Z

Oyyq99999:

This PLL system is used to permute the last layer after orientation. Of the 21 cases, only 6 are needed for '''2-Look PLL''' (commonly abbreviated as '''2LPLL'''). Permutation is broken into 2 steps: corner permutation (two cases), and edge permutation (four cases).

* Step 1: '''Permutation of Corners'''. Requires 2 algorithms , to carry out:
*# adjacent corner swap (any of [[PLL#T Permutation|T-perm]], [[PLL#A Permutation : a|A-perm]], [[PLL#F Permutation|F-perm]], [[PLL#G Permutation : a|G-perm]], [[PLL#J Permutation : a|J-perm]]...)
*# diagonal corner swap (any of [[PLL#Y Permutation|Y-Perm]], [[PLL#V Permutation|V-Perm]], [[PLL#E Permutation|E-Perm]], [[PLL#N Permutation : a|N-Perm]])

* Step 2: '''Permutation of Edges'''. Uses 4 algorithms (3 excluding mirrors):
*# clockwise 3-edge cycle ([[PLL#U Permutation : a|U-perm a]])
*# anticlockwise 3-edge cycle ([[PLL#U Permutation : b|U-perm b]])
*# opposite edges swap ([[PLL#H Permutation|H-Perm]])
*# adjacent edges swap ([[PLL#Z Permutation|Z-Perm]])

== See also ==
* [[PLL]]
* [[2-Look OLL]]
* [[4LLL]]
* [[Last Layer]]

== External links ==
* [http://www.youtube.com/watch?v=S61q3FYVFis Badmephisto's 2-look PLL guide]

[[Category:3x3x3 methods]]

List of web-based cubing software

2016-12-20T05:23:43Z

Oyyq99999: /* Web-Based Timers */

== Description ==
This page contains external links for web-based software, such as timers, applets, or other useful cubing programs.

== Animation Applets ==
* [http://software.rubikscube.info/AnimCube/ AnimCube] (Java) - Relatively lightweight and feature-rich 3x3x3 applet.
* [http://randelshofer.ch/ Randelshofer's Applets] (Java) - Applets for 2x2x2-7x7x7 with many options and variations.

== Web-Based Timers ==
'''Individual Timer'''
* [http://qqtimer.net/ qqTimer] - qqwref's web-based timer. Well developed inspection, averaging, and penatly support. Generates scrambles for a wide range of puzzles.
* [http://gqtimer.kungfoomanchu.com/ gqTimer] - qqTimer with a session logging and graphing function using a Google or Yahoo account.
* [http://www.cstimer.net/old/ CSTimer (Old)] - Essentially qqTimer, in Chinese.
* [http://www.cstimer.net/timer.php CSTimer (Recent)] - javascript timer with pretty UI, fast-random-state scrambles for 3x3 and sq1, (X)cross/eoline solver and many training scrambles. [http://www.speedsolving.com/forum/showthread.php?t=36236 Thread]
* [http://www.cubetimer.com/ cubetimer.com] - Online Rubik's Cube timer.
* [http://www.ctimer.co.uk cTimer] - a JavaScript timer supporting multi-stage timing and random-state scrambles for 3x3. [http://www.speedsolving.com/forum/showthread.php?t=17078 Speedsolving Thread]
* [http://www.ctimer.co.uk/wee weeTimer] - a JavaScript timer optimised for handheld devices.
* [http://www.vanderblonk.com/tools/timer/ CubeTimer] - Timer with animation. Cannot stop inspection countdown midway through.
* [http://molarmanful.github.io/minimalistimer/ MinimalisTimer] - Javascript timer with simple UI and mobile support. [https://www.speedsolving.com/forum/showthread.php?52899-MinimalisTimer-released!]

'''Competitive Timer'''

* [http://www.rubetimer.com RubeTimer] - A timer with statistical graphics, user registration, and multiplayer.
* [http://www.cubemania.org/ Cubemania.org] - An online timer and competition community. Does not support inspection. Much development.
* [http://twisttheweb.com/ Twisttheweb] - Live competitive community with chat and averaging. Account required. See [[Twisttheweb]]

== Image Generators ==
* [http://www.cubezone.be/imagecube.html ImageCube] - (PHP), source provided
* [http://www.solvethecube.110mb.com/index.php?location=tools#nxnimagecube NxNImagecube] - (PHP), source provided
* [http://cube.crider.co.uk/visualcube.php VisualCube] - (PHP), supports algorithms, transparency and cube dimensions up to 9x9. [http://www.speedsolving.com/forum/showthread.php?t=15853 Speedsolving Thread]
* [http://www.vanderblonk.com/tools/wordpress-rubik-plugin Wordpress Rubik Plugin] - Embed cube diagrams as Java applets or images
* [https://www.speedsolving.com/forum/threads/vizarto-puzzle-visualisations.56974/ JavaScript Puzzle Visualisations] - interactive 3D puzzle visualisations in the browser. Supports NxN, megaminx, pyraminx, square-1 and skewb.

== Scramblers and Tools ==
* [http://www.worldcubeassociation.org/regulations/scrambles.zip Official WCA scramblers] - All in one zip file
* [http://www.jaapsch.net/ Jaap's scrambler] - Scrambler, Javascript
* [http://laire.fi/jarcs/ Just Another Rubik's Cube Solver] - Web-based 3x3 solver for common speedcubing sub-steps such as EOLine.
* [http://alg.garron.us/ alg.garron.us] - Algorithm animator for cubes up to 7x7 by Lucas Garron.
* [http://cube.crider.co.uk/scrambler.html Random State Scrambler] - Java applet which creates 3x3 scrambles by inverting solutions to randomly generated cubes.
* [http://cube.crider.co.uk/algtrans.html Algorithm Translator] - Tool for inverting, mirroring and rotating algs. [http://www.speedsolving.com/forum/showthread.php?t=21024 Speedsolving Thread]
* [http://strangepuzzle.com/mirrors.html Algorithm Mirror/Inverse Tool]
* [http://solvethecube.110mb.com/tools.html Joel's Cubing Tools] - Includes an order calculator, scrambler and image generator.
* [http://koii.cubingusa.com/lib/scrambles/scramblers/nml.html NxMxL scrambler] - Scrambler for odd puzzles
* [http://deepcube.net/cube/qbx/ QBX] - A Javascript solver (using the twophase algorithm) licensed under GPLv2.

== Cube Simulators ==
* [[Gelatinbrain]] - One of the biggest collections of virtual puzzles, [http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/index.htm link]
* [http://www.ryanheise.com/cube/speed.html Ryanheise-simulator] - Cubesimulator using the keyboard, with averages
* [http://hi-games.net/ Ryanheise-multiplayer] - Multiplayer cubesimulator using keyboard, cubes: 2x2x2-10x10x10
* [http://www.randelshofer.ch/rubik/virtualcubes/virtual_rubik_en.html 3D Cube Simulator] - Supports dimensions up to 7x7 as well as other shapes. Mouse controlled.
* [http://www.ocf.berkeley.edu/~jfly/projects/qqTimer/qqTimer.htm jflySim + qqTimer] - 2x2x2-NxNxN cubes, Megaminx, Pyraminx and Square-1 simulators integrated with qqTimer

== Competition Software ==
* [http://koii.cubingusa.com/cm/results.zip KOII Live Results System] - Grabs and neatly displays data from WCA Workbooks
* [http://koii.cubingusa.com/cm/workbook/ WCA Workbook Integrity Checker] - Performs various checks on WCA Workbook
* [http://koii.cubingusa.com/main/competitions/tools More KOII Competition Software] - More tools and services such as competition website hosting

== Trainers ==
* [http://expertcuber.by/ ExpertCuber.by] - F2L Trainer
* [http://brunson.com/drillsergeant Last Layer Drills by Brunson]
* [http://wtf2l.com wtf2l.com] - OLL Trainer
* [http://cube.crider.co.uk/coracle.html Coracle] - Corner Lookahead Trainer. [http://www.speedsolving.com/forum/showthread.php?t=21251 Speedsolving Thread]
* [http://s.codepen.io/molarmanful/debug/VYLqLz? Molarmanful's PLL Trainer] - Javascript PLL Trainer with mobile support.
* [http://solvexio.cf Solvexio - The Great Puzzle Defuddler] - Teaches simple cube solving methods using step-by-step instructions.

[[Category:Software]]

Cubing Italy

2016-12-20T05:10:10Z

Oyyq99999: /* External links */

'''Cubing Italy''' is the [[WCA]]-recognized official national cubing organization of [[Italy]].

== External links ==
* [http://www.cubingitaly.org/ Cubing Italy]
* [https://www.worldcubeassociation.org/organisations National Organisations acknowledged by the WCA]

[[Category:National organizations]]