4x4x4 Parity Algorithms

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Contents

Introduction

This page attempts to list move optimal algorithms 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


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.


Despite that there has been debate among the cubing community about what cases are considered to be "parity cases", there is one situation in which any cuber who uses the term "parity" for the 4x4x4 identifies as parity: the single dedge flip.

One Dedge Flip.png


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, but it should never arise during a Reduction solve 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.

Adj2swap.png


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.

Opppllparity.png


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 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.

Oadjpllparity.png Circ4cy.png Circ4cyccw.png Zigzag4cycdedges.png Adj2crnrsp.png Diag2cornerswap.png

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.

DblParity.png


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 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.

Non-Pure Single Dedge Flip.png


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.

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.

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).[1]


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.


This page leaves it to websites such as bigcubes.com to present algorithms with an even number of inner slice quarter turns for the dedge-pairing stage of the Reduction Method.


One such parity case encountered in methods which do not aim to pair up all dedges has already been shown. All last layer 2-cycle cases as well as 4-cycle cases (which are contained within two dedges --There is a total of 110 last layer 4-cycles, but 4-cycles in two dedges are encountered using the most popular 4x4x4 solving methods) are shown on this page.

Below are some examples. (These cases often occur in the ELL stage of the K4 Method.)

Diag.opp.png Adj.case1.png Chkbrd.png Adjchkbd.png


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. Here's one video tutorial that illustrates the typical process.


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 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') Animation


However, 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 (essentially independently found in 2014 by Tom Rokicki and Ed Trice) is f2 r E2 r E2 r f2 (11,7).


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.

Speedsolving Logo tiny.gif f2 r E2 r E2 r f2 (11,7) N Tom Rokicki and Ed Trice [2]


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.

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 metrics is written next to them in the form of the ordered pair, (BQTM, BHTM). (We can clearly see this in the above algorithm bar.)
  • Algorithms with fewer BHTM are listed first in each category.
  • 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 (13,9).

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) algorithm (found in December of 2017) to remember also consists of a short repeated sequence:

Rw' (F U' Lw' U)5 Rw (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.

Speedsolving Logo tiny.gif (Rw B' z')(r' F U2 F')4 r' (z B Rw') (25,21) N Floyd Newberry [3]
Speedsolving Logo tiny.gif (Rw B' z')(r F U2 F')4 r (z B Rw') (25,21) N Floyd Newberry [4]


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 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 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' (25,17)


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

Interesting Note:

On January 24, 2010, speedsolving.com forum member reThinking the Cube showed that Lucas Garron's "Lucas Parity" (published in mid 2008) is equivalent to Stefan Pochmann's "New Dedge Flip" from 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' (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.

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 (25,15)

r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 (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 (25,15)

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.


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 inner slice 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.)

Speedsolving Logo tiny.gif Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2 (25,15) Old Standard Alg Y anonymous [5]


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)", "Alg1(v2)", etc., (short for "algorithm 1, version 1" and "algorithm 1, version 2", 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 "5x5 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

  • Of course, all PLL parity cases can be handled by using the first case shown, commonly called "opposite parity" (OP).


Dedges

  • Algorithms marked as "Safe" are supercube safe.

Two Dedges (Oriented)

Opposite

Opppllparity.png

Speedsolving Logo tiny.gif r2 U2 r2 Uw2 r2 u2 (12,6) N Chris Hardwick [6]
Speedsolving Logo tiny.gif r2 U2 r2 U2 d2 r2 d2 (14,7) N []
Speedsolving Logo tiny.gif U2 r2 U2 r2 Uw2 r2 Uw2 (14,7) N Chris Hardwick [7]
Speedsolving Logo tiny.gif (Uw2 Rw2 U2) r2 (U2 Rw2 Uw2) (14,7) SP01 N Stefan Pochmann [8]
Speedsolving Logo tiny.gif (Dw2 Rw2 U2) r2 (U2 Rw2 Dw2) (14,7) N []
Speedsolving Logo tiny.gif (Rw2 F2 U2) r2 (U2 F2 Rw2) (14,7) N Stefan Pochmann [9]
Speedsolving Logo tiny.gif (Rw2 B2 U2) r2 (U2 B2 Rw2) (14,7) N Stefan Pochmann []
Speedsolving Logo tiny.gif Rw2 (U2 r U2 S2)2 Rw2//Safe (18,10) Y Walter Randelshofer [10]
Speedsolving Logo tiny.gif r2 U2 B2 l r U2 M' U2 r2 B2 U2//Safe (19,11) N []
Speedsolving Logo tiny.gif y Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 y' (20,11) v1 Y []
Speedsolving Logo tiny.gif y Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 y' (20,11) v2 Y []
Speedsolving Logo tiny.gif r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2//Safe (22,12) Y []
Speedsolving Logo tiny.gif r' F U' R F' U l r U' F R' U F' l'//Safe (14,14) N []


Adjacent

Oadjpllparity.png

Speedsolving Logo tiny.gif (R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2) (18,10) N Chris Hardwick [11]
Speedsolving Logo tiny.gif (R2 D' x Uw2 Rw2 U2) r2 (U2 Rw2 Uw2 x' D R2) (20,11) SP02 N Stefan Pochmann [12]
Speedsolving Logo tiny.gif (R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2) (20,11) FB02 N Frédérick Badie [13]
Speedsolving Logo tiny.gif (F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2) (20,11) N Stefan Pochmann []
Speedsolving Logo tiny.gif (R2 D' x Rw2 F2 U2) r2 (U2 F2 Rw2 x' D R2) (20,11) N Stefan Pochmann []
Speedsolving Logo tiny.gif (R2 D' x Rw2 B2 U2) r2 (U2 B2 Rw2 x' D R2) (20,11) N Stefan Pochmann []
Speedsolving Logo tiny.gif (y' R' F) l E F2 E' l' r' E F2 E' r (F' R y)//Safe (16,14) N Christopher Mowla [14]
Speedsolving Logo tiny.gif (y' R' F) l E' F2 E l' r' E' F2 E r (F' R y)//Safe (16,14) N Christopher Mowla []
Speedsolving Logo tiny.gif (R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R') (20,14) N Chris Hardwick [15]
Speedsolving Logo tiny.gif (y2 Uw2 R U R' U' Rw2 U2) r2 (U2 Rw2 U R U' R' Uw2 y2) (22,15) N xyzzy [16]
Speedsolving Logo tiny.gif (R2 D' x) r2 U2 B2 l r U2 M' U2 r2 B2 U2 (x' D R2)//Safe (24,15) N []
Speedsolving Logo tiny.gif (Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw) (22,17) v1 N Christopher Mowla [17]
Speedsolving Logo tiny.gif y' (Rw U' R' U' Rw B2) (Rw B2 r2 B2 Rw') (B2 Rw' U R U Rw') y (22,17) v2 N Christopher Mowla [18]
Speedsolving Logo tiny.gif y2 Rw U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U R' U' R' U y2 (20,20) Y António Gomes [19]
Speedsolving Logo tiny.gif y2 R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U y2 (20,20) Y António Gomes []
Speedsolving Logo tiny.gif y R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' y' (20,20) Y António Gomes []
Speedsolving Logo tiny.gif (y2 Bw2 R2 Bw2) Rw U Rw' U' Lw' U' Lw U2 Rw U' Rw' U' Lw' U Lw (Bw2 R2 Bw2 y2) (28,21) Y Moritz Karl [20]
Speedsolving Logo tiny.gif 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' (30,26) Y Ben Whitmore []


Two Dedges (Unoriented)

Opposite

Uopppllparity.png

Speedsolving Logo tiny.gif F2 l E F2 E' l' r' E F2 E' r F2//Safe (16,12) N Christopher Mowla [21]
Speedsolving Logo tiny.gif F2 l E' F2 E l' r' E' F2 E r F2//Safe (16,12) N Christopher Mowla []
Speedsolving Logo tiny.gif (y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y') (18,12) N Chris Hardwick [22]
Speedsolving Logo tiny.gif r U2 l D2 l' U2 M U2 r D2 r' U2 l'//Safe (19,13) N Kenneth Gustavsson [23]
Speedsolving Logo tiny.gif (y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y) (20,13) N Stefan Pochmann [24]
Speedsolving Logo tiny.gif (y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y') (20,13) N []
Speedsolving Logo tiny.gif l U2 M l U2 M' l' U2 M' U2 Rw M' U2 M r' U2 Rw'//Safe (23,17) N Kenneth Gustavsson []
Speedsolving Logo tiny.gif (F r U' R U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R' U r' F') (24,19) N Christopher Mowla []
Speedsolving Logo tiny.gif (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') (32,25) N Christopher Mowla []


Adjacent

Uoadjpllparity.png

Speedsolving Logo tiny.gif (R B) r2 U2 r2 Uw2 r2 u2 (B' R') (16,10) N Chris Hardwick [25]
Speedsolving Logo tiny.gif (R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R') (18,11) N Stefan Pochmann [26]
Speedsolving Logo tiny.gif (3Lw U Rw2 U2 F2) r2 (F2 U2 Rw2 U' 3Lw') (18,11) N Stefan Pochmann [27]
Speedsolving Logo tiny.gif R B U2 r2 U2 B2 l r U2 M' U2 r2 B R'//Safe (21,14) N []


Four Dedges (Oriented)

O Permutation

Oa

Circ4cyccw.pngOa Perm Diagram.png

Speedsolving Logo tiny.gif r2 Uw2 b2 U' b2 r2 U b2 r2 Uw2 r2 (20,11) CG03 N Clément Gallet [28]
Speedsolving Logo tiny.gif f2 Uw2 r2 U' r2 f2 U r2 f2 Uw2 f2 (20,11) N Clément Gallet []
Speedsolving Logo tiny.gif y2 M2 U' M2 u Uw f2 M2 Dw2 b2 U2 b2 (20,11) N Clément Gallet []
Speedsolving Logo tiny.gif M' U2 Uw2 r2 Uw2 r2 U2 l2 U2 M' U M2 U M2 (22,13) N []
Speedsolving Logo tiny.gif M U2 Uw2 l2 Uw2 l2 U2 r2 U2 M U M2 U M2 (22,13) N []
Speedsolving Logo tiny.gif y2 D2 M E2 M U M2 U' l2 U2 r2 Uw2 r2 Uw2 (22,13) PKF03 N Per Kristen Fredlund [29]
Speedsolving Logo tiny.gif (E2 M)2 U M2 U' l2 U2 r2 Uw2 r2 u2 (22,13) PKF03 N Per Kristen Fredlund [30]
Speedsolving Logo tiny.gif l2 U2 f2 U' l2 f2 U u2 f2 u2 l2 U2 l2 (23,13) N Clément Gallet []
Speedsolving Logo tiny.gif l2 U2 f2 U' l2 f2 U u2 f2 l2 U2 l2 u2 (23,13) N Clément Gallet []
Speedsolving Logo tiny.gif r2 Uw2 b2 U' b2 r2 U b2 R2 Uw2 Rw2 Uw2 R2 (24,13) N Clément Gallet [31]
Speedsolving Logo tiny.gif M2 U M U2 r' l' U2 F2 r2 F2 U2 r2 U M2 (23,14) N []
Speedsolving Logo tiny.gif l' r' 3Dw L' R' u L R 3Dw' M2 3Dw' L R u L' R' 3Dw l' r'//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif l r 3Dw L R u' L' R' 3Dw' M2 3Dw' L' R' u' L R 3Dw l r//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif l' r' 3Dw' L' R' u' L R 3Dw M2 3Dw L R u' L' R' 3Dw' l' r' //Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif l r y' U' L R u L' R' 3Dw M2 3Dw L' R' u L R y' U' l r//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif U2 (R' U' R' F R F' U R) (Uw2 r2 Uw2 r2 U2 r2) (F U R U' R' F') (28,21) N Antoine Cantin [32]
Speedsolving Logo tiny.gif (F2 U2 M U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M' U2 F2) (33,21) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw2 U R2 U R U' R' U R Rw' U2 Rw2 U2 Rw2 U2 Rw' U' R U R' U2 Rw2 U' (31,22) Y António Gomes [33]
Speedsolving Logo tiny.gif Rw2 U2 R' U R U' Rw' U2 Rw2 U2 Rw2 U2 R Rw' U R' U' R U R2 U Rw2 U' (31,22) Y António Gomes []
Speedsolving Logo tiny.gif 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 (24,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 U R2 U R U' R U Rw U R' Rw2 U2 R Rw2 U2 R' Rw2 U Rw' U2 Rw2 U' (29,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 U2 Rw' U R' Rw2 U2 R Rw2 U2 R' Rw2 U Rw U R U' R U R2 U Rw2 U' (29,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 U' R' U' R U R U' Rw U2 Rw2 U2 Rw2 U2 Rw U2 R U' R U R2 Rw2 U' (30,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 U' R' U' R U R U' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R U' R U R2 Rw2 U' (30,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 R2 U R U' R U2 Rw U2 Rw2 U2 Rw2 U2 Rw U' R U R U' R' U' Rw2 U' (30,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 R2 U R U' R U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U' R U R U' R' U' Rw2 U' (30,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 R2 U R2 Rw2 U R2 U' Rw2 U' Rw2 U' Rw U' Rw2 U' R2 U Rw2 U Rw' U' R2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 R2 U R2 Rw2 U R2 U' Rw2 U' Rw2 U' Rw' U' Rw2 U' R2 U Rw2 U Rw U' R2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif R U' R' Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R2 Rw2 U R U R U' R' U' R2 (31,23) Y António Gomes []
Speedsolving Logo tiny.gif R U' R' Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R2 Rw2 U R U R U' R' U' R2 (31,23) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 U R2 U R U' R' U R Rw U2 Rw2 U2 Rw2 U2 Rw U' R U R' U2 Rw2 U' (32,33) Y António Gomes []
Speedsolving Logo tiny.gif Rw2 U2 R' U R U' Rw U2 Rw2 U2 Rw2 U2 R Rw U R' U' R U R2 U Rw2 U' (32,33) Y António Gomes []
Speedsolving Logo tiny.gif R U2 R U R' Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 R2 Rw2 U R2 U' R' U' R2//Safe (33,23) Y António Gomes []
Speedsolving Logo tiny.gif R U2 R U R' Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R2 Rw2 U R2 U' R' U' R2//Safe (33,23) Y António Gomes []


Ob

Circ4cy.pngOb Perm Diagram.png

Speedsolving Logo tiny.gif r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2 (20,11) CG03 N Clément Gallet [34]
Speedsolving Logo tiny.gif f2 Uw2 f2 r2 U' f2 r2 U r2 Uw2 f2 (20,11) N Clément Gallet []
Speedsolving Logo tiny.gif b2 U2 b2 Dw2 M2 f2 Uw' u' M2 U M2 y2 (20,11) N Clément Gallet []
Speedsolving Logo tiny.gif M2 U' M2 U' M U2 l2 U2 r2 Uw2 r2 Uw2 U2 M (22,13) N []
Speedsolving Logo tiny.gif M2 U' M2 U' M' U2 r2 U2 l2 Uw2 l2 Uw2 U2 M' (22,13) N []
Speedsolving Logo tiny.gif Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2 (22,13) PKF03 N Per Kristen Fredlund [35]
Speedsolving Logo tiny.gif u2 r2 Uw2 r2 U2 l2 U M2 U' (M' E2)2 (22,13) PKF03 N Per Kristen Fredlund [36]
Speedsolving Logo tiny.gif l2 U2 l2 u2 f2 u2 U' f2 l2 U f2 U2 l2 (23,13) N Clément Gallet []
Speedsolving Logo tiny.gif u2 l2 U2 l2 f2 u2 U' f2 l2 U f2 U2 l2 (23,13) N Clément Gallet []
Speedsolving Logo tiny.gif R2 Uw2 Rw2 Uw2 R2 b2 U' r2 b2 U b2 Uw2 r2 (24,13) N Clément Gallet [37]
Speedsolving Logo tiny.gif M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2 (23,14) N []
Speedsolving Logo tiny.gif l r 3Dw' L R u' L' R' 3Dw M2 3Dw L' R' u' L R 3Dw' l r//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif l' r' 3Dw' L' R' u L R 3Dw M2 3Dw L R u L' R' 3Dw' l' r'//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif l r 3Dw L R u L' R' 3Dw' M2 3Dw' L' R' u L R 3Dw l r//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif l' r' U y L' R' u' L R 3Dw' M2 3Dw' L R u' L' R' U y l' r'//Safe (20,19) N Christopher Mowla []
Speedsolving Logo tiny.gif (F R U R' U' F') (r2 U2 r2 Uw2 r2 Uw2) (R' U' F R' F' R U R) U2 (28,21) N Antoine Cantin [38]
Speedsolving Logo tiny.gif (F2 U2 M U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M' U2 F2) (33,21) N Christopher Mowla []
Speedsolving Logo tiny.gif U Rw2 U2 R U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw R' U' R U R' U' R2 U' Rw2 (31,22) Y António Gomes [39]
Speedsolving Logo tiny.gif U Rw2 U' R2 U' R' U R U' Rw R' U2 Rw2 U2 Rw2 U2 Rw U R' U' R U2 Rw2 (31,22) Y António Gomes []
Speedsolving Logo tiny.gif 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' (24,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 U2 Rw U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw' U' R' U R' U' R2 U' Rw2 (29,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 U' R2 U' R' U R' U' Rw' U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw U2 Rw2 (29,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 R2 U' R' U R' U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R' U R U Rw2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 R2 U' R' U R' U2 Rw U2 Rw2 U2 Rw2 U2 Rw U R' U' R' U R U Rw2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 U R U R' U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R' U R' U' Rw2 R2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 U R U R' U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw U2 R' U R' U' Rw2 R2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif R2 U Rw U' Rw2 U' R2 U Rw2 U Rw' U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif R2 U Rw' U' Rw2 U' R2 U Rw2 U Rw U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2 (30,23) Y António Gomes []
Speedsolving Logo tiny.gif R2 U R U R' U' R' U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U R' (31,23) Y António Gomes []
Speedsolving Logo tiny.gif R2 U R U R' U' R' U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U R' (31,23) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 U2 R U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' R' U' R U R' U' R2 U' Rw2 (32,33) Y António Gomes []
Speedsolving Logo tiny.gif U Rw2 U' R2 U' R' U R U' Rw' R' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R U2 Rw2 (32,33) Y António Gomes []
Speedsolving Logo tiny.gif R2 U R U R2 U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U' R' U2 R'//Safe (33,23) Y António Gomes []
Speedsolving Logo tiny.gif R2 U R U R2 U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U' R' U2 R'//Safe (33,23) Y António Gomes []


8 Permutation

Zigzag4cycdedges.png8 Perm Diagram.png

  • Note: This is commonly called the "W" permutation.
Speedsolving Logo tiny.gif M2 U M' U2 M U l2 U2 r2 Uw2 r2 Uw2 U2 (20,12) N []
Speedsolving Logo tiny.gif u2 S2 Uw' u' b2 R2 b2 Rw2 f2 r2 U S2 (21,12) N Clément Gallet []
Speedsolving Logo tiny.gif F2 D' f2 d2 b2 D' B2 Dw2 3Uw' M2 3Uw F2 Uw2 (21,13) N Clément Gallet []
Speedsolving Logo tiny.gif (r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2) (22,13) PKF04 N Per Kristen Fredlund [40]
Speedsolving Logo tiny.gif R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2 (26,14) CG04 Y Clément Gallet []
Speedsolving Logo tiny.gif F2 Uw' u' M2 U' F2 D S2 Dw d Bw2 u2 b2 U2 y2 (22,14) N Clément Gallet []
Speedsolving Logo tiny.gif l2 D2 B2 Rw2 B2 D2 l2 F2 U' F2 L2 F2 U' L2 (26,14) N Clément Gallet []
Speedsolving Logo tiny.gif y' M2 U' r2 b2 Rw2 Bw2 R2 Bw2 L2 U2 M2 U2 F2 D M2 x2 y (28,15) N Doug [41]
Speedsolving Logo tiny.gif R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2 (21,16) SP04 N Stefan Pochmann []
Speedsolving Logo tiny.gif R2 U R' U' R2 U R U Rw2 U2 R' Rw U2 R' Rw2 U2 Rw2 U2 Rw U2 Rw2//Safe (30,20) Y António Gomes [42]
Speedsolving Logo tiny.gif R2 U R' U' R2 U R U R' Rw2 U2 R' Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2//Safe (30,20) Y António Gomes [43]
Speedsolving Logo tiny.gif R2 U R' U' R2 U R U R' Rw2 U2 R' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2//Safe (31,21) Y António Gomes [44]
Speedsolving Logo tiny.gif 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' (24,22) Y António Gomes [45]
Speedsolving Logo tiny.gif (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) (41,29) N Christopher Mowla [46]


Four Dedges (Unoriented)

O Permutation

Oa

Oa4unoriented.pngOa Perm Diagram (4 unoriented).png

Speedsolving Logo tiny.gif F2 M F2 U' l2 U2 r2 Uw2 r2 U' Uw2 B2 M B2 (23,14) N Christopher Mowla []
Speedsolving Logo tiny.gif y' U2 Rw2 U2 r2 Uw2 r2 y Uw2 M U' M2 U' F2 U2 M (24,14) N Christopher Mowla []
Speedsolving Logo tiny.gif R2 S' (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S' L2 (24,14) N Per Kristen Fredlund [47]
Speedsolving Logo tiny.gif R2 S (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S L2 (24,14) N Per Kristen Fredlund []
Speedsolving Logo tiny.gif L2 S L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S R2 (24,14) N Per Kristen Fredlund []
Speedsolving Logo tiny.gif L2 S' L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S' R2 (24,14) N Per Kristen Fredlund []
Speedsolving Logo tiny.gif M2 D R' L' u' R L D2 R L y M2 u' M2 y' R' L' D M2 //Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D R L u R' L' D2 R' L' y M2 u M2 y' R L D M2 //Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D' R' L' y M2 d' M2 y' R L D2 R L d' R' L' D' M2 //Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D' R L y M2 d M2 y' R' L' D2 R' L' d R L D' M2 //Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 U F2 D2 r F2 r2 F2 D2 l2 F2 D2 r2 D2 l U' M2 (30,17) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M2) (27,17) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U Fw2 r2 u' S' Rw2 u2) M' (u2 Rw2 S u r2 Fw2 U' M2) (27,17) N Christopher Mowla []


Ob

O Permutation (unoriented).pngOb Perm Diagram (4 unoriented).png

Speedsolving Logo tiny.gif B2 M' B2 Uw2 U r2 Uw2 r2 U2 l2 U F2 M' F2 (23,14) N Christopher Mowla []
Speedsolving Logo tiny.gif M' U2 F2 U M2 U M' Uw2 y' r2 Uw2 r2 U2 Rw2 U2 y (24,14) N Christopher Mowla []
Speedsolving Logo tiny.gif L2 S L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S R2 (24,14) N Per Kristen Fredlund [48]
Speedsolving Logo tiny.gif L2 S' L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S' R2 (24,14) N Per Kristen Fredlund []
Speedsolving Logo tiny.gif R2 S' (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S' L2 (24,14) N Per Kristen Fredlund []
Speedsolving Logo tiny.gif R2 S (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S L2 (24,14) N Per Kristen Fredlund []
Speedsolving Logo tiny.gif M2 D' L R y M2 u M2 y' L' R' D2 L' R' u L R D' M2//Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D' L' R' y M2 u' M2 y' L R D2 L R u' L' R' D' M2//Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D L R d L' R' D2 L' R' y M2 d M2 y' L R D M2//Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D L' R' d' L R D2 L R y M2 d' M2 y' L' R' D M2//Safe (22,17) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 U l' D2 r2 D2 F2 l2 D2 F2 r2 F2 r' D2 F2 U' M2 (30,17) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M2) (27,17) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U Fw2 r2 u' S' Rw2 u2) M (u2 Rw2 S u r2 Fw2 U' M2) (27,17) N Christopher Mowla []


8 Permutation

W Permutation (unoriented).png8 Perm Diagram (4 unoriented).png

  • Note: This is commonly called the "W" permutation.
Speedsolving Logo tiny.gif y' M2 U' D2 r2 S2 l S2 r2 E2 r' U' M2 y'//Safe (19,12) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 U' r U D L2 U D S2 r S2 D' U' L2 D' M2//Safe (22,16) N Christopher Mowla []
Speedsolving Logo tiny.gif y M2 U r' U' D' L2 U' D' S2 r' S2 D U L2 D M2 y'//Safe (22,16) N Christopher Mowla []
Speedsolving Logo tiny.gif M2 D R2 D U r U' D' R2 U' D' S2 r S2 U M2//Safe (22,16) N Christopher Mowla []
Speedsolving Logo tiny.gif y M2 D' R2 D' U' r' U D R2 U D S2 r' S2 U' M2 y'//Safe (22,16) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U')(r' E2 l E2)3 (U M2)//Safe (24,16) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U')(E2 r' E2 l)3 (U M2)//Safe (24,16) N Christopher Mowla []
Speedsolving Logo tiny.gif (y x' M2 Fw f r2 u r2 S' u2) M (u2 S r2 u' r2 f' Fw' M2 x y') (25,17) N Christopher Mowla [49]
Speedsolving Logo tiny.gif (y x' M2 Fw f r2 u' r2 S' u2) M (u2 S r2 u r2 f' Fw' M2 x y') (25,17) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U Fw2 r2 d r2 Uw2 S') M (S Uw2 r2 d' r2 Fw2 U' M2) (27,17) N Christopher Mowla []
Speedsolving Logo tiny.gif (M2 U Fw2 r2 d' r2 Uw2 S') M (S Uw2 r2 d r2 Fw2 U' M2) (27,17) N Christopher Mowla []


Two Corner Swaps

Adjacent

Adj2crnrsp.png

Speedsolving Logo tiny.gif F2 R2 B' D' B R2 F' U Fw2 F L2 f2 Lw2 f2 l2 U' (24,16) N Clément Gallet []
Speedsolving Logo tiny.gif L' U Lw2 L B2 l2 Bw2 l2 b2 U' L2 F2 R' D' R F2 (24,16) N Clément Gallet []
Speedsolving Logo tiny.gif y' B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 y (25,16) PKF10 N Per Kristen Fredlund [50]
Speedsolving Logo tiny.gif R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2 (25,16) N []
Speedsolving Logo tiny.gif F2 L2 B D B' L2 F U' F f2 U2 L2 b2 L2 U2 f2 U (26,17) N Clément Gallet []
Speedsolving Logo tiny.gif R U' 3Lw U2' L' B L U2' 3Lw2' B Lw2 F2 U2' l2' U2' F2 Lw2' x' (27,17) N Clément Gallet &Christopher Mowla []
Speedsolving Logo tiny.gif (F2 D R2 U' R2 F2 U' F2 U F2 D')(r2 U2 r2 Uw2 r2 u2) (29,17) N Per Kristen Fredlund [51]
Speedsolving Logo tiny.gif z r2 U2 R' U2 R' U2 R x U2 Rw2 U2 B2' L U2 L' U2 Rw2 U2' z' y' (29,17) N Christopher Mowla [52]
Speedsolving Logo tiny.gif 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 (33,19) Y Christopher Mowla [53]
Speedsolving Logo tiny.gif r2 U2 r2 Uw2 r2 u2 y' R U R' U' R' F R2 U' R' U' R U R' F' y (27,20) N []
Speedsolving Logo tiny.gif y' (R U R' F') U' r2 U2 r2 Uw2 r2 Uw2 U' (R U R' U') R' F R2 U' R' U' y (28,22) N Stefan Lidström []
Speedsolving Logo tiny.gif 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 (35,22) Y Christopher Mowla [54]
Speedsolving Logo tiny.gif 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 (35,22) Y Christopher Mowla []


Opposite/Diagonal

Diag2cornerswap.png

Speedsolving Logo tiny.gif Rw2 f2 U2 Fw2 D Rw2 U2 Fw2 U' Fw2 L2 U2 B2 Lw2 U (27,15) N Clément Gallet [55]
Speedsolving Logo tiny.gif Rw2 f2 U2 Bw2 D' Rw2 U2 Bw2 U Fw2 R2 D2 B2 Lw2 U (27,15) v1 N Clément Gallet []
Speedsolving Logo tiny.gif Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U (27,15) v2 N Michael Fung [56]
Speedsolving Logo tiny.gif Rw2 f2 D2 Fw2 U' Rw2 U2 Bw2 U Bw2 R2 U2 F2 Rw2 U' (27,15) N Clément Gallet []
Speedsolving Logo tiny.gif Rw2 f2 D2 Fw2 D' Rw2 U2 Bw2 U Bw2 L2 U2 B2 Lw2 U (27,15) N Clément Gallet []
Speedsolving Logo tiny.gif Rw2 f2 D2 Bw2 U Rw2 U2 Fw2 U' Bw2 L2 D2 F2 Rw2 U' (27,15) N Clément Gallet []
Speedsolving Logo tiny.gif Fw2 r2 D2 Lw2 U Bw2 D2 Lw2 D' Rw2 B2 U2 L2 Bw2 U' (27,15) N Clément Gallet []
Speedsolving Logo tiny.gif Fw2 r2 D2 Rw2 U Bw2 D2 Rw2 D' Rw2 F2 D2 L2 Bw2 U (27,15) N Clément Gallet []
Speedsolving Logo tiny.gif Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U (27,16) N Christopher Mowla [57]
Speedsolving Logo tiny.gif Rw2 F2 U2 y Lw2' U Lw2' U' D' Rw2 U Rw2 y' r2 U2 F2 Rw2 U (27,16) N Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 L' U2 Lw2 F2 R' D2 R2 U2 B2 R D2 B2 Rw2 U2 (29,16) Y Clément Gallet []
Speedsolving Logo tiny.gif y' z (R2' Uw2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' Uw2' R2 3Dw' R2) Uw2 U2 x (29,16) reCornerX(BD) v1 N reThinking the Cube [58]
Speedsolving Logo tiny.gif y' U2 Rw2 U2 R U2 F2 R2 F2 R' F2 U2 Rw2 U2 R' F2 r2 y (29,16) reCornerX(BD) v2 N reThinking the Cube [59]
Speedsolving Logo tiny.gif y' Rw' r' S2 U R U' B2 D L' D Lw l D2 F2 Lw l D2 z2 y (22,17) N Frédérick Badie &Clément Gallet []
Speedsolving Logo tiny.gif y' R2 D Rw2 U2' B2 r2 B2 U2' Lw2 R U' 3Lw U2 3Rw' U 3Rw U2 x' y (26,17) N Mario Laurent [60]
Speedsolving Logo tiny.gif F2 L' U2 L R U2 R' F2 Lw2 F2 U2 Lw2' L' U2 F2 Lw2 U2 (28,17) Y Clément Gallet []
Speedsolving Logo tiny.gif y' r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 y (30,17) N Christopher Mowla []
Speedsolving Logo tiny.gif y' r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2 y (31,17) N Christopher Mowla [61]
Speedsolving Logo tiny.gif L2 u2 F2 U2 L2 u2 F2 U' F2 L2 U2 L2 U L2 U2 F2 u2 U (32,18) N Clément Gallet []
Speedsolving Logo tiny.gif y' R Rw2 F2 L U L' B D L D' B2 U B r2 U2 F2 Rw2 R' U2 y (25,19) FB14 N Frédérick Badie [62]
Speedsolving Logo tiny.gif y' r2 U2 r2 Uw2 r2 Uw2 L' U R' U2 L U' L' R U R' U2 L U' R U y (29,21) N []
Speedsolving Logo tiny.gif Rw2 R U2 R U2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' Rw2 (35,22) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw2 R U2 R U2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' Rw2 (35,22) Y Christopher Mowla [63]
Speedsolving Logo tiny.gif l2 U2 F2 l R U2 R' U2 L2 F2 L F2 Lw F2 U2 Lw2 U2 F2 U2 F2 L' U2 (38,22) N Christopher Mowla [64]
Speedsolving Logo tiny.gif (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') (30,25) N Stefan Lidström []


Two Corner Swaps (only 2 supercube center piece exchange)

Adjacent

Adj2crnrsp.png

Speedsolving Logo tiny.gif U Rw2 Bw2 Rw F Rw' Bw2 Rw F' L2 r U' b2 U L' F' L U' b2 U L' F M x (29,23) N Christopher Mowla [65]
Speedsolving Logo tiny.gif 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 (27,24) N Christopher Mowla []
Speedsolving Logo tiny.gif 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 (27,24) N Christopher Mowla []
Speedsolving Logo tiny.gif 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 (27,25) Y Robert Yau []
Speedsolving Logo tiny.gif 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 (28,26) N Robert Yau [66]
Speedsolving Logo tiny.gif 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 (28,26) N Robert Yau [67]
Speedsolving Logo tiny.gif 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' (29,26) N Robert Yau [68]
Speedsolving Logo tiny.gif 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 (31,26) N Chris Hardwick [69]
Speedsolving Logo tiny.gif 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 (29,27) N []
Speedsolving Logo tiny.gif 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 (29,28) N Christopher Mowla [70]


Opposite/Diagonal

Diag2cornerswap.png

Speedsolving Logo tiny.gif F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L Fw' L2 Uw F' U R U' (27,24) N Christopher Mowla []
Speedsolving Logo tiny.gif 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' (30,28) N Robert Yau [71]


Two X-Center Piece Swap Algorithms

2xcentpswp.png

  • 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.


Speedsolving Logo tiny.gif y Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U y' (13,10) Y []
Speedsolving Logo tiny.gif Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U' (13,12) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' (15,14) Y []
Speedsolving Logo tiny.gif Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U (15,15) Y Christopher Mowla []


Two Corner Swap and a Dedge 3-cycle

D Permutation

Da

PLL Parity13.pngDa Perm Diagram.png

Speedsolving Logo tiny.gif z2 F2 R2 Dw2 F2 U' R2 Uw2 U R2 U F2 Uw2 U M2 F2 U' (25,16) Y Clément Gallet []
Speedsolving Logo tiny.gif F2 U Rw2 U' B2 U' F2 U B2 U' r2 F2 U2 Rw2 U' F2 U' (27,17) FB07 N Frédérick Badie []
Speedsolving Logo tiny.gif y2 U' R2 b2 l2 Fw2 l2 F2 r2 L D L' B2 L D' L' F2 R2 (27,17) N Clément Gallet []
Speedsolving Logo tiny.gif R2 U' f2 D2 L2 b2 D' R2 D L2 D' R2 D' f2 U R2 U' (27,17) N Clément Gallet []


Db

PLL Parity12.pngDb Perm Diagram.png

Speedsolving Logo tiny.gif U F2 M2 Uw2 U' F2 U' R2 Uw2 U' R2 U F2 Dw2 R2 F2 z2 (25,16) Y Clément Gallet []
Speedsolving Logo tiny.gif U F2 U Rw2 U2 F2 r2 U B2 U' F2 U B2 U Rw2 U' F2 (27,17) FB07 N Frédérick Badie []
Speedsolving Logo tiny.gif R2 F2 L D L' B2 L D' L' r2 F2 l2 Fw2 l2 b2 R2 U y2 (27,17) N Clément Gallet []
Speedsolving Logo tiny.gif U R2 U' f2 D R2 D L2 D' R2 D b2 L2 D2 f2 U R2 (27,17) N Clément Gallet []


K Permutation

Ka

PLL Parity10.pngKa Perm Diagram.png

Speedsolving Logo tiny.gif U R U' L U2 R' U L l2 F2 Lw2 Fw2 l2 Fw2 (20,14) N Clément Gallet []
Speedsolving Logo tiny.gif Dw2 R2 D B2 Dw2 D' B2 D' R2 Dw2 D' B2 L2 U' L2 (23,15) Y Clément Gallet []
Speedsolving Logo tiny.gif u2 r2 Uw2 r2 U2 Rw2 D R D' R F2 L' U L F2 (23,15) PKF06 N Per Kristen Fredlund [72]
Speedsolving Logo tiny.gif d2 D' B2 L2 U d2 L2 D' B2 U R2 U R2 Dw2 L2 (24,15) N Clément Gallet []
Speedsolving Logo tiny.gif y (Rw2' D' Rw U2 Rw' D Rw U2 Rw) U (Rw U2 Rw D Rw' U2 Rw D' Rw2') U2 y' (27,20) Y Daniel Sheppard [73]
Speedsolving Logo tiny.gif R U R' F' R U R' U' R' F R2 U' R' U (r2 U2 r2 Uw2 r2 Uw2) (27,20) N Stefan Lidström []


Kb

PLL Parity11.pngKb Perm Diagram.png

Speedsolving Logo tiny.gif Fw2 l2 Fw2 Lw2 F2 l2 L' U' R U2 L' U R' U' (20,14) N Clément Gallet []
Speedsolving Logo tiny.gif L2 U L2 B2 Dw2 D R2 D B2 Dw2 D B2 D' R2 Dw2 (23,15) Y Clément Gallet []
Speedsolving Logo tiny.gif F2 L' U' L F2 R' D R' D' Rw2 U2 r2 Uw2 r2 u2 (23,15) PKF06 N Per Kristen Fredlund [74]
Speedsolving Logo tiny.gif L2 Dw2 R2 U' R2 U' B2 D L2 d2 U' L2 B2 D d2 (24,15) N Clément Gallet []
Speedsolving Logo tiny.gif y' (Rw2 D Rw' U2 Rw D' Rw' U2 Rw') U' (Rw' U2 Rw' D' Rw U2 Rw' D Rw2') y U2 (27,20) Y Daniel Sheppard [75]
Speedsolving Logo tiny.gif (r2 U2 r2 Uw2 r2 Uw2 U2) R U R' F' R U R' U' R' F R2 U' R' U' (27,20) N Stefan Lidström []


P Permutation

Pa

PLL Parity8.pngPa Perm Diagram.png

Speedsolving Logo tiny.gif U' z' U2 B2 Lw2 U2 L' B2 Lw2' L B2 L U2 Lw2' L U2 z (23,15) CG05 Y Clément Gallet [76]
Speedsolving Logo tiny.gif y U L2 3Uw' L2 U L2 y u2 l2 Uw2 l2 U2 Lw2 3Uw L2 U' L2 y2 (27,16) N Stefan Pochmann [77]
Speedsolving Logo tiny.gif R2 U R2 U' R2 F2 U' (Fw2 r2)2 F2 r2 D R2 D' (27,16) PKF05 N Per Kristen Fredlund []
Speedsolving Logo tiny.gif y2 L' U' L U L F' L2 U L (r2 U2 r2 Uw2 r2 Uw2) U' L' U' L F y2 (26,20) N Stefan Lidström []


Pb

PLL Parity9.pngPb Perm Diagram.png

Speedsolving Logo tiny.gif z' U2 Lw2 L' U2 L' B2 Lw2' L' B2 L U2 Lw2' B2 U2 z U (23,15) CG05 Y Clément Gallet [78]
Speedsolving Logo tiny.gif y2 L2 U L2 3Uw' Lw2 U2 l2 Uw2 l2 u2 y' L2 U' L2 3Uw L2 U' y' (27,16) N Stefan Pochmann [79]
Speedsolving Logo tiny.gif R2 D' r2 F2 (r2 Fw2)2 U F2 R2 U R2 U' R2 D (27,16) PKF05 N Per Kristen Fredlund [80]
Speedsolving Logo tiny.gif R U R' U (r2 U2 r2 Uw2 r2 Uw2) R' F R2 U' R' U' R U R' F' (27,20) N Stefan Lidström []


Pc

PLL Parity7.pngPc Perm Diagram.png

Speedsolving Logo tiny.gif z' U2 Lw2' L U2 L F2 Lw2' L F2 L' U2 Lw2 F2 U2 z U' (23,15) CG05 Y Clément Gallet [81]
Speedsolving Logo tiny.gif R2' U' R2 3Uw Rw2 U2 r2 Uw2 r2 u2 y R2 U R2' 3Uw' R2 U y' (27,16) N Stefan Pochmann [82]
Speedsolving Logo tiny.gif R2 D r2 B2 (r2 Bw2)2 U' B2 R2 U' R2 U R2 D' (27,16) PKF05 N Per Kristen Fredlund []
Speedsolving Logo tiny.gif y2 L' U' L U' (r2 U2 r2 Uw2 r2 Uw2) L F' L2 U L U L' U' L F y2 (27,20) N Stefan Lidström []


Pd

PLL Parity6.pngPd Perm Diagram.png

Speedsolving Logo tiny.gif U z' U2 F2 Lw2' U2 L F2 Lw2 L' F2 L' U2 Lw2 L' U2 z (23,15) CG05 Y Clément Gallet [83]
Speedsolving Logo tiny.gif y U' R2 3Uw R2 U' R2 y' u2 r2 Uw2 r2 U2 Rw2 3Uw' R2 U R2 (27,16) N Stefan Pochmann [84]
Speedsolving Logo tiny.gif R2 U' R2 U R2 B2 U (Bw2 r2)2 B2 r2 D' R2 D (27,16) PKF05 N Per Kristen Fredlund []
Speedsolving Logo tiny.gif R U R' U' R' F R2 U' R' (r2 U2 r2 Uw2 r2 Uw2) U R U R' F' (25,20) N Stefan Lidström []


Q Permutation

Qa

PLL Parity18.pngQa Perm Diagram.png

Speedsolving Logo tiny.gif y' z U2 R' U2 Rw2 B2 R U2 Rw2 R' U2 R2 B2 Rw2 R U2 z' y U (25,16) CG11 Y Clément Gallet [85]
Speedsolving Logo tiny.gif B2 L2 U2 L2 d2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2 (30,17) N Clément Gallet []
Speedsolving Logo tiny.gif B2 d2 L2 U2 L2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2 (30,17) N Clément Gallet []
Speedsolving Logo tiny.gif R' U' R F2 R' U R U F2 U' F2 U' Fw2 U2 f2 Uw2 f2 u2 (27,18) PKF11 N Per Kristen Fredlund []


Qb

PLL Parity19.pngQb Perm Diagram.png

Speedsolving Logo tiny.gif y' z U2 R U2 Rw2 F2 R' U2 Rw2 R U2 R2 F2 Rw2 R' U2 z' y U (25,16) CG11 Y Clément Gallet [86]
Speedsolving Logo tiny.gif u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' d2 F2 U2 F2 R2 (30,17) N Clément Gallet []
Speedsolving Logo tiny.gif u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' F2 U2 F2 d2 R2 (30,17) N Clément Gallet []
Speedsolving Logo tiny.gif u2 l2 Uw2 l2 U2 Lw2 U' L2 U' L2 3Dw L U L' F2 L U' L' y (27,18) PKF11 N Per Kristen Fredlund []
Speedsolving Logo tiny.gif y2 u2 r2 Uw2 r2 U2 Rw2 U' R2 U' R2 U F U F' R2 F U' F' y2 (27,18) N Per Kristen Fredlund [87]


Two Corner Swap and a Dedge 2 2-cycle

C Permutation

Ca

PLL Parity15.pngCa Perm Diagram.png

Speedsolving Logo tiny.gif y' Rw2 F2 U2 r2 U' B2 U' F2 U B2 U' Rw2 U y (21,13) N Clément Gallet []
Speedsolving Logo tiny.gif Lw2 U F2 U' B2 U F2 U l2 U2 B2 Lw2 U' (21,13) AO09 N Alexander Ooms [88]
Speedsolving Logo tiny.gif U Lw2 B2 U2 l2 U' F2 U' B2 U F2 U' Lw2 (21,13) Inv of AO09 N Alexander Ooms [89]
Speedsolving Logo tiny.gif y' Rw r B' R F2 R' B R U2 r2 U2 F2 Rw2 U y (20,14) N Frédérick Badie &Clément Gallet []
Speedsolving Logo tiny.gif r2 F2 R2 D2 l2 D L2 D R2 D' L2 D F2 r2 U' (25,15) N Clément Gallet []
Speedsolving Logo tiny.gif U Dw2 Lw2 B2 U F2 U' B2 U F2 U l2 U2 Lw2 Dw2 (25,15) N Frédérick Badie [90]
Speedsolving Logo tiny.gif l r U2 x U' L U' R2 U L' U' Rw2 U2 x' U2 l' r' U' (21,16) N Christopher Mowla []


Cb

PLL Parity16.pngCb Perm Diagram.png

Speedsolving Logo tiny.gif y Rw2 B2 U2 r2 U F2 U B2 U' F2 U Rw2 U' y' (21,13) N Clément Gallet []
Speedsolving Logo tiny.gif Lw2 U' B2 U F2 U' B2 U' l2 U2 F2 Lw2 U (21,13) AO09 N Alexander Ooms [91]
Speedsolving Logo tiny.gif U' Lw2 F2 U2 l2 U B2 U F2 U' B2 U Lw2 (21,13) Inv of AO09 N Alexander Ooms [92]
Speedsolving Logo tiny.gif y Rw2 R F R' B2 R F' R' U2 r2 U2 B2 Rw2 U' y' (20,14) N Frédérick Badie &Clément Gallet [93]
Speedsolving Logo tiny.gif r2 B2 R2 D2 l2 D' L2 D' R2 D L2 D' B2 r2 U (25,15) N Clément Gallet []
Speedsolving Logo tiny.gif l' r' U2 x' U L' U R2 U' L U Rw2 U2 x U2 l r U (21,16) N Christopher Mowla []


I Permutation

PLL Parity14.pngI Perm Diagram.png

Speedsolving Logo tiny.gif L2 Uw2 L2 U' L2 D' B2 R2 d2 U' R2 D B2 u2 U (24,15) N Clément Gallet [94]
Speedsolving Logo tiny.gif L2 Uw2 L2 U L2 3Uw L2 F2 U z l2 F2 L' U2 Lw2 z' U y (25,15) CG08 N Clément Gallet []
Speedsolving Logo tiny.gif R2 D' F2 D R2 B2 D L2 D' Bw2 U2 b2 Uw2 b2 Uw2 U' (26,16) N Kenneth Gustavsson [95]
Speedsolving Logo tiny.gif Lw2 U F2 L D' L D L' U L U' L' U l2 U2 F2 Lw2 (23,17) AO08 N Alexander Ooms [96]
Speedsolving Logo tiny.gif Rw2 U2 r2 Uw2 r2 u2 D' F2 U F2 R2 U R2 U' R2 D (27,16) N Per Kristen Fredlund [97]


Theta (θ) Permutation

PLL Parity20.pngTheta Perm Diagram.png

Speedsolving Logo tiny.gif R2 U B2 Uw2 R2 U' B2 Uw2 U B2 U2 R2 Uw2 U' R2 U' (25,16) Y Clément Gallet []
Speedsolving Logo tiny.gif z F2 Rw2 R' F2 R2 U2 Rw2 R U2 R' F2 Rw2 U2 R F2 z' U (25,16) CG12 Y Clément Gallet [98]
Speedsolving Logo tiny.gif u2 D F2 U R2 U2 u2 F2 D' F2 U L2 D2 B2 U' u2 R2 y2 (29,17) N Clément Gallet []
Speedsolving Logo tiny.gif R' B' R F D' R' D B R Fw' f' R2 f2 Rw2 f2 Rw2 U R2 (24,18) N Per Kristen Fredlund &Clément Gallet []
Speedsolving Logo tiny.gif F U F' R2 F U' F' U' R2 U f2 R2 (f2 Rw2)2 U R2 (27,18) PKF12 N Per Kristen Fredlund [99]
Speedsolving Logo tiny.gif F R U' R' U' R U R' F' (r2 U2 r2 Uw2 r2 u2) R U R' U' R' F R F' (29,23) N Stefan Lidström []


Xi (Ξ) Permutation

PLL Parity21.pngXi Perm Diagram.png

Speedsolving Logo tiny.gif Uw d B2 D M2 U L2 B2 U B2 Uw2 R2 D F2 Uw2 3Lw2 y' (26,16) N Clément Gallet []
Speedsolving Logo tiny.gif R2 Uw2 U' M2 U R2 F2 Uw2 U' F2 U2 3Rw2 Uw2 U' F2 U2 R2 U (28,18) Y Clément Gallet []
Speedsolving Logo tiny.gif Uw2 Lw2 U' B' U B U2 F U' F' U F' L2 F Lw2 U2 Lw2 Uw2 U' (26,19) FB13 Y Frédérick Badie []
Speedsolving Logo tiny.gif U L2 U2 F2 D B2 u2 D' F2 L2 F2 D B2 D u2 R2 D2 F2 d2 (33,19) N Clément Gallet []
Speedsolving Logo tiny.gif Dw2 l' r' F' L' B' L F L' R' F' R B R' F' l2 F2 Lw2 Bw2 F' x (24,20) N Frédérick Badie &Clément Gallet []
Speedsolving Logo tiny.gif 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' (29,21) N Matthew Sheerin [100]
Speedsolving Logo tiny.gif 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 (29,21) N Matthew Sheerin [101]


The Shortest PLL Parity Fixes in BQTM

  • Note that these are the only PLL parity algorithms on this page which only use two inner layer slice quarter turns.
    • This alg set is for theoretical purposes only, as they scramble the pseudo 3x3x3 state of the 4x4x4.


Speedsolving Logo tiny.gif Rw U D L2 U D S2 Rw (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U D L2 U D S2 Rw' (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U' D' L2 U' D' S2 Rw (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U' D' L2 U' D' S2 Rw' (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U D R2 U D S2 Rw (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U D R2 U D S2 Rw' (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U' D' R2 U' D' S2 Rw (10,8) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U' D' R2 U' D' S2 Rw' (10,8) Y Christopher Mowla [102]


  • 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:
Speedsolving Logo tiny.gif r U D L2 U D S2 r S2 D' U' L2 D' U' (18,14) N Christopher Mowla []


  • However, note that this is not the shortest solution to this 4x4x4 position, as the following is a shorter supercube safe algorithm.
Speedsolving Logo tiny.gif (l E2 r' E2)3 (18,12) N Christopher Mowla []



One Dedge Flip

One Dedge Flip.png


Shortest Half Turn Algorithms

  • All 288 possible (25,15) solutions which flip the upper front dedge and which affect the top or front centers of the 4x4x4 supercube are listed and rigorously categorized below. (15 block half turns is move optimal for this case.)
  • All such algorithms can be obtained by running the 3x3x3 Classic Setup through a 3x3x3 solver like Cube Explorer; but a custom-written program was made to sort and label them in the manner shown.
  • For the sake of conciseness, note that an algorithm labelled Alg.1(v1) is a transformation of Alg.1(v2), Alg.1(v3), Alg.1(v4), and Alg.1(v5), for example. In general, any given algorithm in any subgroup is a transformation of any given algorithm in another subgroup which is in the same group. This was proved directly (in old WCA notation) by Christopher Mowla in 2012.


(Non-Symmetrical Algorithms)

Group 1

Speedsolving Logo tiny.gif r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 (25,15) Alg.1(v1) Y Frédérick_Badie [103]
Speedsolving Logo tiny.gif l U2 r' F2 r F2 l2 U2 l' U2 l U2 F2 l2 F2 (25,15) Mirror[Alg.1(v1)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 r2 F2 U2 r U2 r' U2 r2 F2 l F2 l' U2 r (25,15) Inverse[Alg.1(v1)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif l' F2 r U2 r' U2 l2 F2 l F2 l' F2 U2 l2 U2 (25,15) Rotation[Alg.1(v1)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l' (25,15) Mirror[Inverse[Alg.1(v1)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif r F2 l' U2 l U2 r2 F2 r' F2 r F2 U2 r2 U2 (25,15) Mirror[Rotation[Alg.1(v1)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 l2 U2 F2 l F2 l' F2 l2 U2 r U2 r' F2 l (25,15) Inverse[Rotation[Alg.1(v1)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 r2 U2 F2 r' F2 r F2 r2 U2 l' U2 l F2 r' (25,15) Mirror[Inverse[Rotation[Alg.1(v1)]]] Y Frédérick_Badie []


Speedsolving Logo tiny.gif r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2 (25,15) Alg.1(v2) Y Frédérick_Badie []
Speedsolving Logo tiny.gif l U2 l' U2 r U2 r2 F2 l' F2 r U2 F2 l2 F2 (25,15) Mirror[Alg.1(v2)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 r2 F2 U2 l F2 r' F2 l2 U2 l U2 r' U2 r (25,15) Inverse[Alg.1(v2)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif l' F2 l F2 r' F2 r2 U2 l U2 r' F2 U2 l2 U2 (25,15) Rotation[Alg.1(v2)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 l2 F2 U2 r' F2 l F2 r2 U2 r' U2 l U2 l' (25,15) Mirror[Inverse[Alg.1(v2)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif r F2 r' F2 l F2 l2 U2 r' U2 l F2 U2 r2 U2 (25,15) Mirror[Rotation[Alg.1(v2)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 l2 U2 F2 r U2 l' U2 r2 F2 r F2 l' F2 l (25,15) Inverse[Rotation[Alg.1(v2)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 r2 U2 F2 l' U2 r U2 l2 F2 l' F2 r F2 r' (25,15) Mirror[Inverse[Rotation[Alg.1(v2)]]] Y Frédérick_Badie []


Speedsolving Logo tiny.gif r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2 (25,15) Alg.1(v3) Y Frédérick_Badie []
Speedsolving Logo tiny.gif l' B2 l U2 l' U2 l2 F2 l D2 r' D2 B2 l2 F2 (25,15) Mirror[Alg.1(v3)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 r2 B2 D2 l' D2 r F2 r2 U2 r' U2 r B2 r' (25,15) Inverse[Alg.1(v3)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif l D2 l' F2 l F2 l2 U2 l' B2 r B2 D2 l2 U2 (25,15) Rotation[Alg.1(v3)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 l2 B2 D2 r D2 l' F2 l2 U2 l U2 l' B2 l (25,15) Mirror[Inverse[Alg.1(v3)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif r' D2 r F2 r' F2 r2 U2 r B2 l' B2 D2 r2 U2 (25,15) Mirror[Rotation[Alg.1(v3)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 l2 D2 B2 r' B2 l U2 l2 F2 l' F2 l D2 l' (25,15) Inverse[Rotation[Alg.1(v3)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 r2 D2 B2 l B2 r' U2 r2 F2 r F2 r' D2 r (25,15) Mirror[Inverse[Rotation[Alg.1(v3)]]] Y Frédérick_Badie []


Speedsolving Logo tiny.gif r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2 (25,15) Alg.1(v4) Y Frédérick_Badie []
Speedsolving Logo tiny.gif l' B2 l U2 l' U2 r2 B2 l U2 r' U2 F2 r2 F2 (25,15) Mirror[Alg.1(v4)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 l2 F2 U2 l' U2 r B2 l2 U2 r' U2 r B2 r' (25,15) Inverse[Alg.1(v4)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif l D2 l' F2 l F2 r2 D2 l' F2 r F2 U2 r2 U2 (25,15) Rotation[Alg.1(v4)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 r2 F2 U2 r U2 l' B2 r2 U2 l U2 l' B2 l (25,15) Mirror[Inverse[Alg.1(v4)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif r' D2 r F2 r' F2 l2 D2 r F2 l' F2 U2 l2 U2 (25,15) Mirror[Rotation[Alg.1(v4)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 r2 U2 F2 r' F2 l D2 r2 F2 l' F2 l D2 l' (25,15) Inverse[Rotation[Alg.1(v4)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 l2 U2 F2 l F2 r' D2 l2 F2 r F2 r' D2 r (25,15) Mirror[Inverse[Rotation[Alg.1(v4)]]] Y Frédérick_Badie []


Speedsolving Logo tiny.gif r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2 (25,15) Alg.1(v5) Y Frédérick_Badie []
Speedsolving Logo tiny.gif l' B2 r B2 r' U2 l2 F2 r F2 l' U2 F2 r2 F2 (25,15) Mirror[Alg.1(v5)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 l2 F2 U2 r' F2 l F2 r2 U2 l' B2 l B2 r' (25,15) Inverse[Alg.1(v5)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif l D2 r' D2 r F2 l2 U2 r' U2 l F2 U2 r2 U2 (25,15) Rotation[Alg.1(v5)] Y Frédérick_Badie []
Speedsolving Logo tiny.gif F2 r2 F2 U2 l F2 r' F2 l2 U2 r B2 r' B2 l (25,15) Mirror[Inverse[Alg.1(v5)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif r' D2 l D2 l' F2 r2 U2 l U2 r' F2 U2 l2 U2 (25,15) Mirror[Rotation[Alg.1(v5)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 r2 U2 F2 l' U2 r U2 l2 F2 r' D2 r D2 l' (25,15) Inverse[Rotation[Alg.1(v5)]] Y Frédérick_Badie []
Speedsolving Logo tiny.gif U2 l2 U2 F2 r U2 l' U2 r2 F2 l D2 l' D2 r (25,15) Mirror[Inverse[Rotation[Alg.1(v5)]]] Y Frédérick_Badie []


Group 2: F2 Move Conjugation + Rotation of Group 1

Speedsolving Logo tiny.gif r2 U2 B2 r B2 r' B2 r2 U2 l U2 l' B2 r U2 (25,15) Alg.2(v1) Y []
Speedsolving Logo tiny.gif l2 U2 B2 l' B2 l B2 l2 U2 r' U2 r B2 l' U2 (25,15) Mirror[Alg.2(v1)] Y []
Speedsolving Logo tiny.gif U2 r' B2 l U2 l' U2 r2 B2 r B2 r' B2 U2 r2 (25,15) Inverse[Alg.2(v1)] Y []
Speedsolving Logo tiny.gif l2 F2 D2 l D2 l' D2 l2 F2 r F2 r' D2 l F2 (25,15) Rotation[Alg.2(v1)] Y []
Speedsolving Logo tiny.gif U2 l B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2 (25,15) Mirror[Inverse[Alg.2(v1)]] Y []
Speedsolving Logo tiny.gif r2 F2 D2 r' D2 r D2 r2 F2 l' F2 l D2 r' F2 (25,15) Mirror[Rotation[Alg.2(v1)]] Y []
Speedsolving Logo tiny.gif F2 l' D2 r F2 r' F2 l2 D2 l D2 l' D2 F2 l2 (25,15) Inverse[Rotation[Alg.2(v1)]] Y []
Speedsolving Logo tiny.gif F2 r D2 l' F2 l F2 r2 D2 r' D2 r D2 F2 r2 (25,15) Mirror[Inverse[Rotation[Alg.2(v1)]]] Y []


Speedsolving Logo tiny.gif r2 U2 B2 l U2 r' U2 l2 B2 l B2 r' B2 r U2 (25,15) Alg.2(v2) Y []
Speedsolving Logo tiny.gif l2 U2 B2 r' U2 l U2 r2 B2 r' B2 l B2 l' U2 (25,15) Mirror[Alg.2(v2)] Y []
Speedsolving Logo tiny.gif U2 r' B2 r B2 l' B2 l2 U2 r U2 l' B2 U2 r2 (25,15) Inverse[Alg.2(v2)] Y []
Speedsolving Logo tiny.gif l2 F2 D2 r F2 l' F2 r2 D2 r D2 l' D2 l F2 (25,15) Rotation[Alg.2(v2)] Y []
Speedsolving Logo tiny.gif U2 l B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2 (25,15) Mirror[Inverse[Alg.2(v2)]] Y []
Speedsolving Logo tiny.gif r2 F2 D2 l' F2 r F2 l2 D2 l' D2 r D2 r' F2 (25,15) Mirror[Rotation[Alg.2(v2)]] Y []
Speedsolving Logo tiny.gif F2 l' D2 l D2 r' D2 r2 F2 l F2 r' D2 F2 l2 (25,15) Inverse[Rotation[Alg.2(v2)]] Y []
Speedsolving Logo tiny.gif F2 r D2 r' D2 l D2 l2 F2 r' F2 l D2 F2 r2 (25,15) Mirror[Inverse[Rotation[Alg.2(v2)]]] Y []


Speedsolving Logo tiny.gif r2 D2 F2 l' F2 r U2 r2 B2 r' B2 r D2 r' U2 (25,15) Alg.2(v3) Y []
Speedsolving Logo tiny.gif l2 D2 F2 r F2 l' U2 l2 B2 l B2 l' D2 l U2 (25,15) Mirror[Alg.2(v3)] Y []
Speedsolving Logo tiny.gif U2 r D2 r' B2 r B2 r2 U2 r' F2 l F2 D2 r2 (25,15) Inverse[Alg.2(v3)] Y []
Speedsolving Logo tiny.gif l2 B2 U2 r' U2 l F2 l2 D2 l' D2 l B2 l' F2 (25,15) Rotation[Alg.2(v3)] Y []
Speedsolving Logo tiny.gif U2 l' D2 l B2 l' B2 l2 U2 l F2 r' F2 D2 l2 (25,15) Mirror[Inverse[Alg.2(v3)]] Y []
Speedsolving Logo tiny.gif r2 B2 U2 l U2 r' F2 r2 D2 r D2 r' B2 r F2 (25,15) Mirror[Rotation[Alg.2(v3)]] Y []
Speedsolving Logo tiny.gif F2 l B2 l' D2 l D2 l2 F2 l' U2 r U2 B2 l2 (25,15) Inverse[Rotation[Alg.2(v3)]] Y []
Speedsolving Logo tiny.gif F2 r' B2 r D2 r' D2 r2 F2 r U2 l' U2 B2 r2 (25,15) Mirror[Inverse[Rotation[Alg.2(v3)]]] Y []


Speedsolving Logo tiny.gif r2 U2 B2 r B2 l' D2 r2 B2 l B2 l' D2 l U2 (25,15) Alg.2(v4) Y []
Speedsolving Logo tiny.gif l2 U2 B2 l' B2 r D2 l2 B2 r' B2 r D2 r' U2 (25,15) Mirror[Alg.2(v4)] Y []
Speedsolving Logo tiny.gif U2 l' D2 l B2 l' B2 r2 D2 l B2 r' B2 U2 r2 (25,15) Inverse[Alg.2(v4)] Y []
Speedsolving Logo tiny.gif l2 F2 D2 l D2 r' B2 l2 D2 r D2 r' B2 r F2 (25,15) Rotation[Alg.2(v4)] Y []
Speedsolving Logo tiny.gif U2 r D2 r' B2 r B2 l2 D2 r' B2 l B2 U2 l2 (25,15) Mirror[Inverse[Alg.2(v4)]] Y []
Speedsolving Logo tiny.gif r2 F2 D2 r' D2 l B2 r2 D2 l' D2 l B2 l' F2 (25,15) Mirror[Rotation[Alg.2(v4)]] Y []
Speedsolving Logo tiny.gif F2 r' B2 r D2 r' D2 l2 B2 r D2 l' D2 F2 l2 (25,15) Inverse[Rotation[Alg.2(v4)]] Y []
Speedsolving Logo tiny.gif F2 l B2 l' D2 l D2 r2 B2 l' D2 r D2 F2 r2 (25,15) Mirror[Inverse[Rotation[Alg.2(v4)]]] Y []


Speedsolving Logo tiny.gif r2 U2 B2 l U2 r' U2 l2 B2 r D2 r' D2 l U2 (25,15) Alg.2(v5) Y []
Speedsolving Logo tiny.gif l2 U2 B2 r' U2 l U2 r2 B2 l' D2 l D2 r' U2 (25,15) Mirror[Alg.2(v5)] Y []
Speedsolving Logo tiny.gif U2 l' D2 r D2 r' B2 l2 U2 r U2 l' B2 U2 r2 (25,15) Inverse[Alg.2(v5)] Y []
Speedsolving Logo tiny.gif l2 F2 D2 r F2 l' F2 r2 D2 l B2 l' B2 r F2 (25,15) Rotation[Alg.2(v5)] Y []
Speedsolving Logo tiny.gif U2 r D2 l' D2 l B2 r2 U2 l' U2 r B2 U2 l2 (25,15) Mirror[Inverse[Alg.2(v5)]] Y []
Speedsolving Logo tiny.gif r2 F2 D2 l' F2 r F2 l2 D2 r' B2 r B2 l' F2 (25,15) Mirror[Rotation[Alg.2(v5)]] Y []
Speedsolving Logo tiny.gif F2 r' B2 l B2 l' D2 r2 F2 l F2 r' D2 F2 l2 (25,15) Inverse[Rotation[Alg.2(v5)]] Y []
Speedsolving Logo tiny.gif F2 l B2 r' B2 r D2 l2 F2 r' F2 l D2 F2 r2 (25,15) Mirror[Inverse[Rotation[Alg.2(v5)]]] Y []


Group 3: Cyclic Shift of Group 1

Speedsolving Logo tiny.gif r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2 (25,15) Alg.3(v1) Y []
Speedsolving Logo tiny.gif l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2 (25,15) Mirror[Alg.3(v1)] Y []
Speedsolving Logo tiny.gif B2 l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r' (25,15) Inverse[Alg.3(v1)] Y []
Speedsolving Logo tiny.gif l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2 D2 (25,15) Rotation[Alg.3(v1)] Y []
Speedsolving Logo tiny.gif B2 r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l (25,15) Mirror[Inverse[Alg.3(v1)]] Y []
Speedsolving Logo tiny.gif r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2 D2 (25,15) Mirror[Rotation[Alg.3(v1)]] Y []
Speedsolving Logo tiny.gif D2 r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l' (25,15) Inverse[Rotation[Alg.3(v1)]] Y []
Speedsolving Logo tiny.gif D2 l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r (25,15) Mirror[Inverse[Rotation[Alg.3(v1)]]] Y []


Speedsolving Logo tiny.gif r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2 (25,15) Alg.3(v2) Y []
Speedsolving Logo tiny.gif l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2 B2 (25,15) Mirror[Alg.3(v2)] Y []
Speedsolving Logo tiny.gif B2 r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r' (25,15) Inverse[Alg.3(v2)] Y []
Speedsolving Logo tiny.gif l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2 D2 (25,15) Rotation[Alg.3(v2)] Y []
Speedsolving Logo tiny.gif B2 l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l (25,15) Mirror[Inverse[Alg.3(v2)]] Y []
Speedsolving Logo tiny.gif r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2 D2 (25,15) Mirror[Rotation[Alg.3(v2)]] Y []
Speedsolving Logo tiny.gif D2 l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l' (25,15) Inverse[Rotation[Alg.3(v2)]] Y []
Speedsolving Logo tiny.gif D2 r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r (25,15) Mirror[Inverse[Rotation[Alg.3(v2)]]] Y []


Speedsolving Logo tiny.gif r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2 (25,15) Alg.3(v3) Y []
Speedsolving Logo tiny.gif l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2 B2 (25,15) Mirror[Alg.3(v3)] Y []
Speedsolving Logo tiny.gif B2 l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r' (25,15) Inverse[Alg.3(v3)] Y []
Speedsolving Logo tiny.gif l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2 D2 (25,15) Rotation[Alg.3(v3)] Y []
Speedsolving Logo tiny.gif B2 r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l (25,15) Mirror[Inverse[Alg.3(v3)]] Y []
Speedsolving Logo tiny.gif r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2 D2 (25,15) Mirror[Rotation[Alg.3(v3)]] Y []
Speedsolving Logo tiny.gif D2 r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l' (25,15) Inverse[Rotation[Alg.3(v3)]] Y []
Speedsolving Logo tiny.gif D2 l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r (25,15) Mirror[Inverse[Rotation[Alg.3(v3)]]] Y []


Speedsolving Logo tiny.gif r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2 (25,15) Alg.3(v4) Y []
Speedsolving Logo tiny.gif l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2 B2 (25,15) Mirror[Alg.3(v4)] Y []
Speedsolving Logo tiny.gif B2 r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r' (25,15) Inverse[Alg.3(v4)] Y []
Speedsolving Logo tiny.gif l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2 D2 (25,15) Rotation[Alg.3(v4)] Y []
Speedsolving Logo tiny.gif B2 l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l (25,15) Mirror[Inverse[Alg.3(v4)]] Y []
Speedsolving Logo tiny.gif r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2 D2 (25,15) Mirror[Rotation[Alg.3(v4)]] Y []
Speedsolving Logo tiny.gif D2 l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l' (25,15) Inverse[Rotation[Alg.3(v4)]] Y []
Speedsolving Logo tiny.gif D2 r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r (25,15) Mirror[Inverse[Rotation[Alg.3(v4)]]] Y []


Speedsolving Logo tiny.gif r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2 (25,15) Alg.3(v5) Y []
Speedsolving Logo tiny.gif l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2 B2 (25,15) Mirror[Alg.3(v5)] Y []
Speedsolving Logo tiny.gif B2 l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r (25,15) Inverse[Alg.3(v5)] Y []
Speedsolving Logo tiny.gif l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2 D2 (25,15) Rotation[Alg.3(v5)] Y []
Speedsolving Logo tiny.gif B2 r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l' (25,15) Mirror[Inverse[Alg.3(v5)]] Y []
Speedsolving Logo tiny.gif r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2 D2 (25,15) Mirror[Rotation[Alg.3(v5)]] Y []
Speedsolving Logo tiny.gif D2 r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l (25,15) Inverse[Rotation[Alg.3(v5)]] Y []
Speedsolving Logo tiny.gif D2 l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r' (25,15) Mirror[Inverse[Rotation[Alg.3(v5)]]] Y []


Group 4: B2 Move Conjugation of Group 3

Speedsolving Logo tiny.gif r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l B2 (25,15) Alg.4(v1) Y []
Speedsolving Logo tiny.gif l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r' B2 (25,15) Mirror[Alg.4(v1)] Y []
Speedsolving Logo tiny.gif B2 l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2 (25,15) Inverse[Alg.4(v1)] Y []
Speedsolving Logo tiny.gif l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r D2 (25,15) Rotation[Alg.4(v1)] Y []
Speedsolving Logo tiny.gif B2 r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 (25,15) Mirror[Inverse[Alg.4(v1)]] Y []
Speedsolving Logo tiny.gif r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l' D2 (25,15) Mirror[Rotation[Alg.4(v1)]] Y []
Speedsolving Logo tiny.gif D2 r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2 (25,15) Inverse[Rotation[Alg.4(v1)]] Y []
Speedsolving Logo tiny.gif D2 l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2 (25,15) Mirror[Inverse[Rotation[Alg.4(v1)]]] Y []


Speedsolving Logo tiny.gif r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r' B2 (25,15) Alg.4(v2) Y []
Speedsolving Logo tiny.gif l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l B2 (25,15) Mirror[Alg.4(v2)] Y []
Speedsolving Logo tiny.gif B2 r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 (25,15) Inverse[Alg.4(v2)] Y []
Speedsolving Logo tiny.gif l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l' D2 (25,15) Rotation[Alg.4(v2)] Y []
Speedsolving Logo tiny.gif B2 l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2 (25,15) Mirror[Inverse[Alg.4(v2)]] Y []
Speedsolving Logo tiny.gif r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r D2 (25,15) Mirror[Rotation[Alg.4(v2)]] Y []
Speedsolving Logo tiny.gif D2 l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2 (25,15) Inverse[Rotation[Alg.4(v2)]] Y []
Speedsolving Logo tiny.gif D2 r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2 (25,15) Mirror[Inverse[Rotation[Alg.4(v2)]]] Y []


Speedsolving Logo tiny.gif r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l B2 (25,15) Alg.4(v3) Y []
Speedsolving Logo tiny.gif l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r' B2 (25,15) Mirror[Alg.4(v3)] Y []
Speedsolving Logo tiny.gif B2 l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2 (25,15) Inverse[Alg.4(v3)] Y []
Speedsolving Logo tiny.gif l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r D2 (25,15) Rotation[Alg.4(v3)] Y []
Speedsolving Logo tiny.gif B2 r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 (25,15) Mirror[Inverse[Alg.4(v3)]] Y []
Speedsolving Logo tiny.gif r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l' D2 (25,15) Mirror[Rotation[Alg.4(v3)]] Y []
Speedsolving Logo tiny.gif D2 r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2 (25,15) Inverse[Rotation[Alg.4(v3)]] Y []
Speedsolving Logo tiny.gif D2 l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2 (25,15) Mirror[Inverse[Rotation[Alg.4(v3)]]] Y []


Speedsolving Logo tiny.gif r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r' B2 (25,15) Alg.4(v4) Y []
Speedsolving Logo tiny.gif l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l B2 (25,15) Mirror[Alg.4(v4)] Y []
Speedsolving Logo tiny.gif B2 r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 (25,15) Inverse[Alg.4(v4)] Y []
Speedsolving Logo tiny.gif l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l' D2 (25,15) Rotation[Alg.4(v4)] Y []
Speedsolving Logo tiny.gif B2 l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2 (25,15) Mirror[Inverse[Alg.4(v4)]] Y []
Speedsolving Logo tiny.gif r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r D2 (25,15) Mirror[Rotation[Alg.4(v4)]] Y []
Speedsolving Logo tiny.gif D2 l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2 (25,15) Inverse[Rotation[Alg.4(v4)]] Y []
Speedsolving Logo tiny.gif D2 r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2 (25,15) Mirror[Inverse[Rotation[Alg.4(v4)]]] Y []


Speedsolving Logo tiny.gif r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l' B2 (25,15) Alg.4(v5) Y []
Speedsolving Logo tiny.gif l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r B2 (25,15) Mirror[Alg.4(v5)] Y []
Speedsolving Logo tiny.gif B2 l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2 (25,15) Inverse[Alg.4(v5)] Y []
Speedsolving Logo tiny.gif l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r' D2 (25,15) Rotation[Alg.4(v5)] Y []
Speedsolving Logo tiny.gif B2 r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 (25,15) Mirror[Inverse[Alg.4(v5)]] Y []
Speedsolving Logo tiny.gif r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l D2 (25,15) Mirror[Rotation[Alg.4(v5)]] Y []
Speedsolving Logo tiny.gif D2 r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2 (25,15) Inverse[Rotation[Alg.4(v5)]] Y []
Speedsolving Logo tiny.gif D2 l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2 (25,15) Mirror[Inverse[Rotation[Alg.4(v5)]]] Y []


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.
Speedsolving Logo tiny.gif r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 (25,15) Alg.5(v1) Y [104]
Speedsolving Logo tiny.gif l2 B2 U2 r' U2 l U2 l' U2 F2 l' F2 r B2 l2 (25,15) Mirror[Alg.5(v1)] Y []
Speedsolving Logo tiny.gif r2 B2 l F2 r' F2 U2 r' U2 r U2 l' U2 B2 r2 (25,15) Inverse[Alg.5(v1)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 r F2 l' F2 l F2 U2 l U2 r' D2 l2 (25,15) Rotation[Alg.5(v1)] Y []
Speedsolving Logo tiny.gif l2 B2 r' F2 l F2 U2 l U2 l' U2 r U2 B2 l2 (25,15) Mirror[Inverse[Alg.5(v1)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 l' F2 r F2 r' F2 U2 r' U2 l D2 r2 (25,15) Mirror[Rotation[Alg.5(v1)]] Y []
Speedsolving Logo tiny.gif l2 D2 r U2 l' U2 F2 l' F2 l F2 r' F2 D2 l2 (25,15) Inverse[Rotation[Alg.5(v1)]] Y []
Speedsolving Logo tiny.gif r2 D2 l' U2 r U2 F2 r F2 r' F2 l F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v1)]]] Y []


Speedsolving Logo tiny.gif r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2 (25,15) Alg.5(v2) Y []
Speedsolving Logo tiny.gif l2 B2 U2 r' U2 r B2 l' B2 U2 l' U2 l B2 l2 (25,15) Mirror[Alg.5(v2)] Y []
Speedsolving Logo tiny.gif r2 B2 r U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2 (25,15) Inverse[Alg.5(v2)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 r F2 r' D2 l D2 F2 l F2 l' D2 l2 (25,15) Rotation[Alg.5(v2)] Y []
Speedsolving Logo tiny.gif l2 B2 l' U2 l U2 B2 l B2 r' U2 r U2 B2 l2 (25,15) Mirror[Inverse[Alg.5(v2)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 l' F2 l D2 r' D2 F2 r' F2 r D2 r2 (25,15) Mirror[Rotation[Alg.5(v2)]] Y []
Speedsolving Logo tiny.gif l2 D2 l F2 l' F2 D2 l' D2 r F2 r' F2 D2 l2 (25,15) Inverse[Rotation[Alg.5(v2)]] Y []
Speedsolving Logo tiny.gif r2 D2 r' F2 r F2 D2 r D2 l' F2 l F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v2)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2 (25,15) Alg.5(v3) Y []
Speedsolving Logo tiny.gif l2 F2 D2 l D2 l' F2 r F2 D2 r D2 r' F2 l2 (25,15) Mirror[Alg.5(v3)] Y []
Speedsolving Logo tiny.gif r2 F2 l' D2 l D2 F2 l F2 r' D2 r D2 F2 r2 (25,15) Inverse[Alg.5(v3)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 l' B2 l U2 r' U2 B2 r' B2 r U2 l2 (25,15) Rotation[Alg.5(v3)] Y []
Speedsolving Logo tiny.gif l2 F2 r D2 r' D2 F2 r' F2 l D2 l' D2 F2 l2 (25,15) Mirror[Inverse[Alg.5(v3)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 r B2 r' U2 l U2 B2 l B2 l' U2 r2 (25,15) Mirror[Rotation[Alg.5(v3)]] Y []
Speedsolving Logo tiny.gif l2 U2 r' B2 r B2 U2 r U2 l' B2 l B2 U2 l2 (25,15) Inverse[Rotation[Alg.5(v3)]] Y []
Speedsolving Logo tiny.gif r2 U2 l B2 l' B2 U2 l' U2 r B2 r' B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v3)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2 (25,15) Alg.5(v4) Y []
Speedsolving Logo tiny.gif l2 F2 D2 l D2 r' D2 r D2 B2 r B2 l' F2 l2 (25,15) Mirror[Alg.5(v4)] Y []
Speedsolving Logo tiny.gif r2 F2 r' B2 l B2 D2 l D2 l' D2 r D2 F2 r2 (25,15) Inverse[Alg.5(v4)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 l' B2 r B2 r' B2 D2 r' D2 l U2 l2 (25,15) Rotation[Alg.5(v4)] Y []
Speedsolving Logo tiny.gif l2 F2 l B2 r' B2 D2 r' D2 r D2 l' D2 F2 l2 (25,15) Mirror[Inverse[Alg.5(v4)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 r B2 l' B2 l B2 D2 l D2 r' U2 r2 (25,15) Mirror[Rotation[Alg.5(v4)]] Y []
Speedsolving Logo tiny.gif l2 U2 l' D2 r D2 B2 r B2 r' B2 l B2 U2 l2 (25,15) Inverse[Rotation[Alg.5(v4)]] Y []
Speedsolving Logo tiny.gif r2 U2 r D2 l' D2 B2 l' B2 l B2 r' B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v4)]]] Y []


Speedsolving Logo tiny.gif r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2 (25,15) Alg.5(v5) Y []
Speedsolving Logo tiny.gif l2 B2 U2 l' B2 l B2 r' U2 F2 l' F2 r B2 l2 (25,15) Mirror[Alg.5(v5)] Y []
Speedsolving Logo tiny.gif r2 B2 l F2 r' F2 U2 l' B2 r B2 r' U2 B2 r2 (25,15) Inverse[Alg.5(v5)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 l D2 l' D2 r F2 U2 l U2 r' D2 l2 (25,15) Rotation[Alg.5(v5)] Y []
Speedsolving Logo tiny.gif l2 B2 r' F2 l F2 U2 r B2 l' B2 l U2 B2 l2 (25,15) Mirror[Inverse[Alg.5(v5)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 r' D2 r D2 l' F2 U2 r' U2 l D2 r2 (25,15) Mirror[Rotation[Alg.5(v5)]] Y []
Speedsolving Logo tiny.gif l2 D2 r U2 l' U2 F2 r' D2 l D2 l' F2 D2 l2 (25,15) Inverse[Rotation[Alg.5(v5)]] Y []
Speedsolving Logo tiny.gif r2 D2 l' U2 r U2 F2 l D2 r' D2 r F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v5)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2 (25,15) Alg.5(v6) Y []
Speedsolving Logo tiny.gif l2 F2 D2 r F2 r' F2 l D2 B2 r B2 l' F2 l2 (25,15) Mirror[Alg.5(v6)] Y []
Speedsolving Logo tiny.gif r2 F2 r' B2 l B2 D2 r F2 l' F2 l D2 F2 r2 (25,15) Inverse[Alg.5(v6)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 r' U2 r U2 l' B2 D2 r' D2 l U2 l2 (25,15) Rotation[Alg.5(v6)] Y []
Speedsolving Logo tiny.gif l2 F2 l B2 r' B2 D2 l' F2 r F2 r' D2 F2 l2 (25,15) Mirror[Inverse[Alg.5(v6)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 l U2 l' U2 r B2 D2 l D2 r' U2 r2 (25,15) Mirror[Rotation[Alg.5(v6)]] Y []
Speedsolving Logo tiny.gif l2 U2 l' D2 r D2 B2 l U2 r' U2 r B2 U2 l2 (25,15) Inverse[Rotation[Alg.5(v6)]] Y []
Speedsolving Logo tiny.gif r2 U2 r D2 l' D2 B2 r' U2 l U2 l' B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v6)]]] Y []


Speedsolving Logo tiny.gif r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2 (25,15) Alg.5(v7) Y []
Speedsolving Logo tiny.gif l2 B2 U2 l' B2 r D2 l' D2 B2 r' U2 l B2 l2 (25,15) Mirror[Alg.5(v7)] Y []
Speedsolving Logo tiny.gif r2 B2 r U2 l' B2 D2 r' D2 l B2 r' U2 B2 r2 (25,15) Inverse[Alg.5(v7)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 l D2 r' B2 l B2 D2 r F2 l' D2 l2 (25,15) Rotation[Alg.5(v7)] Y []
Speedsolving Logo tiny.gif l2 B2 l' U2 r B2 D2 l D2 r' B2 l U2 B2 l2 (25,15) Mirror[Inverse[Alg.5(v7)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 r' D2 l B2 r' B2 D2 l' F2 r D2 r2 (25,15) Mirror[Rotation[Alg.5(v7)]] Y []
Speedsolving Logo tiny.gif l2 D2 l F2 r' D2 B2 l' B2 r D2 l' F2 D2 l2 (25,15) Inverse[Rotation[Alg.5(v7)]] Y []
Speedsolving Logo tiny.gif r2 D2 r' F2 l D2 B2 r B2 l' D2 r F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v7)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2 (25,15) Alg.5(v8) Y []
Speedsolving Logo tiny.gif l2 F2 D2 r F2 l' U2 r U2 F2 l D2 r' F2 l2 (25,15) Mirror[Alg.5(v8)] Y []
Speedsolving Logo tiny.gif r2 F2 l' D2 r F2 U2 l U2 r' F2 l D2 F2 r2 (25,15) Inverse[Alg.5(v8)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 r' U2 l F2 r' F2 U2 l' B2 r U2 l2 (25,15) Rotation[Alg.5(v8)] Y []
Speedsolving Logo tiny.gif l2 F2 r D2 l' F2 U2 r' U2 l F2 r' D2 F2 l2 (25,15) Mirror[Inverse[Alg.5(v8)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 l U2 r' F2 l F2 U2 r B2 l' U2 r2 (25,15) Mirror[Rotation[Alg.5(v8)]] Y []
Speedsolving Logo tiny.gif l2 U2 r' B2 l U2 F2 r F2 l' U2 r B2 U2 l2 (25,15) Inverse[Rotation[Alg.5(v8)]] Y []
Speedsolving Logo tiny.gif r2 U2 l B2 r' U2 F2 l' F2 r U2 l' B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.5(v8)]]] Y []


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.
Speedsolving Logo tiny.gif r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2 (25,15) Alg.6(v1) Y []
Speedsolving Logo tiny.gif l2 B2 U2 r U2 l' U2 l U2 B2 l B2 r' B2 l2 (25,15) Mirror[Alg.6(v1)] Y []
Speedsolving Logo tiny.gif r2 B2 l' B2 r B2 U2 r U2 r' U2 l U2 B2 r2 (25,15) Inverse[Alg.6(v1)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 r' F2 l F2 l' F2 D2 l' D2 r D2 l2 (25,15) Rotation[Alg.6(v1)] Y []
Speedsolving Logo tiny.gif l2 B2 r B2 l' B2 U2 l' U2 l U2 r' U2 B2 l2 (25,15) Mirror[Inverse[Alg.6(v1)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 l F2 r' F2 r F2 D2 r D2 l' D2 r2 (25,15) Mirror[Rotation[Alg.6(v1)]] Y []
Speedsolving Logo tiny.gif l2 D2 r' D2 l D2 F2 l F2 l' F2 r F2 D2 l2 (25,15) Inverse[Rotation[Alg.6(v1)]] Y []
Speedsolving Logo tiny.gif r2 D2 l D2 r' D2 F2 r' F2 r F2 l' F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v1)]]] Y []


Speedsolving Logo tiny.gif r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2 (25,15) Alg.6(v2) Y []
Speedsolving Logo tiny.gif l2 B2 U2 r U2 r' F2 l F2 U2 l U2 l' B2 l2 (25,15) Mirror[Alg.6(v2)] Y []
Speedsolving Logo tiny.gif r2 B2 r' U2 r U2 F2 r F2 l' U2 l U2 B2 r2 (25,15) Inverse[Alg.6(v2)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 r' F2 r U2 l' U2 F2 l' F2 l D2 l2 (25,15) Rotation[Alg.6(v2)] Y []
Speedsolving Logo tiny.gif l2 B2 l U2 l' U2 F2 l' F2 r U2 r' U2 B2 l2 (25,15) Mirror[Inverse[Alg.6(v2)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 l F2 l' U2 r U2 F2 r F2 r' D2 r2 (25,15) Mirror[Rotation[Alg.6(v2)]] Y []
Speedsolving Logo tiny.gif l2 D2 l' F2 l F2 U2 l U2 r' F2 r F2 D2 l2 (25,15) Inverse[Rotation[Alg.6(v2)]] Y []
Speedsolving Logo tiny.gif r2 D2 r F2 r' F2 U2 r' U2 l F2 l' F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v2)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2 (25,15) Alg.6(v3) Y []
Speedsolving Logo tiny.gif l2 F2 D2 l' D2 l B2 r' B2 D2 r' D2 r F2 l2 (25,15) Mirror[Alg.6(v3)] Y []
Speedsolving Logo tiny.gif r2 F2 l D2 l' D2 B2 l' B2 r D2 r' D2 F2 r2 (25,15) Inverse[Alg.6(v3)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 l B2 l' D2 r D2 B2 r B2 r' U2 l2 (25,15) Rotation[Alg.6(v3)] Y []
Speedsolving Logo tiny.gif l2 F2 r' D2 r D2 B2 r B2 l' D2 l D2 F2 l2 (25,15) Mirror[Inverse[Alg.6(v3)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 r' B2 r D2 l' D2 B2 l' B2 l U2 r2 (25,15) Mirror[Rotation[Alg.6(v3)]] Y []
Speedsolving Logo tiny.gif l2 U2 r B2 r' B2 D2 r' D2 l B2 l' B2 U2 l2 (25,15) Inverse[Rotation[Alg.6(v3)]] Y []
Speedsolving Logo tiny.gif r2 U2 l' B2 l B2 D2 l D2 r' B2 r B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v3)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2 (25,15) Alg.6(v4) Y []
Speedsolving Logo tiny.gif l2 F2 D2 l' D2 r D2 r' D2 F2 r' F2 l F2 l2 (25,15) Mirror[Alg.6(v4)] Y []
Speedsolving Logo tiny.gif r2 F2 r F2 l' F2 D2 l' D2 l D2 r' D2 F2 r2 (25,15) Inverse[Alg.6(v4)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 l B2 r' B2 r B2 U2 r U2 l' U2 l2 (25,15) Rotation[Alg.6(v4)] Y []
Speedsolving Logo tiny.gif l2 F2 l' F2 r F2 D2 r D2 r' D2 l D2 F2 l2 (25,15) Mirror[Inverse[Alg.6(v4)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 r' B2 l B2 l' B2 U2 l' U2 r U2 r2 (25,15) Mirror[Rotation[Alg.6(v4)]] Y []
Speedsolving Logo tiny.gif l2 U2 l U2 r' U2 B2 r' B2 r B2 l' B2 U2 l2 (25,15) Inverse[Rotation[Alg.6(v4)]] Y []
Speedsolving Logo tiny.gif r2 U2 r' U2 l U2 B2 l B2 l' B2 r B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v4)]]] Y []


Speedsolving Logo tiny.gif r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2 (25,15) Alg.6(v5) Y []
Speedsolving Logo tiny.gif l2 B2 U2 l F2 l' F2 r U2 B2 l B2 r' B2 l2 (25,15) Mirror[Alg.6(v5)] Y []
Speedsolving Logo tiny.gif r2 B2 l' B2 r B2 U2 l F2 r' F2 r U2 B2 r2 (25,15) Inverse[Alg.6(v5)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 l' U2 l U2 r' F2 D2 l' D2 r D2 l2 (25,15) Rotation[Alg.6(v5)] Y []
Speedsolving Logo tiny.gif l2 B2 r B2 l' B2 U2 r' F2 l F2 l' U2 B2 l2 (25,15) Mirror[Inverse[Alg.6(v5)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 r U2 r' U2 l F2 D2 r D2 l' D2 r2 (25,15) Mirror[Rotation[Alg.6(v5)]] Y []
Speedsolving Logo tiny.gif l2 D2 r' D2 l D2 F2 r U2 l' U2 l F2 D2 l2 (25,15) Inverse[Rotation[Alg.6(v5)]] Y []
Speedsolving Logo tiny.gif r2 D2 l D2 r' D2 F2 l' U2 r U2 r' F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v5)]]] Y []


Speedsolving Logo tiny.gif r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2 (25,15) Alg.6(v6) Y []
Speedsolving Logo tiny.gif l2 B2 U2 l F2 r' D2 l D2 F2 r U2 l' B2 l2 (25,15) Mirror[Alg.6(v6)] Y []
Speedsolving Logo tiny.gif r2 B2 r' U2 l F2 D2 r D2 l' F2 r U2 B2 r2 (25,15) Inverse[Alg.6(v6)] Y []
Speedsolving Logo tiny.gif l2 D2 F2 l' U2 r B2 l' B2 U2 r' F2 l D2 l2 (25,15) Rotation[Alg.6(v6)] Y []
Speedsolving Logo tiny.gif l2 B2 l U2 r' F2 D2 l' D2 r F2 l' U2 B2 l2 (25,15) Mirror[Inverse[Alg.6(v6)]] Y []
Speedsolving Logo tiny.gif r2 D2 F2 r U2 l' B2 r B2 U2 l F2 r' D2 r2 (25,15) Mirror[Rotation[Alg.6(v6)]] Y []
Speedsolving Logo tiny.gif l2 D2 l' F2 r U2 B2 l B2 r' U2 l F2 D2 l2 (25,15) Inverse[Rotation[Alg.6(v6)]] Y []
Speedsolving Logo tiny.gif r2 D2 r F2 l' U2 B2 r' B2 l U2 r' F2 D2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v6)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2 (25,15) Alg.6(v7) Y []
Speedsolving Logo tiny.gif l2 F2 D2 r' B2 l U2 r' U2 B2 l' D2 r F2 l2 (25,15) Mirror[Alg.6(v7)] Y []
Speedsolving Logo tiny.gif r2 F2 l D2 r' B2 U2 l' U2 r B2 l' D2 F2 r2 (25,15) Inverse[Alg.6(v7)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 r D2 l' F2 r F2 D2 l B2 r' U2 l2 (25,15) Rotation[Alg.6(v7)] Y []
Speedsolving Logo tiny.gif l2 F2 r' D2 l B2 U2 r U2 l' B2 r D2 F2 l2 (25,15) Mirror[Inverse[Alg.6(v7)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 l' D2 r F2 l' F2 D2 r' B2 l U2 r2 (25,15) Mirror[Rotation[Alg.6(v7)]] Y []
Speedsolving Logo tiny.gif l2 U2 r B2 l' D2 F2 r' F2 l D2 r' B2 U2 l2 (25,15) Inverse[Rotation[Alg.6(v7)]] Y []
Speedsolving Logo tiny.gif r2 U2 l' B2 r D2 F2 l F2 r' D2 l B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v7)]]] Y []


Speedsolving Logo tiny.gif r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2 (25,15) Alg.6(v8) Y []
Speedsolving Logo tiny.gif l2 F2 D2 r' B2 r B2 l' D2 F2 r' F2 l F2 l2 (25,15) Mirror[Alg.6(v8)] Y []
Speedsolving Logo tiny.gif r2 F2 r F2 l' F2 D2 r' B2 l B2 l' D2 F2 r2 (25,15) Inverse[Alg.6(v8)] Y []
Speedsolving Logo tiny.gif l2 U2 B2 r D2 r' D2 l B2 U2 r U2 l' U2 l2 (25,15) Rotation[Alg.6(v8)] Y []
Speedsolving Logo tiny.gif l2 F2 l' F2 r F2 D2 l B2 r' B2 r D2 F2 l2 (25,15) Mirror[Inverse[Alg.6(v8)]] Y []
Speedsolving Logo tiny.gif r2 U2 B2 l' D2 l D2 r' B2 U2 l' U2 r U2 r2 (25,15) Mirror[Rotation[Alg.6(v8)]] Y []
Speedsolving Logo tiny.gif l2 U2 l U2 r' U2 B2 l' D2 r D2 r' B2 U2 l2 (25,15) Inverse[Rotation[Alg.6(v8)]] Y []
Speedsolving Logo tiny.gif r2 U2 r' U2 l U2 B2 r D2 l' D2 l B2 U2 r2 (25,15) Mirror[Inverse[Rotation[Alg.6(v8)]]] Y []


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.


It's worthy to note that the majority of algorithms in this section, like the (25,15) solutions, were found by using the 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 classic setup is used up to depth 21, some 21 slice quarter turn solutions may be found.

Speedsolving Logo tiny.gif r' F l' F2 r F r' F2 D F' D l D' F D' l F2 r (21,18) N Christopher Mowla []


  • 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. (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.)


Speedsolving Logo tiny.gif x Rw2 U2 Rw U2 l' U2 Rw' F2 U' l' U F2 U' l U' Rw2 x' (23,16) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif x Rw2 U2 Lw F2 l' F2 Lw' F2 U' l' U F2 U' l U' Rw2 x' (23,16) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif x Rw2 U2 Rw U2 l' U2 Rw' F2 U l' U' F2 U l U Rw2 x' (23,16) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif x Rw2 U2 Lw F2 l' F2 Lw' F2 U l' U' F2 U l U Rw2 x' (23,16) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif x' Rw2 U2 Lw' U2 r U2 Lw F2 U r U' F2 U r' U Rw2 x (23,16) cmowlaparity Y Christopher Mowla [105]
Speedsolving Logo tiny.gif x' Rw2 U2 Rw' F2 r F2 Rw F2 U r U' F2 U r' U Rw2 x (23,16) cmowlaparity(v2) Y Christopher Mowla []
Speedsolving Logo tiny.gif x' Rw2 U2 Lw' U2 r U2 Lw F2 U' r U F2 U' r' U' Rw2 x (23,16) v1 N Christopher Mowla [106]
Speedsolving Logo tiny.gif x' Rw2 U2 Rw' F2 r F2 Rw F2 U' r U F2 U' r' U' Rw2 x (23,16) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw (22,17) v1 Y Christopher Mowla [107]
Speedsolving Logo tiny.gif Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw (22,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 B Rw (22,17) v1 N Christopher Mowla [108]
Speedsolving Logo tiny.gif Rw' U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 B Rw (22,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r' U' r' U B2 U' r U' r' U2 r' B2 l U2 l' U2 r2 (23,17) Y Christopher Mowla []
Speedsolving Logo tiny.gif r' U r' U' B2 U r U r' U2 r' B2 l U2 l' U2 r2 (23,17) N Christopher Mowla []
Speedsolving Logo tiny.gif r B l B' D2 B l' B l B2 r F2 l' F2 l D2 r2 (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif r B l B' D2 B l' B l B2 l D2 l' D2 r D2 r2 (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif r B' l B D2 B' l' B' l B2 r F2 l' F2 l D2 r2 (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif r B' l B D2 B' l' B' l B2 l D2 l' D2 r D2 r2 (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw D B2 D' l D B2 U2 Rw D2 l D2 Rw' D' l' U2 Rw' (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw D B2 D' l D B2 U2 Lw B2 l B2 Lw' D' l' U2 Rw' (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw D' B2 D l D' B2 U2 Rw D2 l D2 Rw' D l' U2 Rw' (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw D' B2 D l D' B2 U2 Lw B2 l B2 Lw' D l' U2 Rw' (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D2 B l B' D2 B l' B' Rw' B2 l B2 Rw F2 Rw (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D2 B l B' D2 B l' B' Lw' D2 l D2 Lw F2 Rw (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D2 B' l B D2 B' l' B Rw' B2 l B2 Rw F2 Rw (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D2 B' l B D2 B' l' B Lw' D2 l D2 Lw F2 Rw (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 D2 r D2 l' D l D' F2 D l' D l D2 l F2 r (23,17) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 D2 r D2 l' D' l D F2 D' l' D' l D2 l F2 r (23,17) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' B' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 Rw (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' B' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 Rw (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' B U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 Rw (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' B U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 Rw (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif l' r' D' r D' B2 D r' D' B2 l' D2 l' F2 l F2 l2 (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif l r U' r U' F2 U r' U' F2 l' U2 l' B2 l B2 r2 (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif l' r' D r D B2 D' r' D B2 l' D2 l' F2 l F2 l2 (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif l r U r U F2 U' r' U F2 l' U2 l' B2 l B2 r2 (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F2 D' r' D F2 D' r D Lw D2 r' D2 Lw' U2 Rw' (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw' (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F2 D r' D' F2 D r D' Lw D2 r' D2 Lw' U2 Rw' (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw' (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 B' r B' U2 B r' B' U2 l' B2 Lw' D2 l D2 Lw r (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif l2 F' r F' D2 F r' F' D2 l' F2 l' U2 l U2 l' r' (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 B r B U2 B' r' B U2 l' B2 Lw' D2 l D2 Lw r (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif l2 F r F D2 F' r' F D2 l' F2 l' U2 l U2 l' r' (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 U2 l' U2 l F' r' F U2 F' r F' r' F2 r' U2 r' (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 U2 r' F2 l D' r' D F2 D' r D' r' D2 l' U2 r' (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 U2 l' U2 l F r' F' U2 F r F r' F2 r' U2 r' (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 U2 r' F2 l D r' D' F2 D r D r' D2 l' U2 r' (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 B2 D2 r D b' D F2 D' b D r' B2 l r F2 r (23,17) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 B2 D2 r D' f' D' F2 D f D' r' B2 l r F2 r (23,17) N Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 U2 l' U' f U' B2 U f' U' r' B2 r l F2 r (23,17) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 U2 l' U b U B2 U' b' U r' B2 r l F2 r (23,17) N Christopher Mowla []
Speedsolving Logo tiny.gif r2 D f D' B2 D f' D r D2 F2 r' B2 l r F2 r (23,17) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 D' b D B2 D' b' D' r D2 F2 r' B2 l r F2 r (23,17) N Christopher Mowla []
Speedsolving Logo tiny.gif r2 U' b' U F2 U' b U' l' U2 B2 r' B2 r l F2 r (23,17) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 U f' U' F2 U f U l' U2 B2 r' B2 r l F2 r (23,17) N Christopher Mowla []
Speedsolving Logo tiny.gif r2 D2 r D b' D F2 D' b D r' B2 l B2 r F2 r (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 D2 r D b' D F2 D' b D l' D2 l D2 l F2 r (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 D2 r D' f' D' F2 D f D' r' B2 l B2 r F2 r (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 D2 r D' f' D' F2 D f D' l' D2 l D2 l F2 r (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 r' B2 l D f D' B2 D f' D r D2 r F2 r (23,17) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 l' D2 l F u F' D2 F u' F r F2 l F2 r (23,17) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 B2 r U2 r' B' d' B U2 B' d B' r' U2 r' U2 r' (23,17) v3 Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 r' B2 l D' b D B2 D' b' D' r D2 r F2 r (23,17) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 F2 l' D2 l F' d F D2 F' d' F' r F2 l F2 r (23,17) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 B2 r U2 r' B u' B' U2 B u B r' U2 r' U2 r' (23,17) v3 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw2 B r' U R' U r U' R U' r B U2 r U2 r' B2 Rw2 (23,18) N Christopher Mowla [109]
Speedsolving Logo tiny.gif Lw' B' r' B D2 B' r B' r' B2 r' D2 l B2 l' B2 r Lw (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif Lw' B r' B' D2 B r B r' B2 r' D2 l B2 l' B2 r Lw (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif r Lw F2 l' F2 l D' r' D F2 D' r D' r' D2 r' F2 Lw' (23,18) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F2 l' F2 r F' r' F U2 F' r F' r' F2 r' U2 Rw' (23,18) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif r Lw F2 r' D2 l B' r' B D2 B' r B' r' B2 l' F2 Lw' (23,18) v3 Y Christopher Mowla []
Speedsolving Logo tiny.gif r Lw F2 l' F2 l D r' D' F2 D r D r' D2 r' F2 Lw' (23,18) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F2 l' F2 r F r' F' U2 F r F r' F2 r' U2 Rw' (23,18) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r Lw F2 r' D2 l B r' B' D2 B r B r' B2 l' F2 Lw' (23,18) v3 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U' r' U B2 U' r U' r' U2 l' D2 r D2 r' B2 Rw l (23,18) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U' r' U B2 U' r U' r' U2 r' B2 r B2 l' B2 Rw l (23,18) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U r' U' B2 U r U r' U2 l' D2 r D2 r' B2 Rw l (23,18) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' U r' U' B2 U r U r' U2 r' B2 r B2 l' B2 Rw l (23,18) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D b' D l D2 l' D' b D Rw' B2 l B2 Rw F2 Rw (23,18) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D b' D l D2 l' D' b D Lw' D2 l D2 Lw F2 Rw (23,18) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D' f' D' l D2 l' D f D' Rw' B2 l B2 Rw F2 Rw (23,18) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' F2 D' f' D' l D2 l' D f D' Lw' D2 l D2 Lw F2 Rw (23,18) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r2 B' D2 r D b' D F2 D' b D r' B2 l B' r F2 r (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 B D2 r D' f' D' F2 D f D' r' B2 l B r F2 r (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif r2 B D2 r D b' D F2 D' b D r' B2 l B r F2 r (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif r2 B' D2 r D' f' D' F2 D f D' r' B2 l B' r F2 r (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif r' Lw' B' d' B U2 B' d B' l' B2 D2 r' D2 r l U2 Lw (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif r' Lw' B u' B' U2 B u B l' B2 D2 r' D2 r l U2 Lw (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw l D2 F2 l' F' d F' U2 F d' F' l D2 r' l' U2 Rw' (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw l D2 F2 l' F u F U2 F' u' F l D2 r' l' U2 Rw' (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F' u' F D2 F' u F' l' F2 U2 l D2 r' l' U2 Rw' (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F d' F' D2 F d F l' F2 U2 l D2 r' l' U2 Rw' (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F2 l' F' d F' U2 F d' F' Lw D2 r' D2 Lw' U2 Rw' (23,18) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F2 l' F' d F' U2 F d' F' Rw F2 r' F2 Rw' U2 Rw' (23,18) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F2 l' F u F U2 F' u' F Lw D2 r' D2 Lw' U2 Rw' (23,18) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw l F2 l' F u F U2 F' u' F Rw F2 r' F2 Rw' U2 Rw' (23,18) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif r' Lw' U2 B2 l' B' u B' D2 B u' B' r' D2 r l U2 Lw (23,18) Y Christopher Mowla []
Speedsolving Logo tiny.gif r' Lw' U2 B2 l' B d B D2 B' d' B r' D2 r l U2 Lw (23,18) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw l U2 r F2 r' U' b' U F2 U' b U' l' U2 r' U2 Rw' (23,18) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif r Lw U2 r F2 r' U' b' U F2 U' b U' r' F2 r' F2 Lw' (23,18) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw l U2 r F2 r' U f' U' F2 U f U l' U2 r' U2 Rw' (23,18) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif r Lw U2 r F2 r' U f' U' F2 U f U r' F2 r' F2 Lw' (23,18) v2 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F' d F' r' F2 r F d' F' Lw D2 r' D2 Lw' U2 Rw' (23,18) v1 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F' d F' r' F2 r F d' F' Rw F2 r' F2 Rw' U2 Rw' (23,18) v2 Y Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F u F r' F2 r F' u' F Lw D2 r' D2 Lw' U2 Rw' (23,18) v1 N Christopher Mowla []
Speedsolving Logo tiny.gif Rw U2 F u F r' F2 r F' u' F Rw F2 r' F2 Rw' U2 Rw' (23,18) v2 N Christopher Mowla []


Shortest BQTM 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.


Symmetrical Algorithms

Speedsolving Logo tiny.gif Lw E Rw2 Uw r' Uw' Rw2 Dw R2 Uw r' Uw' Rw R Dw' E' Lw' (20,17) N Christopher Mowla [110]
Speedsolving Logo tiny.gif Rw' E' Lw2 Uw' l Uw Lw2 Dw' L2 Uw' l Uw Lw' L' Dw E Rw (20,17) N Christopher Mowla [111]
Speedsolving Logo tiny.gif y' Rw Uw2 x' U D r y Uw2 Rw2 Uw r Uw' Rw2 Dw r' u D' x Uw2 Rw' y (22,17) N Christopher Mowla [112]
Speedsolving Logo tiny.gif Rw' 3Uw' u' Lw' r' Uw' r' Uw 3Lw r' Uw Lw' Uw' r' Uw Lw E' Rw (18,18) N Christopher Mowla [113]
Speedsolving Logo tiny.gif y' Rw Uw' L Uw' y R Uw' r Uw Rw' Dw Rw2 Uw' r Uw Rw2 L' Uw Rw' y (19,18) Challenger N Christopher Mowla [114]
Speedsolving Logo tiny.gif y' Rw' Uw L' Uw y' R' Uw r' Uw' Rw Dw' Rw2 Uw r' Uw' Rw2 L Uw' Rw y (19,18) Reverter N Christopher Mowla [115]
Speedsolving Logo tiny.gif z Dw' M D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' M' Uw x2 z' (19,18) Holy Grail N Christopher Mowla [116]
Speedsolving Logo tiny.gif Rw' E Uw2 Fw Uw Rw' r' Fw' r Fw Rw Uw' Fw' Uw r Uw E' Rw (19,18) N Christopher Mowla [117]
Speedsolving Logo tiny.gif Lw' S Bw2 Dw r Dw' Bw Dw r' Dw' r' Bw' r Bw r Bw S' Lw (19,18) N Christopher Mowla []
Speedsolving Logo tiny.gif Lw' F' b' Rw' Bw' Rw u Rw' Bw Rw u2 Bw' u Bw u b F Lw (19,18) N Christopher Mowla []
Speedsolving Logo tiny.gif Uw' Fw2 L' R' u Lw Rw Uw2 Rw d Lw' Bw2 Lw d' 3Rw Rw R Fw2 Uw (23,18) N Christopher Mowla [118]
Speedsolving Logo tiny.gif Rw' E Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw E' Rw (19,19) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' E Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw r Rw Fw' Uw Lw E' Rw (19,19) N Christopher Mowla []
Speedsolving Logo tiny.gif Rw' D' u' Uw' Rw f Rw' Uw Rw f' Rw' f' Uw' f Uw f u D Rw (19,19) N Christopher Mowla []
Speedsolving Logo tiny.gif Dw' F' z Rw2 B2 x' l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l u' U Rw2 D Rw z' (24,19) N Christopher Mowla []
Speedsolving Logo tiny.gif Uw Fw' D r' Dw b Dw b' Dw' r Dw b' Dw' b Dw b Dw2 D' Fw Uw' (21,20) N Christopher Mowla []
Speedsolving Logo tiny.gif Fw' U' l u2 Lw Bw' Lw' u Lw Uw Bw u' Bw' Uw' Bw Lw' u l' U Fw (21,20) N Christopher Mowla []
Speedsolving Logo tiny.gif (Rw U L F' U) l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l Uw' (U' F L' U' Rw') (23,20) N Christopher Mowla [119]
Speedsolving Logo tiny.gif Bw' R' u Rw' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' Rw u' R Bw (21,21) N Christopher Mowla [120]
Speedsolving Logo tiny.gif Bw' R' u Rw' l' Dw Bw' Dw' l Dw Lw Bw l' Bw' Lw' Bw Dw' Rw u' R Bw (21,21) N Christopher Mowla []


Non-Symmetrical Algorithms

Speedsolving Logo tiny.gif z' Fw' Uw r' Uw' Fw Uw r' Fw' U L u l Uw' r' Uw l' u' L' U' Fw r2 Uw' z (23,22) N Christopher Mowla [121]
Speedsolving Logo tiny.gif z' Fw' Uw r' Uw' Fw Uw r' Fw' f' U L U' f r' f' U L' U' f Fw r2 Uw' z (23,22) N Christopher Mowla [122]
Speedsolving Logo tiny.gif z' Fw' Uw r' Uw' Fw Uw r' Fw' f' L Fw R' F' r' F R Fw' L' f Fw r2 Uw' z (23,22) N Christopher Mowla [123]
Speedsolving Logo tiny.gif 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 (25,24) 5x5 Alg N Christopher Mowla [124]


Longer/Faster Algorithms

  • The following list of algorithms are all unique solutions generated with the classic setup which use 2 different face turns.


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 of such algorithms.).

Speedsolving Logo tiny.gif r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r' (27,18) Alg.1 Y []
Speedsolving Logo tiny.gif r U2 r2 l' U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' (27,18) Inverse[Alg.1(v1)] Y []
Speedsolving Logo tiny.gif l' U2 l' U2 l U2 l' U2 r U2 l' U2 l U2 r' l2 U2 l (27,18) Mirror[Alg.1(v1)] Y []
Speedsolving Logo tiny.gif l' U2 l2 r U2 l' U2 l U2 r' U2 l U2 l' U2 l U2 l (27,18) Inverse[Mirror[Alg.1(v1)]] Y []


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.

Speedsolving Logo tiny.gif r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 (M r') U2 r' (26,18) Alg.1 (v2) N []


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 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.


Speedsolving Logo tiny.gif r' U2 r U2 l F2 l' r' F2 r' U2 r' U2 F2 r2 F2 (25,16) Y []
Speedsolving Logo tiny.gif r' U2 r U2 l' U2 l r U2 r U2 r' U2 F2 r2 F2 (25,16) Y []
Speedsolving Logo tiny.gif r' U2 l F2 l' F2 l r F2 r F2 l' U2 F2 r2 F2 (25,16) Y []


Speedsolving Logo tiny.gif r B2 r' U2 l B2 l2 B2 U2 r B2 l' B2 l' r' B2 (25,16) Y []
Speedsolving Logo tiny.gif l' r' B2 r' B2 l U2 B2 r2 B2 r U2 l' B2 l B2 (25,16) Y []


Speedsolving Logo tiny.gif r' U2 r U2 r U2 r2 F2 l r2 F2 l' U2 F2 r2 F2 (27,16) Y []
Speedsolving Logo tiny.gif r' U2 l F2 r F2 l2 U2 l r2 U2 r' U2 F2 r2 F2 (27,16) Y []


Speedsolving Logo tiny.gif r' U2 r' U2 r2 U2 r U2 r2 B2 r U2 r U2 r2 B2 (27,16) Y []
Speedsolving Logo tiny.gif r' U2 l' B2 r2 B2 l U2 r2 B2 r U2 r U2 r2 B2 (27,16) Y []


Speedsolving Logo tiny.gif r U2 r U2 r' U2 l F2 l' F2 r F2 r' F2 r' U2 r' (25,17) Y []
Speedsolving Logo tiny.gif r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r' (25,17) Y []