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):
- 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 is 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 parity case.
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 edge-pairing stage of a 5x5x5 Reduction solve.
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.
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.
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.
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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.
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 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.
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.
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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]
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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.
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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 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.
Unlike reduction parity, which also includes algorithms which contain an even number if inner slice quarter turns, edge-pairing algorithms used in Reduction which contain an even number of inner slice quarter turns are not included on this page.
One such parity case encountered during 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.)
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, 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
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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.
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f2 r E2 r E2 r f2
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(11,7)
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N
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Tom Rokicki and Ed Trice
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[2]
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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 mean in the algorithm bar above later.)
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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 turns (BQTM). We can count that this algorithm has 7 block half turns (BHTM) without breaking it up.
In fact, in addition to the fact that all parity cases on this page are each represented by a case image,
- The number of moves each algorithm contains in these two big cube move metrics are 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 slice half turns (BHTM) are listed first in each category.
- Algorithms which have fewer slice quarter turn moves (BQTM) are listed before other algorithms which have the same number of BHTM as they.
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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.
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Finally, one of the simplest OLL parity (more specifically, a double parity) algorithm (found in December, 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.
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(Rw B' z')(r' F U2 F')4 r' (z B Rw')
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(25,21)
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N
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Floyd Newberry
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[3]
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(Rw B' z')(r F U2 F')4 r (z B Rw')
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(25,21)
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N
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Floyd Newberry
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[4]
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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 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. (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 commonly practiced 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).
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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.
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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 algorithms 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.
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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.)
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Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2
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(25,15)
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Old Standard Alg
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Y
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anonymous
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[5]
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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.
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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 the same algorithm
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 4x4x4 and the 5x5x5.
PLL Parity
- This section shows all 22 possible PLL parity cases. In addition, algorithms for the two cases when two dedges are unoriented (and corners are solved) and the two cases when all four last layer dedges are unoriented (and the corners are solved) are also included.
- Of course, all PLL parity cases can be handled by using the first case shown, commonly called "opposite parity" (OP).
Here's a link to a PDF resource on how to handle 22 of the cases by using a combination of OP and 3x3x3 PLL algorithms.
Dedges
- Algorithms marked as "Safe" are supercube safe.
Two Dedges (Oriented)
Opposite
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r2 U2 r2 Uw2 r2 u2
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(12,6)
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N
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Chris Hardwick
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[6]
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r2 U2 r2 U2 d2 r2 d2
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(14,7)
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N
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[]
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U2 r2 U2 r2 Uw2 r2 Uw2
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(14,7)
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N
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Chris Hardwick
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[7]
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(Uw2 Rw2 U2) r2 (U2 Rw2 Uw2)
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(14,7)
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SP01
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N
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Stefan Pochmann
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[8]
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(Dw2 Rw2 U2) r2 (U2 Rw2 Dw2)
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(14,7)
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N
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[]
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(Rw2 F2 U2) r2 (U2 F2 Rw2)
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(14,7)
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N
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Stefan Pochmann
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[9]
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(Rw2 B2 U2) r2 (U2 B2 Rw2)
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(14,7)
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N
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Stefan Pochmann
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[]
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Rw2 (U2 r U2 S2)2 Rw2//Safe
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(18,10)
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Y
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Walter Randelshofer
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[10]
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r2 U2 B2 l r U2 M' U2 r2 B2 U2//Safe
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(19,11)
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N
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[]
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y Rw2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 y'
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(20,11)
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v1
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Y
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[]
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y Rw2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 y'
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(20,11)
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v2
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Y
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[]
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r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2//Safe
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(22,12)
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Y
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[]
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r' F U' R F' U l r U' F R' U F' l'//Safe
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(14,14)
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N
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[]
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Adjacent
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(R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2)
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(18,10)
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N
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Chris Hardwick
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[11]
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(R2 D' x Uw2 Rw2 U2) r2 (U2 Rw2 Uw2 x' D R2)
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(20,11)
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SP02
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N
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Stefan Pochmann
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[12]
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(R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2)
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(20,11)
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FB02
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N
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Frédérick Badie
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[13]
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(F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2)
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(20,11)
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N
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Stefan Pochmann
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[]
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(R2 D' x Rw2 F2 U2) r2 (U2 F2 Rw2 x' D R2)
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(20,11)
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N
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Stefan Pochmann
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[]
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(R2 D' x Rw2 B2 U2) r2 (U2 B2 Rw2 x' D R2)
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(20,11)
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N
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Stefan Pochmann
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[]
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(y' R' F) l E F2 E' l' r' E F2 E' r (F' R y)//Safe
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(16,14)
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N
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Christopher Mowla
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[14]
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(y' R' F) l E' F2 E l' r' E' F2 E r (F' R y)//Safe
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(16,14)
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N
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Christopher Mowla
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[]
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(R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R')
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(20,14)
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N
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Chris Hardwick
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[15]
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(y2 Uw2 R U R' U' Rw2 U2) r2 (U2 Rw2 U R U' R' Uw2 y2)
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(22,15)
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N
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xyzzy
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[16]
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(R2 D' x) r2 U2 B2 l r U2 M' U2 r2 B2 U2 (x' D R2)//Safe
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(24,15)
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N
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[]
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(Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw)
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(22,17)
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v1
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N
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Christopher Mowla
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[17]
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y' (Rw U' R' U' Rw B2) (Rw B2 r2 B2 Rw') (B2 Rw' U R U Rw') y
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(22,17)
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v2
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N
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Christopher Mowla
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[18]
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y2 Rw U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U R' U' R' U y2
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(20,20)
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Y
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António Gomes
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[19]
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y2 R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U y2
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(20,20)
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Y
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António Gomes
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[]
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y R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' y'
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(20,20)
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Y
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António Gomes
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[]
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(y2 Bw2 R2 Bw2) Rw U Rw' U' Lw' U' Lw U2 Rw U' Rw' U' Lw' U Lw (Bw2 R2 Bw2 y2)
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(28,21)
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Y
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Moritz Karl
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[20]
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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'
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(30,26)
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Y
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Ben Whitmore
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[]
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Two Dedges (Unoriented)
Opposite
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F2 l E F2 E' l' r' E F2 E' r F2//Safe
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(16,12)
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N
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Christopher Mowla
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[21]
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F2 l E' F2 E l' r' E' F2 E r F2//Safe
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(16,12)
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N
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Christopher Mowla
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[]
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(y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y')
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(18,12)
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N
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Chris Hardwick
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[22]
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r U2 l D2 l' U2 M U2 r D2 r' U2 l'//Safe
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(19,13)
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N
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Kenneth Gustavsson
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[23]
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(y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y)
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(20,13)
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N
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Stefan Pochmann
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[24]
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(y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y')
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(20,13)
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N
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[]
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l U2 M l U2 M' l' U2 M' U2 Rw M' U2 M r' U2 Rw'//Safe
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(23,17)
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N
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Kenneth Gustavsson
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[]
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(F r U' R U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R' U r' F')
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(24,19)
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N
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Christopher Mowla
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[]
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(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')
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(32,25)
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N
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Christopher Mowla
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[]
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Adjacent
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(R B) r2 U2 r2 Uw2 r2 u2 (B' R')
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(16,10)
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N
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Chris Hardwick
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[25]
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(R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R')
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(18,11)
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N
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Stefan Pochmann
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[26]
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(3Lw U Rw2 U2 F2) r2 (F2 U2 Rw2 U' 3Lw')
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(18,11)
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N
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Stefan Pochmann
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[27]
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R B U2 r2 U2 B2 l r U2 M' U2 r2 B R'//Safe
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(21,14)
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N
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[]
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Four Dedges (Oriented)
O Permutation
Oa
|
r2 Uw2 b2 U' b2 r2 U b2 r2 Uw2 r2
|
(20,11)
|
CG03
|
N
|
Clément Gallet
|
[28]
|
|
f2 Uw2 r2 U' r2 f2 U r2 f2 Uw2 f2
|
(20,11)
|
|
N
|
Clément Gallet
|
[]
|
|
y2 M2 U' M2 u Uw f2 M2 Dw2 b2 U2 b2
|
(20,11)
|
|
N
|
Clément Gallet
|
[]
|
|
M' U2 Uw2 r2 Uw2 r2 U2 l2 U2 M' U M2 U M2
|
(22,13)
|
|
N
|
|
[]
|
|
M U2 Uw2 l2 Uw2 l2 U2 r2 U2 M U M2 U M2
|
(22,13)
|
|
N
|
|
[]
|
|
y2 D2 M E2 M U M2 U' l2 U2 r2 Uw2 r2 Uw2
|
(22,13)
|
PKF03
|
N
|
Per Kristen Fredlund
|
[29]
|
|
(E2 M)2 U M2 U' l2 U2 r2 Uw2 r2 u2
|
(22,13)
|
PKF03
|
N
|
Per Kristen Fredlund
|
[30]
|
|
l2 U2 f2 U' l2 f2 U u2 f2 u2 l2 U2 l2
|
(23,13)
|
|
N
|
Clément Gallet
|
[]
|
|
l2 U2 f2 U' l2 f2 U u2 f2 l2 U2 l2 u2
|
(23,13)
|
|
N
|
Clément Gallet
|
[]
|
|
r2 Uw2 b2 U' b2 r2 U b2 R2 Uw2 Rw2 Uw2 R2
|
(24,13)
|
|
N
|
Clément Gallet
|
[31]
|
|
M2 U M U2 r' l' U2 F2 r2 F2 U2 r2 U M2
|
(23,14)
|
|
N
|
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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]
|
|
(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
|
[]
|
|
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]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2
|
(20,11)
|
CG03
|
N
|
Clément Gallet
|
[34]
|
|
f2 Uw2 f2 r2 U' f2 r2 U r2 Uw2 f2
|
(20,11)
|
|
N
|
Clément Gallet
|
[]
|
|
b2 U2 b2 Dw2 M2 f2 Uw' u' M2 U M2 y2
|
(20,11)
|
|
N
|
Clément Gallet
|
[]
|
|
M2 U' M2 U' M U2 l2 U2 r2 Uw2 r2 Uw2 U2 M
|
(22,13)
|
|
N
|
|
[]
|
|
M2 U' M2 U' M' U2 r2 U2 l2 Uw2 l2 Uw2 U2 M'
|
(22,13)
|
|
N
|
|
[]
|
|
Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2
|
(22,13)
|
PKF03
|
N
|
Per Kristen Fredlund
|
[35]
|
|
u2 r2 Uw2 r2 U2 l2 U M2 U' (M' E2)2
|
(22,13)
|
PKF03
|
N
|
Per Kristen Fredlund
|
[36]
|
|
l2 U2 l2 u2 f2 u2 U' f2 l2 U f2 U2 l2
|
(23,13)
|
|
N
|
Clément Gallet
|
[]
|
|
u2 l2 U2 l2 f2 u2 U' f2 l2 U f2 U2 l2
|
(23,13)
|
|
N
|
Clément Gallet
|
[]
|
|
R2 Uw2 Rw2 Uw2 R2 b2 U' r2 b2 U b2 Uw2 r2
|
(24,13)
|
|
N
|
Clément Gallet
|
[37]
|
|
M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2
|
(23,14)
|
|
N
|
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
(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]
|
|
(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
|
[]
|
|
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]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
- Note: This is commonly called the "W" permutation.
|
M2 U M' U2 M U l2 U2 r2 Uw2 r2 Uw2 U2
|
(20,12)
|
|
N
|
|
[]
|
|
u2 S2 Uw' u' b2 R2 b2 Rw2 f2 r2 U S2
|
(21,12)
|
|
N
|
Clément Gallet
|
[]
|
|
F2 D' f2 d2 b2 D' B2 Dw2 3Uw' M2 3Uw F2 Uw2
|
(21,13)
|
|
N
|
Clément Gallet
|
[]
|
|
(r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)
|
(22,13)
|
PKF04
|
N
|
Per Kristen Fredlund
|
[40]
|
|
R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2
|
(26,14)
|
CG04
|
Y
|
Clément Gallet
|
[]
|
|
F2 Uw' u' M2 U' F2 D S2 Dw d Bw2 u2 b2 U2 y2
|
(22,14)
|
|
N
|
Clément Gallet
|
[]
|
|
l2 D2 B2 Rw2 B2 D2 l2 F2 U' F2 L2 F2 U' L2
|
(26,14)
|
|
N
|
Clément Gallet
|
[]
|
|
y' M2 U' r2 b2 Rw2 Bw2 R2 Bw2 L2 U2 M2 U2 F2 D M2 x2 y
|
(28,15)
|
|
N
|
Doug
|
[41]
|
|
R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2
|
(21,16)
|
SP04
|
N
|
Stefan Pochmann
|
[]
|
|
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]
|
|
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]
|
|
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]
|
|
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]
|
|
(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
|
F2 M F2 U' l2 U2 r2 Uw2 r2 U' Uw2 B2 M B2
|
(23,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
y' U2 Rw2 U2 r2 Uw2 r2 y Uw2 M U' M2 U' F2 U2 M
|
(24,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
R2 S' (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S' L2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[47]
|
|
R2 S (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S L2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
L2 S L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S R2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
L2 S' L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S' R2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
M2 U F2 D2 r F2 r2 F2 D2 l2 F2 D2 r2 D2 l U' M2
|
(30,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(M2 U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M2)
|
(27,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(M2 U Fw2 r2 u' S' Rw2 u2) M' (u2 Rw2 S u r2 Fw2 U' M2)
|
(27,17)
|
|
N
|
Christopher Mowla
|
[]
|
Ob
|
B2 M' B2 Uw2 U r2 Uw2 r2 U2 l2 U F2 M' F2
|
(23,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
M' U2 F2 U M2 U M' Uw2 y' r2 Uw2 r2 U2 Rw2 U2 y
|
(24,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
L2 S L2 U' S2 U Rw2 (U2 r2 Uw2 r2 u2) S R2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[48]
|
|
L2 S' L2 U S2 U' Rw2 (U2 r2 Uw2 r2 u2) S' R2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
R2 S' (u2 r2 Uw2 r2 U2) Rw2 U S2 U' L2 S' L2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
R2 S (u2 r2 Uw2 r2 U2) Rw2 U' S2 U L2 S L2
|
(24,14)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
M2 U l' D2 r2 D2 F2 l2 D2 F2 r2 F2 r' D2 F2 U' M2
|
(30,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(M2 U Fw2 r2 u S' Rw2 u2) M (u2 Rw2 S u' r2 Fw2 U' M2)
|
(27,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(M2 U Fw2 r2 u' S' Rw2 u2) M (u2 Rw2 S u r2 Fw2 U' M2)
|
(27,17)
|
|
N
|
Christopher Mowla
|
[]
|
8 Permutation
- Note: This is commonly called the "W" permutation.
|
y' M2 U' D2 r2 S2 l S2 r2 E2 r' U' M2 y'//Safe
|
(19,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
M2 U' r U D L2 U D S2 r S2 D' U' L2 D' M2//Safe
|
(22,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M2 U r' U' D' L2 U' D' S2 r' S2 D U L2 D M2 y'//Safe
|
(22,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
M2 D R2 D U r U' D' R2 U' D' S2 r S2 U M2//Safe
|
(22,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M2 D' R2 D' U' r' U D R2 U D S2 r' S2 U' M2 y'//Safe
|
(22,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
(M2 U')(r' E2 l E2)3 (U M2)//Safe
|
(24,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
(M2 U')(E2 r' E2 l)3 (U M2)//Safe
|
(24,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
(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]
|
|
(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
|
[]
|
|
(M2 U Fw2 r2 d r2 Uw2 S') M (S Uw2 r2 d' r2 Fw2 U' M2)
|
(27,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(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
|
F2 R2 B' D' B R2 F' U Fw2 F L2 f2 Lw2 f2 l2 U'
|
(24,16)
|
|
N
|
Clément Gallet
|
[]
|
|
L' U Lw2 L B2 l2 Bw2 l2 b2 U' L2 F2 R' D' R F2
|
(24,16)
|
|
N
|
Clément Gallet
|
[]
|
|
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]
|
|
R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2
|
(25,16)
|
|
N
|
|
[]
|
|
F2 L2 B D B' L2 F U' F f2 U2 L2 b2 L2 U2 f2 U
|
(26,17)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
[]
|
|
(F2 D R2 U' R2 F2 U' F2 U F2 D')(r2 U2 r2 Uw2 r2 u2)
|
(29,17)
|
|
N
|
Per Kristen Fredlund
|
[51]
|
|
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]
|
|
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]
|
|
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
|
|
[]
|
|
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
|
[]
|
|
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]
|
|
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
|
Rw2 f2 U2 Fw2 D Rw2 U2 Fw2 U' Fw2 L2 U2 B2 Lw2 U
|
(27,15)
|
|
N
|
Clément Gallet
|
[55]
|
|
Rw2 f2 U2 Bw2 D' Rw2 U2 Bw2 U Fw2 R2 D2 B2 Lw2 U
|
(27,15)
|
Alg2
|
N
|
Clément Gallet
|
[]
|
|
Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U
|
(27,15)
|
Alg2(v2)
|
N
|
Michael Fung
|
[56]
|
|
Rw2 f2 D2 Fw2 U' Rw2 U2 Bw2 U Bw2 R2 U2 F2 Rw2 U'
|
(27,15)
|
|
N
|
Clément Gallet
|
[]
|
|
Rw2 f2 D2 Fw2 D' Rw2 U2 Bw2 U Bw2 L2 U2 B2 Lw2 U
|
(27,15)
|
|
N
|
Clément Gallet
|
[]
|
|
Rw2 f2 D2 Bw2 U Rw2 U2 Fw2 U' Bw2 L2 D2 F2 Rw2 U'
|
(27,15)
|
|
N
|
Clément Gallet
|
[]
|
|
Fw2 r2 D2 Lw2 U Bw2 D2 Lw2 D' Rw2 B2 U2 L2 Bw2 U'
|
(27,15)
|
|
N
|
Clément Gallet
|
[]
|
|
Fw2 r2 D2 Rw2 U Bw2 D2 Rw2 D' Rw2 F2 D2 L2 Bw2 U
|
(27,15)
|
|
N
|
Clément Gallet
|
[]
|
|
Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U
|
(27,16)
|
|
N
|
Christopher Mowla
|
[57]
|
|
Rw2 F2 U2 y Lw2' U Lw2' U' D' Rw2 U Rw2 y' r2 U2 F2 Rw2 U
|
(27,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 F2 L' U2 Lw2 F2 R' D2 R2 U2 B2 R D2 B2 Rw2 U2
|
(29,16)
|
|
Y
|
Clément Gallet
|
[]
|
|
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)
|
N
|
reThinking the Cube
|
[58]
|
|
y' U2 Rw2 U2 R U2 F2 R2 F2 R' F2 U2 Rw2 U2 R' F2 r2 y
|
(29,16)
|
reCornerX(BD)
|
N
|
reThinking the Cube
|
[59]
|
|
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
|
[]
|
|
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]
|
|
F2 L' U2 L R U2 R' F2 Lw2 F2 U2 Lw2' L' U2 F2 Lw2 U2
|
(28,17)
|
|
Y
|
Clément Gallet
|
[]
|
|
y' r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 y
|
(30,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
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]
|
|
L2 u2 F2 U2 L2 u2 F2 U' F2 L2 U2 L2 U L2 U2 F2 u2 U
|
(32,18)
|
|
N
|
Clément Gallet
|
[]
|
|
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]
|
|
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
|
|
[]
|
|
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
|
[]
|
|
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]
|
|
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
|
[]
|
|
(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
|
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
|
[64]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[65]
|
|
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
|
[66]
|
|
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
|
[67]
|
|
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
|
[68]
|
|
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
|
|
[]
|
|
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
|
[69]
|
Opposite/Diagonal
|
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
|
[]
|
|
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
|
[70]
|
Two X-Center Piece Swap Algorithms
- 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.
|
y Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U y'
|
(13,10)
|
|
Y
|
|
[]
|
|
Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U'
|
(13,12)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'
|
(15,14)
|
|
Y
|
|
[]
|
|
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
|
z2 F2 R2 Dw2 F2 U' R2 Uw2 U R2 U F2 Uw2 U M2 F2 U'
|
(25,16)
|
|
Y
|
Clément Gallet
|
[]
|
|
F2 U Rw2 U' B2 U' F2 U B2 U' r2 F2 U2 Rw2 U' F2 U'
|
(27,17)
|
FB07
|
N
|
Frédérick Badie
|
[]
|
|
y2 U' R2 b2 l2 Fw2 l2 F2 r2 L D L' B2 L D' L' F2 R2
|
(27,17)
|
|
N
|
Clément Gallet
|
[]
|
|
R2 U' f2 D2 L2 b2 D' R2 D L2 D' R2 D' f2 U R2 U'
|
(27,17)
|
|
N
|
Clément Gallet
|
[]
|
Db
|
U F2 M2 Uw2 U' F2 U' R2 Uw2 U' R2 U F2 Dw2 R2 F2 z2
|
(25,16)
|
|
Y
|
Clément Gallet
|
[]
|
|
U F2 U Rw2 U2 F2 r2 U B2 U' F2 U B2 U Rw2 U' F2
|
(27,17)
|
FB07
|
N
|
Frédérick Badie
|
[]
|
|
R2 F2 L D L' B2 L D' L' r2 F2 l2 Fw2 l2 b2 R2 U y2
|
(27,17)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
U R U' L U2 R' U L l2 F2 Lw2 Fw2 l2 Fw2
|
(20,14)
|
|
N
|
Clément Gallet
|
[]
|
|
Dw2 R2 D B2 Dw2 D' B2 D' R2 Dw2 D' B2 L2 U' L2
|
(23,15)
|
|
Y
|
Clément Gallet
|
[]
|
|
u2 r2 Uw2 r2 U2 Rw2 D R D' R F2 L' U L F2
|
(23,15)
|
PKF06
|
N
|
Per Kristen Fredlund
|
[71]
|
|
d2 D' B2 L2 U d2 L2 D' B2 U R2 U R2 Dw2 L2
|
(24,15)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
[72]
|
|
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
|
Fw2 l2 Fw2 Lw2 F2 l2 L' U' R U2 L' U R' U'
|
(20,14)
|
|
N
|
Clément Gallet
|
[]
|
|
L2 U L2 B2 Dw2 D R2 D B2 Dw2 D B2 D' R2 Dw2
|
(23,15)
|
|
Y
|
Clément Gallet
|
[]
|
|
F2 L' U' L F2 R' D R' D' Rw2 U2 r2 Uw2 r2 u2
|
(23,15)
|
PKF06
|
N
|
Per Kristen Fredlund
|
[73]
|
|
L2 Dw2 R2 U' R2 U' B2 D L2 d2 U' L2 B2 D d2
|
(24,15)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
[74]
|
|
(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
|
U' z' U2 B2 Lw2 U2 L' B2 Lw2' L B2 L U2 Lw2' L U2 z
|
(23,15)
|
CG05
|
Y
|
Clément Gallet
|
[75]
|
|
y U L2 3Uw' L2 U L2 y u2 l2 Uw2 l2 U2 Lw2 3Uw L2 U' L2 y2
|
(27,16)
|
|
N
|
Stefan Pochmann
|
[76]
|
|
R2 U R2 U' R2 F2 U' (Fw2 r2)2 F2 r2 D R2 D'
|
(27,16)
|
PKF05
|
N
|
Per Kristen Fredlund
|
[]
|
|
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
|
z' U2 Lw2 L' U2 L' B2 Lw2' L' B2 L U2 Lw2' B2 U2 z U
|
(23,15)
|
CG05
|
Y
|
Clément Gallet
|
[77]
|
|
y2 L2 U L2 3Uw' Lw2 U2 l2 Uw2 l2 u2 y' L2 U' L2 3Uw L2 U' y'
|
(27,16)
|
|
N
|
Stefan Pochmann
|
[78]
|
|
R2 D' r2 F2 (r2 Fw2)2 U F2 R2 U R2 U' R2 D
|
(27,16)
|
PKF05
|
N
|
Per Kristen Fredlund
|
[79]
|
|
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
|
z' U2 Lw2' L U2 L F2 Lw2' L F2 L' U2 Lw2 F2 U2 z U'
|
(23,15)
|
CG05
|
Y
|
Clément Gallet
|
[80]
|
|
R2' U' R2 3Uw Rw2 U2 r2 Uw2 r2 u2 y R2 U R2' 3Uw' R2 U y'
|
(27,16)
|
|
N
|
Stefan Pochmann
|
[81]
|
|
R2 D r2 B2 (r2 Bw2)2 U' B2 R2 U' R2 U R2 D'
|
(27,16)
|
PKF05
|
N
|
Per Kristen Fredlund
|
[]
|
|
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
|
U z' U2 F2 Lw2' U2 L F2 Lw2 L' F2 L' U2 Lw2 L' U2 z
|
(23,15)
|
CG05
|
Y
|
Clément Gallet
|
[82]
|
|
y U' R2 3Uw R2 U' R2 y' u2 r2 Uw2 r2 U2 Rw2 3Uw' R2 U R2
|
(27,16)
|
|
N
|
Stefan Pochmann
|
[83]
|
|
R2 U' R2 U R2 B2 U (Bw2 r2)2 B2 r2 D' R2 D
|
(27,16)
|
PKF05
|
N
|
Per Kristen Fredlund
|
[]
|
|
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
|
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
|
[84]
|
|
B2 L2 U2 L2 d2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2
|
(30,17)
|
|
N
|
Clément Gallet
|
[]
|
|
B2 d2 L2 U2 L2 D' R2 U2 F2 d2 D B2 U2 R2 U L2 R2 u2
|
(30,17)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
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
|
[85]
|
|
u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' d2 F2 U2 F2 R2
|
(30,17)
|
|
N
|
Clément Gallet
|
[]
|
|
u2 F2 B2 U B2 U2 R2 D d2 L2 U2 B2 D' F2 U2 F2 d2 R2
|
(30,17)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
[]
|
|
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
|
[86]
|
Two Corner Swap and a Dedge 2 2-cycle
C Permutation
Ca
|
y' Rw2 F2 U2 r2 U' B2 U' F2 U B2 U' Rw2 U y
|
(21,13)
|
|
N
|
Clément Gallet
|
[]
|
|
Lw2 U F2 U' B2 U F2 U l2 U2 B2 Lw2 U'
|
(21,13)
|
AO09
|
N
|
Alexander Ooms
|
[87]
|
|
U Lw2 B2 U2 l2 U' F2 U' B2 U F2 U' Lw2
|
(21,13)
|
Inv of AO09
|
N
|
Alexander Ooms
|
[88]
|
|
y' Rw r B' R F2 R' B R U2 r2 U2 F2 Rw2 U y
|
(20,14)
|
|
N
|
Frédérick Badie &Clément Gallet
|
[]
|
|
r2 F2 R2 D2 l2 D L2 D R2 D' L2 D F2 r2 U'
|
(25,15)
|
|
N
|
Clément Gallet
|
[]
|
|
U Dw2 Lw2 B2 U F2 U' B2 U F2 U l2 U2 Lw2 Dw2
|
(25,15)
|
|
N
|
Frédérick Badie
|
[89]
|
|
l r U2 x U' L U' R2 U L' U' Rw2 U2 x' U2 l' r' U'
|
(21,16)
|
|
N
|
Christopher Mowla
|
[]
|
Cb
|
y Rw2 B2 U2 r2 U F2 U B2 U' F2 U Rw2 U' y'
|
(21,13)
|
|
N
|
Clément Gallet
|
[]
|
|
Lw2 U' B2 U F2 U' B2 U' l2 U2 F2 Lw2 U
|
(21,13)
|
AO09
|
N
|
Alexander Ooms
|
[90]
|
|
U' Lw2 F2 U2 l2 U B2 U F2 U' B2 U Lw2
|
(21,13)
|
Inv of AO09
|
N
|
Alexander Ooms
|
[91]
|
|
y Rw2 R F R' B2 R F' R' U2 r2 U2 B2 Rw2 U' y'
|
(20,14)
|
|
N
|
Frédérick Badie &Clément Gallet
|
[92]
|
|
r2 B2 R2 D2 l2 D' L2 D' R2 D L2 D' B2 r2 U
|
(25,15)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
L2 Uw2 L2 U' L2 D' B2 R2 d2 U' R2 D B2 u2 U
|
(24,15)
|
|
N
|
Clément Gallet
|
[93]
|
|
L2 Uw2 L2 U L2 3Uw L2 F2 U z l2 F2 L' U2 Lw2 z' U y
|
(25,15)
|
CG08
|
N
|
Clément Gallet
|
[]
|
|
R2 D' F2 D R2 B2 D L2 D' Bw2 U2 b2 Uw2 b2 Uw2 U'
|
(26,16)
|
|
N
|
Kenneth Gustavsson
|
[94]
|
|
Lw2 U F2 L D' L D L' U L U' L' U l2 U2 F2 Lw2
|
(23,17)
|
AO08
|
N
|
Alexander Ooms
|
[95]
|
|
Rw2 U2 r2 Uw2 r2 u2 D' F2 U F2 R2 U R2 U' R2 D
|
(27,16)
|
|
N
|
Per Kristen Fredlund
|
[96]
|
Theta (θ) Permutation
|
R2 U B2 Uw2 R2 U' B2 Uw2 U B2 U2 R2 Uw2 U' R2 U'
|
(25,16)
|
|
Y
|
Clément Gallet
|
[]
|
|
z F2 Rw2 R' F2 R2 U2 Rw2 R U2 R' F2 Rw2 U2 R F2 z' U
|
(25,16)
|
CG12
|
Y
|
Clément Gallet
|
[97]
|
|
u2 D F2 U R2 U2 u2 F2 D' F2 U L2 D2 B2 U' u2 R2 y2
|
(29,17)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
[]
|
|
F U F' R2 F U' F' U' R2 U f2 R2 (f2 Rw2)2 U R2
|
(27,18)
|
PKF12
|
N
|
Per Kristen Fredlund
|
[98]
|
|
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
|
Uw d B2 D M2 U L2 B2 U B2 Uw2 R2 D F2 Uw2 3Lw2 y'
|
(26,16)
|
|
N
|
Clément Gallet
|
[]
|
|
R2 Uw2 U' M2 U R2 F2 Uw2 U' F2 U2 3Rw2 Uw2 U' F2 U2 R2 U
|
(28,18)
|
|
Y
|
Clément Gallet
|
[]
|
|
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
|
[]
|
|
U L2 U2 F2 D B2 u2 D' F2 L2 F2 D B2 D u2 R2 D2 F2 d2
|
(33,19)
|
|
N
|
Clément Gallet
|
[]
|
|
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
|
[]
|
|
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
|
[99]
|
|
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
|
[100]
|
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.
|
Rw U D L2 U D S2 Rw
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U D L2 U D S2 Rw'
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U' D' L2 U' D' S2 Rw
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U' D' L2 U' D' S2 Rw'
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U D R2 U D S2 Rw
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U D R2 U D S2 Rw'
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U' D' R2 U' D' S2 Rw
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U' D' R2 U' D' S2 Rw'
|
(10,8)
|
|
Y
|
Christopher Mowla
|
[101]
|
- 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:
|
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.
|
(l E2 r' E2)3
|
(18,12)
|
|
N
|
Christopher Mowla
|
[]
|
One Dedge Flip
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 WCA notation) by Christopher Mowla in 2012.
(Non-Symmetrical Algorithms)
Group 1
|
r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2
|
(25,15)
|
Alg.1(v1)
|
Y
|
Frédérick_Badie
|
[102]
|
|
l U2 r' F2 r F2 l2 U2 l' U2 l U2 F2 l2 F2
|
(25,15)
|
Mirror[Alg.1(v1)]
|
Y
|
Frédérick_Badie
|
[]
|
|
F2 r2 F2 U2 r U2 r' U2 r2 F2 l F2 l' U2 r
|
(25,15)
|
Inverse[Alg.1(v1)]
|
Y
|
Frédérick_Badie
|
[]
|
|
l' F2 r U2 r' U2 l2 F2 l F2 l' F2 U2 l2 U2
|
(25,15)
|
Rotation[Alg.1(v1)]
|
Y
|
Frédérick_Badie
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2
|
(25,15)
|
Alg.1(v2)
|
Y
|
Frédérick_Badie
|
[]
|
|
l U2 l' U2 r U2 r2 F2 l' F2 r U2 F2 l2 F2
|
(25,15)
|
Mirror[Alg.1(v2)]
|
Y
|
Frédérick_Badie
|
[]
|
|
F2 r2 F2 U2 l F2 r' F2 l2 U2 l U2 r' U2 r
|
(25,15)
|
Inverse[Alg.1(v2)]
|
Y
|
Frédérick_Badie
|
[]
|
|
l' F2 l F2 r' F2 r2 U2 l U2 r' F2 U2 l2 U2
|
(25,15)
|
Rotation[Alg.1(v2)]
|
Y
|
Frédérick_Badie
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2
|
(25,15)
|
Alg.1(v3)
|
Y
|
Frédérick_Badie
|
[]
|
|
l' B2 l U2 l' U2 l2 F2 l D2 r' D2 B2 l2 F2
|
(25,15)
|
Mirror[Alg.1(v3)]
|
Y
|
Frédérick_Badie
|
[]
|
|
F2 r2 B2 D2 l' D2 r F2 r2 U2 r' U2 r B2 r'
|
(25,15)
|
Inverse[Alg.1(v3)]
|
Y
|
Frédérick_Badie
|
[]
|
|
l D2 l' F2 l F2 l2 U2 l' B2 r B2 D2 l2 U2
|
(25,15)
|
Rotation[Alg.1(v3)]
|
Y
|
Frédérick_Badie
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2
|
(25,15)
|
Alg.1(v4)
|
Y
|
Frédérick_Badie
|
[]
|
|
l' B2 l U2 l' U2 r2 B2 l U2 r' U2 F2 r2 F2
|
(25,15)
|
Mirror[Alg.1(v4)]
|
Y
|
Frédérick_Badie
|
[]
|
|
F2 l2 F2 U2 l' U2 r B2 l2 U2 r' U2 r B2 r'
|
(25,15)
|
Inverse[Alg.1(v4)]
|
Y
|
Frédérick_Badie
|
[]
|
|
l D2 l' F2 l F2 r2 D2 l' F2 r F2 U2 r2 U2
|
(25,15)
|
Rotation[Alg.1(v4)]
|
Y
|
Frédérick_Badie
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2
|
(25,15)
|
Alg.1(v5)
|
Y
|
Frédérick_Badie
|
[]
|
|
l' B2 r B2 r' U2 l2 F2 r F2 l' U2 F2 r2 F2
|
(25,15)
|
Mirror[Alg.1(v5)]
|
Y
|
Frédérick_Badie
|
[]
|
|
F2 l2 F2 U2 r' F2 l F2 r2 U2 l' B2 l B2 r'
|
(25,15)
|
Inverse[Alg.1(v5)]
|
Y
|
Frédérick_Badie
|
[]
|
|
l D2 r' D2 r F2 l2 U2 r' U2 l F2 U2 r2 U2
|
(25,15)
|
Rotation[Alg.1(v5)]
|
Y
|
Frédérick_Badie
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
r2 U2 B2 r B2 r' B2 r2 U2 l U2 l' B2 r U2
|
(25,15)
|
Alg.2(v1)
|
Y
|
|
[]
|
|
l2 U2 B2 l' B2 l B2 l2 U2 r' U2 r B2 l' U2
|
(25,15)
|
Mirror[Alg.2(v1)]
|
Y
|
|
[]
|
|
U2 r' B2 l U2 l' U2 r2 B2 r B2 r' B2 U2 r2
|
(25,15)
|
Inverse[Alg.2(v1)]
|
Y
|
|
[]
|
|
l2 F2 D2 l D2 l' D2 l2 F2 r F2 r' D2 l F2
|
(25,15)
|
Rotation[Alg.2(v1)]
|
Y
|
|
[]
|
|
U2 l B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2
|
(25,15)
|
Mirror[Inverse[Alg.2(v1)]]
|
Y
|
|
[]
|
|
r2 F2 D2 r' D2 r D2 r2 F2 l' F2 l D2 r' F2
|
(25,15)
|
Mirror[Rotation[Alg.2(v1)]]
|
Y
|
|
[]
|
|
F2 l' D2 r F2 r' F2 l2 D2 l D2 l' D2 F2 l2
|
(25,15)
|
Inverse[Rotation[Alg.2(v1)]]
|
Y
|
|
[]
|
|
F2 r D2 l' F2 l F2 r2 D2 r' D2 r D2 F2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.2(v1)]]]
|
Y
|
|
[]
|
|
r2 U2 B2 l U2 r' U2 l2 B2 l B2 r' B2 r U2
|
(25,15)
|
Alg.2(v2)
|
Y
|
|
[]
|
|
l2 U2 B2 r' U2 l U2 r2 B2 r' B2 l B2 l' U2
|
(25,15)
|
Mirror[Alg.2(v2)]
|
Y
|
|
[]
|
|
U2 r' B2 r B2 l' B2 l2 U2 r U2 l' B2 U2 r2
|
(25,15)
|
Inverse[Alg.2(v2)]
|
Y
|
|
[]
|
|
l2 F2 D2 r F2 l' F2 r2 D2 r D2 l' D2 l F2
|
(25,15)
|
Rotation[Alg.2(v2)]
|
Y
|
|
[]
|
|
U2 l B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2
|
(25,15)
|
Mirror[Inverse[Alg.2(v2)]]
|
Y
|
|
[]
|
|
r2 F2 D2 l' F2 r F2 l2 D2 l' D2 r D2 r' F2
|
(25,15)
|
Mirror[Rotation[Alg.2(v2)]]
|
Y
|
|
[]
|
|
F2 l' D2 l D2 r' D2 r2 F2 l F2 r' D2 F2 l2
|
(25,15)
|
Inverse[Rotation[Alg.2(v2)]]
|
Y
|
|
[]
|
|
F2 r D2 r' D2 l D2 l2 F2 r' F2 l D2 F2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.2(v2)]]]
|
Y
|
|
[]
|
|
r2 D2 F2 l' F2 r U2 r2 B2 r' B2 r D2 r' U2
|
(25,15)
|
Alg.2(v3)
|
Y
|
|
[]
|
|
l2 D2 F2 r F2 l' U2 l2 B2 l B2 l' D2 l U2
|
(25,15)
|
Mirror[Alg.2(v3)]
|
Y
|
|
[]
|
|
U2 r D2 r' B2 r B2 r2 U2 r' F2 l F2 D2 r2
|
(25,15)
|
Inverse[Alg.2(v3)]
|
Y
|
|
[]
|
|
l2 B2 U2 r' U2 l F2 l2 D2 l' D2 l B2 l' F2
|
(25,15)
|
Rotation[Alg.2(v3)]
|
Y
|
|
[]
|
|
U2 l' D2 l B2 l' B2 l2 U2 l F2 r' F2 D2 l2
|
(25,15)
|
Mirror[Inverse[Alg.2(v3)]]
|
Y
|
|
[]
|
|
r2 B2 U2 l U2 r' F2 r2 D2 r D2 r' B2 r F2
|
(25,15)
|
Mirror[Rotation[Alg.2(v3)]]
|
Y
|
|
[]
|
|
F2 l B2 l' D2 l D2 l2 F2 l' U2 r U2 B2 l2
|
(25,15)
|
Inverse[Rotation[Alg.2(v3)]]
|
Y
|
|
[]
|
|
F2 r' B2 r D2 r' D2 r2 F2 r U2 l' U2 B2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.2(v3)]]]
|
Y
|
|
[]
|
|
r2 U2 B2 r B2 l' D2 r2 B2 l B2 l' D2 l U2
|
(25,15)
|
Alg.2(v4)
|
Y
|
|
[]
|
|
l2 U2 B2 l' B2 r D2 l2 B2 r' B2 r D2 r' U2
|
(25,15)
|
Mirror[Alg.2(v4)]
|
Y
|
|
[]
|
|
U2 l' D2 l B2 l' B2 r2 D2 l B2 r' B2 U2 r2
|
(25,15)
|
Inverse[Alg.2(v4)]
|
Y
|
|
[]
|
|
l2 F2 D2 l D2 r' B2 l2 D2 r D2 r' B2 r F2
|
(25,15)
|
Rotation[Alg.2(v4)]
|
Y
|
|
[]
|
|
U2 r D2 r' B2 r B2 l2 D2 r' B2 l B2 U2 l2
|
(25,15)
|
Mirror[Inverse[Alg.2(v4)]]
|
Y
|
|
[]
|
|
r2 F2 D2 r' D2 l B2 r2 D2 l' D2 l B2 l' F2
|
(25,15)
|
Mirror[Rotation[Alg.2(v4)]]
|
Y
|
|
[]
|
|
F2 r' B2 r D2 r' D2 l2 B2 r D2 l' D2 F2 l2
|
(25,15)
|
Inverse[Rotation[Alg.2(v4)]]
|
Y
|
|
[]
|
|
F2 l B2 l' D2 l D2 r2 B2 l' D2 r D2 F2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.2(v4)]]]
|
Y
|
|
[]
|
|
r2 U2 B2 l U2 r' U2 l2 B2 r D2 r' D2 l U2
|
(25,15)
|
Alg.2(v5)
|
Y
|
|
[]
|
|
l2 U2 B2 r' U2 l U2 r2 B2 l' D2 l D2 r' U2
|
(25,15)
|
Mirror[Alg.2(v5)]
|
Y
|
|
[]
|
|
U2 l' D2 r D2 r' B2 l2 U2 r U2 l' B2 U2 r2
|
(25,15)
|
Inverse[Alg.2(v5)]
|
Y
|
|
[]
|
|
l2 F2 D2 r F2 l' F2 r2 D2 l B2 l' B2 r F2
|
(25,15)
|
Rotation[Alg.2(v5)]
|
Y
|
|
[]
|
|
U2 r D2 l' D2 l B2 r2 U2 l' U2 r B2 U2 l2
|
(25,15)
|
Mirror[Inverse[Alg.2(v5)]]
|
Y
|
|
[]
|
|
r2 F2 D2 l' F2 r F2 l2 D2 r' B2 r B2 l' F2
|
(25,15)
|
Mirror[Rotation[Alg.2(v5)]]
|
Y
|
|
[]
|
|
F2 r' B2 l B2 l' D2 r2 F2 l F2 r' D2 F2 l2
|
(25,15)
|
Inverse[Rotation[Alg.2(v5)]]
|
Y
|
|
[]
|
|
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
|
r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2
|
(25,15)
|
Alg.3(v1)
|
Y
|
|
[]
|
|
l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2
|
(25,15)
|
Mirror[Alg.3(v1)]
|
Y
|
|
[]
|
|
B2 l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r'
|
(25,15)
|
Inverse[Alg.3(v1)]
|
Y
|
|
[]
|
|
l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2 D2
|
(25,15)
|
Rotation[Alg.3(v1)]
|
Y
|
|
[]
|
|
B2 r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l
|
(25,15)
|
Mirror[Inverse[Alg.3(v1)]]
|
Y
|
|
[]
|
|
r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2 D2
|
(25,15)
|
Mirror[Rotation[Alg.3(v1)]]
|
Y
|
|
[]
|
|
D2 r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l'
|
(25,15)
|
Inverse[Rotation[Alg.3(v1)]]
|
Y
|
|
[]
|
|
D2 l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.3(v1)]]]
|
Y
|
|
[]
|
|
r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2
|
(25,15)
|
Alg.3(v2)
|
Y
|
|
[]
|
|
l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2 B2
|
(25,15)
|
Mirror[Alg.3(v2)]
|
Y
|
|
[]
|
|
B2 r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r'
|
(25,15)
|
Inverse[Alg.3(v2)]
|
Y
|
|
[]
|
|
l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2 D2
|
(25,15)
|
Rotation[Alg.3(v2)]
|
Y
|
|
[]
|
|
B2 l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l
|
(25,15)
|
Mirror[Inverse[Alg.3(v2)]]
|
Y
|
|
[]
|
|
r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2 D2
|
(25,15)
|
Mirror[Rotation[Alg.3(v2)]]
|
Y
|
|
[]
|
|
D2 l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l'
|
(25,15)
|
Inverse[Rotation[Alg.3(v2)]]
|
Y
|
|
[]
|
|
D2 r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.3(v2)]]]
|
Y
|
|
[]
|
|
r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2
|
(25,15)
|
Alg.3(v3)
|
Y
|
|
[]
|
|
l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2 B2
|
(25,15)
|
Mirror[Alg.3(v3)]
|
Y
|
|
[]
|
|
B2 l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r'
|
(25,15)
|
Inverse[Alg.3(v3)]
|
Y
|
|
[]
|
|
l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2 D2
|
(25,15)
|
Rotation[Alg.3(v3)]
|
Y
|
|
[]
|
|
B2 r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l
|
(25,15)
|
Mirror[Inverse[Alg.3(v3)]]
|
Y
|
|
[]
|
|
r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2 D2
|
(25,15)
|
Mirror[Rotation[Alg.3(v3)]]
|
Y
|
|
[]
|
|
D2 r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l'
|
(25,15)
|
Inverse[Rotation[Alg.3(v3)]]
|
Y
|
|
[]
|
|
D2 l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.3(v3)]]]
|
Y
|
|
[]
|
|
r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2
|
(25,15)
|
Alg.3(v4)
|
Y
|
|
[]
|
|
l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2 B2
|
(25,15)
|
Mirror[Alg.3(v4)]
|
Y
|
|
[]
|
|
B2 r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r'
|
(25,15)
|
Inverse[Alg.3(v4)]
|
Y
|
|
[]
|
|
l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2 D2
|
(25,15)
|
Rotation[Alg.3(v4)]
|
Y
|
|
[]
|
|
B2 l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l
|
(25,15)
|
Mirror[Inverse[Alg.3(v4)]]
|
Y
|
|
[]
|
|
r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2 D2
|
(25,15)
|
Mirror[Rotation[Alg.3(v4)]]
|
Y
|
|
[]
|
|
D2 l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l'
|
(25,15)
|
Inverse[Rotation[Alg.3(v4)]]
|
Y
|
|
[]
|
|
D2 r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.3(v4)]]]
|
Y
|
|
[]
|
|
r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2
|
(25,15)
|
Alg.3(v5)
|
Y
|
|
[]
|
|
l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2 B2
|
(25,15)
|
Mirror[Alg.3(v5)]
|
Y
|
|
[]
|
|
B2 l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r
|
(25,15)
|
Inverse[Alg.3(v5)]
|
Y
|
|
[]
|
|
l' F2 l F2 r' B2 l2 B2 D2 r' B2 l B2 r2 D2
|
(25,15)
|
Rotation[Alg.3(v5)]
|
Y
|
|
[]
|
|
B2 r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l'
|
(25,15)
|
Mirror[Inverse[Alg.3(v5)]]
|
Y
|
|
[]
|
|
r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2 D2
|
(25,15)
|
Mirror[Rotation[Alg.3(v5)]]
|
Y
|
|
[]
|
|
D2 r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l
|
(25,15)
|
Inverse[Rotation[Alg.3(v5)]]
|
Y
|
|
[]
|
|
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
|
r2 U2 r' U2 r U2 B2 r2 B2 r U2 l' B2 l B2
|
(25,15)
|
Alg.4(v1)
|
Y
|
|
[]
|
|
l2 U2 l U2 l' U2 B2 l2 B2 l' U2 r B2 r' B2
|
(25,15)
|
Mirror[Alg.4(v1)]
|
Y
|
|
[]
|
|
B2 l' B2 l U2 r' B2 r2 B2 U2 r' U2 r U2 r2
|
(25,15)
|
Inverse[Alg.4(v1)]
|
Y
|
|
[]
|
|
l2 F2 l' F2 l F2 D2 l2 D2 l F2 r' D2 r D2
|
(25,15)
|
Rotation[Alg.4(v1)]
|
Y
|
|
[]
|
|
B2 r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2
|
(25,15)
|
Mirror[Inverse[Alg.4(v1)]]
|
Y
|
|
[]
|
|
r2 F2 r F2 r' F2 D2 r2 D2 r' F2 l D2 l' D2
|
(25,15)
|
Mirror[Rotation[Alg.4(v1)]]
|
Y
|
|
[]
|
|
D2 r' D2 r F2 l' D2 l2 D2 F2 l' F2 l F2 l2
|
(25,15)
|
Inverse[Rotation[Alg.4(v1)]]
|
Y
|
|
[]
|
|
D2 l D2 l' F2 r D2 r2 D2 F2 r F2 r' F2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.4(v1)]]]
|
Y
|
|
[]
|
|
r2 D2 r F2 l' F2 U2 r2 D2 r' U2 r B2 r' B2
|
(25,15)
|
Alg.4(v2)
|
Y
|
|
[]
|
|
l2 D2 l' F2 r F2 U2 l2 D2 l U2 l' B2 l B2
|
(25,15)
|
Mirror[Alg.4(v2)]
|
Y
|
|
[]
|
|
B2 r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2
|
(25,15)
|
Inverse[Alg.4(v2)]
|
Y
|
|
[]
|
|
l2 B2 l U2 r' U2 F2 l2 B2 l' F2 l D2 l' D2
|
(25,15)
|
Rotation[Alg.4(v2)]
|
Y
|
|
[]
|
|
B2 l' B2 l U2 l' D2 l2 U2 F2 r' F2 l D2 l2
|
(25,15)
|
Mirror[Inverse[Alg.4(v2)]]
|
Y
|
|
[]
|
|
r2 B2 r' U2 l U2 F2 r2 B2 r F2 r' D2 r D2
|
(25,15)
|
Mirror[Rotation[Alg.4(v2)]]
|
Y
|
|
[]
|
|
D2 l D2 l' F2 l B2 l2 F2 U2 r U2 l' B2 l2
|
(25,15)
|
Inverse[Rotation[Alg.4(v2)]]
|
Y
|
|
[]
|
|
D2 r' D2 r F2 r' B2 r2 F2 U2 l' U2 r B2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.4(v2)]]]
|
Y
|
|
[]
|
|
r2 U2 l' B2 r B2 D2 r2 D2 l U2 l' B2 l B2
|
(25,15)
|
Alg.4(v3)
|
Y
|
|
[]
|
|
l2 U2 r B2 l' B2 D2 l2 D2 r' U2 r B2 r' B2
|
(25,15)
|
Mirror[Alg.4(v3)]
|
Y
|
|
[]
|
|
B2 l' B2 l U2 l' D2 r2 D2 B2 r' B2 l U2 r2
|
(25,15)
|
Inverse[Alg.4(v3)]
|
Y
|
|
[]
|
|
l2 F2 r' D2 l D2 B2 l2 B2 r F2 r' D2 r D2
|
(25,15)
|
Rotation[Alg.4(v3)]
|
Y
|
|
[]
|
|
B2 r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2
|
(25,15)
|
Mirror[Inverse[Alg.4(v3)]]
|
Y
|
|
[]
|
|
r2 F2 l D2 r' D2 B2 r2 B2 l' F2 l D2 l' D2
|
(25,15)
|
Mirror[Rotation[Alg.4(v3)]]
|
Y
|
|
[]
|
|
D2 r' D2 r F2 r' B2 l2 B2 D2 l' D2 r F2 l2
|
(25,15)
|
Inverse[Rotation[Alg.4(v3)]]
|
Y
|
|
[]
|
|
D2 l D2 l' F2 l B2 r2 B2 D2 r D2 l' F2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.4(v3)]]]
|
Y
|
|
[]
|
|
r2 D2 l D2 r' B2 D2 l2 D2 l' B2 l B2 r' B2
|
(25,15)
|
Alg.4(v4)
|
Y
|
|
[]
|
|
l2 D2 r' D2 l B2 D2 r2 D2 r B2 r' B2 l B2
|
(25,15)
|
Mirror[Alg.4(v4)]
|
Y
|
|
[]
|
|
B2 r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2
|
(25,15)
|
Inverse[Alg.4(v4)]
|
Y
|
|
[]
|
|
l2 B2 r B2 l' D2 B2 r2 B2 r' D2 r D2 l' D2
|
(25,15)
|
Rotation[Alg.4(v4)]
|
Y
|
|
[]
|
|
B2 l' B2 r B2 r' D2 r2 D2 B2 l' D2 r D2 l2
|
(25,15)
|
Mirror[Inverse[Alg.4(v4)]]
|
Y
|
|
[]
|
|
r2 B2 l' B2 r D2 B2 l2 B2 l D2 l' D2 r D2
|
(25,15)
|
Mirror[Rotation[Alg.4(v4)]]
|
Y
|
|
[]
|
|
D2 l D2 r' D2 r B2 r2 B2 D2 l B2 r' B2 l2
|
(25,15)
|
Inverse[Rotation[Alg.4(v4)]]
|
Y
|
|
[]
|
|
D2 r' D2 l D2 l' B2 l2 B2 D2 r' B2 l B2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.4(v4)]]]
|
Y
|
|
[]
|
|
r2 D2 l D2 r' B2 D2 l2 D2 r' U2 l U2 l' B2
|
(25,15)
|
Alg.4(v5)
|
Y
|
|
[]
|
|
l2 D2 r' D2 l B2 D2 r2 D2 l U2 r' U2 r B2
|
(25,15)
|
Mirror[Alg.4(v5)]
|
Y
|
|
[]
|
|
B2 l U2 l' U2 r D2 l2 D2 B2 r D2 l' D2 r2
|
(25,15)
|
Inverse[Alg.4(v5)]
|
Y
|
|
[]
|
|
l2 B2 r B2 l' D2 B2 r2 B2 l' F2 r F2 r' D2
|
(25,15)
|
Rotation[Alg.4(v5)]
|
Y
|
|
[]
|
|
B2 r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2
|
(25,15)
|
Mirror[Inverse[Alg.4(v5)]]
|
Y
|
|
[]
|
|
r2 B2 l' B2 r D2 B2 l2 B2 r F2 l' F2 l D2
|
(25,15)
|
Mirror[Rotation[Alg.4(v5)]]
|
Y
|
|
[]
|
|
D2 r F2 r' F2 l B2 r2 B2 D2 l B2 r' B2 l2
|
(25,15)
|
Inverse[Rotation[Alg.4(v5)]]
|
Y
|
|
[]
|
|
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.
|
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
|
(25,15)
|
Alg.5(v1)
|
Y
|
|
[103]
|
|
l2 B2 U2 r' U2 l U2 l' U2 F2 l' F2 r B2 l2
|
(25,15)
|
Mirror[Alg.5(v1)]
|
Y
|
|
[]
|
|
r2 B2 l F2 r' F2 U2 r' U2 r U2 l' U2 B2 r2
|
(25,15)
|
Inverse[Alg.5(v1)]
|
Y
|
|
[]
|
|
l2 D2 F2 r F2 l' F2 l F2 U2 l U2 r' D2 l2
|
(25,15)
|
Rotation[Alg.5(v1)]
|
Y
|
|
[]
|
|
l2 B2 r' F2 l F2 U2 l U2 l' U2 r U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v1)]]
|
Y
|
|
[]
|
|
r2 D2 F2 l' F2 r F2 r' F2 U2 r' U2 l D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v1)]]
|
Y
|
|
[]
|
|
l2 D2 r U2 l' U2 F2 l' F2 l F2 r' F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v1)]]
|
Y
|
|
[]
|
|
r2 D2 l' U2 r U2 F2 r F2 r' F2 l F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v1)]]]
|
Y
|
|
[]
|
|
r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2
|
(25,15)
|
Alg.5(v2)
|
Y
|
|
[]
|
|
l2 B2 U2 r' U2 r B2 l' B2 U2 l' U2 l B2 l2
|
(25,15)
|
Mirror[Alg.5(v2)]
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2
|
(25,15)
|
Inverse[Alg.5(v2)]
|
Y
|
|
[]
|
|
l2 D2 F2 r F2 r' D2 l D2 F2 l F2 l' D2 l2
|
(25,15)
|
Rotation[Alg.5(v2)]
|
Y
|
|
[]
|
|
l2 B2 l' U2 l U2 B2 l B2 r' U2 r U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v2)]]
|
Y
|
|
[]
|
|
r2 D2 F2 l' F2 l D2 r' D2 F2 r' F2 r D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v2)]]
|
Y
|
|
[]
|
|
l2 D2 l F2 l' F2 D2 l' D2 r F2 r' F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v2)]]
|
Y
|
|
[]
|
|
r2 D2 r' F2 r F2 D2 r D2 l' F2 l F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v2)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2
|
(25,15)
|
Alg.5(v3)
|
Y
|
|
[]
|
|
l2 F2 D2 l D2 l' F2 r F2 D2 r D2 r' F2 l2
|
(25,15)
|
Mirror[Alg.5(v3)]
|
Y
|
|
[]
|
|
r2 F2 l' D2 l D2 F2 l F2 r' D2 r D2 F2 r2
|
(25,15)
|
Inverse[Alg.5(v3)]
|
Y
|
|
[]
|
|
l2 U2 B2 l' B2 l U2 r' U2 B2 r' B2 r U2 l2
|
(25,15)
|
Rotation[Alg.5(v3)]
|
Y
|
|
[]
|
|
l2 F2 r D2 r' D2 F2 r' F2 l D2 l' D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v3)]]
|
Y
|
|
[]
|
|
r2 U2 B2 r B2 r' U2 l U2 B2 l B2 l' U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v3)]]
|
Y
|
|
[]
|
|
l2 U2 r' B2 r B2 U2 r U2 l' B2 l B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v3)]]
|
Y
|
|
[]
|
|
r2 U2 l B2 l' B2 U2 l' U2 r B2 r' B2 U2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v3)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2
|
(25,15)
|
Alg.5(v4)
|
Y
|
|
[]
|
|
l2 F2 D2 l D2 r' D2 r D2 B2 r B2 l' F2 l2
|
(25,15)
|
Mirror[Alg.5(v4)]
|
Y
|
|
[]
|
|
r2 F2 r' B2 l B2 D2 l D2 l' D2 r D2 F2 r2
|
(25,15)
|
Inverse[Alg.5(v4)]
|
Y
|
|
[]
|
|
l2 U2 B2 l' B2 r B2 r' B2 D2 r' D2 l U2 l2
|
(25,15)
|
Rotation[Alg.5(v4)]
|
Y
|
|
[]
|
|
l2 F2 l B2 r' B2 D2 r' D2 r D2 l' D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v4)]]
|
Y
|
|
[]
|
|
r2 U2 B2 r B2 l' B2 l B2 D2 l D2 r' U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v4)]]
|
Y
|
|
[]
|
|
l2 U2 l' D2 r D2 B2 r B2 r' B2 l B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v4)]]
|
Y
|
|
[]
|
|
r2 U2 r D2 l' D2 B2 l' B2 l B2 r' B2 U2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v4)]]]
|
Y
|
|
[]
|
|
r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2
|
(25,15)
|
Alg.5(v5)
|
Y
|
|
[]
|
|
l2 B2 U2 l' B2 l B2 r' U2 F2 l' F2 r B2 l2
|
(25,15)
|
Mirror[Alg.5(v5)]
|
Y
|
|
[]
|
|
r2 B2 l F2 r' F2 U2 l' B2 r B2 r' U2 B2 r2
|
(25,15)
|
Inverse[Alg.5(v5)]
|
Y
|
|
[]
|
|
l2 D2 F2 l D2 l' D2 r F2 U2 l U2 r' D2 l2
|
(25,15)
|
Rotation[Alg.5(v5)]
|
Y
|
|
[]
|
|
l2 B2 r' F2 l F2 U2 r B2 l' B2 l U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v5)]]
|
Y
|
|
[]
|
|
r2 D2 F2 r' D2 r D2 l' F2 U2 r' U2 l D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v5)]]
|
Y
|
|
[]
|
|
l2 D2 r U2 l' U2 F2 r' D2 l D2 l' F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v5)]]
|
Y
|
|
[]
|
|
r2 D2 l' U2 r U2 F2 l D2 r' D2 r F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v5)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2
|
(25,15)
|
Alg.5(v6)
|
Y
|
|
[]
|
|
l2 F2 D2 r F2 r' F2 l D2 B2 r B2 l' F2 l2
|
(25,15)
|
Mirror[Alg.5(v6)]
|
Y
|
|
[]
|
|
r2 F2 r' B2 l B2 D2 r F2 l' F2 l D2 F2 r2
|
(25,15)
|
Inverse[Alg.5(v6)]
|
Y
|
|
[]
|
|
l2 U2 B2 r' U2 r U2 l' B2 D2 r' D2 l U2 l2
|
(25,15)
|
Rotation[Alg.5(v6)]
|
Y
|
|
[]
|
|
l2 F2 l B2 r' B2 D2 l' F2 r F2 r' D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v6)]]
|
Y
|
|
[]
|
|
r2 U2 B2 l U2 l' U2 r B2 D2 l D2 r' U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v6)]]
|
Y
|
|
[]
|
|
l2 U2 l' D2 r D2 B2 l U2 r' U2 r B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v6)]]
|
Y
|
|
[]
|
|
r2 U2 r D2 l' D2 B2 r' U2 l U2 l' B2 U2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v6)]]]
|
Y
|
|
[]
|
|
r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2
|
(25,15)
|
Alg.5(v7)
|
Y
|
|
[]
|
|
l2 B2 U2 l' B2 r D2 l' D2 B2 r' U2 l B2 l2
|
(25,15)
|
Mirror[Alg.5(v7)]
|
Y
|
|
[]
|
|
r2 B2 r U2 l' B2 D2 r' D2 l B2 r' U2 B2 r2
|
(25,15)
|
Inverse[Alg.5(v7)]
|
Y
|
|
[]
|
|
l2 D2 F2 l D2 r' B2 l B2 D2 r F2 l' D2 l2
|
(25,15)
|
Rotation[Alg.5(v7)]
|
Y
|
|
[]
|
|
l2 B2 l' U2 r B2 D2 l D2 r' B2 l U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v7)]]
|
Y
|
|
[]
|
|
r2 D2 F2 r' D2 l B2 r' B2 D2 l' F2 r D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v7)]]
|
Y
|
|
[]
|
|
l2 D2 l F2 r' D2 B2 l' B2 r D2 l' F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v7)]]
|
Y
|
|
[]
|
|
r2 D2 r' F2 l D2 B2 r B2 l' D2 r F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.5(v7)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2
|
(25,15)
|
Alg.5(v8)
|
Y
|
|
[]
|
|
l2 F2 D2 r F2 l' U2 r U2 F2 l D2 r' F2 l2
|
(25,15)
|
Mirror[Alg.5(v8)]
|
Y
|
|
[]
|
|
r2 F2 l' D2 r F2 U2 l U2 r' F2 l D2 F2 r2
|
(25,15)
|
Inverse[Alg.5(v8)]
|
Y
|
|
[]
|
|
l2 U2 B2 r' U2 l F2 r' F2 U2 l' B2 r U2 l2
|
(25,15)
|
Rotation[Alg.5(v8)]
|
Y
|
|
[]
|
|
l2 F2 r D2 l' F2 U2 r' U2 l F2 r' D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.5(v8)]]
|
Y
|
|
[]
|
|
r2 U2 B2 l U2 r' F2 l F2 U2 r B2 l' U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.5(v8)]]
|
Y
|
|
[]
|
|
l2 U2 r' B2 l U2 F2 r F2 l' U2 r B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.5(v8)]]
|
Y
|
|
[]
|
|
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.
|
r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2
|
(25,15)
|
Alg.6(v1)
|
Y
|
|
[]
|
|
l2 B2 U2 r U2 l' U2 l U2 B2 l B2 r' B2 l2
|
(25,15)
|
Mirror[Alg.6(v1)]
|
Y
|
|
[]
|
|
r2 B2 l' B2 r B2 U2 r U2 r' U2 l U2 B2 r2
|
(25,15)
|
Inverse[Alg.6(v1)]
|
Y
|
|
[]
|
|
l2 D2 F2 r' F2 l F2 l' F2 D2 l' D2 r D2 l2
|
(25,15)
|
Rotation[Alg.6(v1)]
|
Y
|
|
[]
|
|
l2 B2 r B2 l' B2 U2 l' U2 l U2 r' U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v1)]]
|
Y
|
|
[]
|
|
r2 D2 F2 l F2 r' F2 r F2 D2 r D2 l' D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v1)]]
|
Y
|
|
[]
|
|
l2 D2 r' D2 l D2 F2 l F2 l' F2 r F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v1)]]
|
Y
|
|
[]
|
|
r2 D2 l D2 r' D2 F2 r' F2 r F2 l' F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v1)]]]
|
Y
|
|
[]
|
|
r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2
|
(25,15)
|
Alg.6(v2)
|
Y
|
|
[]
|
|
l2 B2 U2 r U2 r' F2 l F2 U2 l U2 l' B2 l2
|
(25,15)
|
Mirror[Alg.6(v2)]
|
Y
|
|
[]
|
|
r2 B2 r' U2 r U2 F2 r F2 l' U2 l U2 B2 r2
|
(25,15)
|
Inverse[Alg.6(v2)]
|
Y
|
|
[]
|
|
l2 D2 F2 r' F2 r U2 l' U2 F2 l' F2 l D2 l2
|
(25,15)
|
Rotation[Alg.6(v2)]
|
Y
|
|
[]
|
|
l2 B2 l U2 l' U2 F2 l' F2 r U2 r' U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v2)]]
|
Y
|
|
[]
|
|
r2 D2 F2 l F2 l' U2 r U2 F2 r F2 r' D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v2)]]
|
Y
|
|
[]
|
|
l2 D2 l' F2 l F2 U2 l U2 r' F2 r F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v2)]]
|
Y
|
|
[]
|
|
r2 D2 r F2 r' F2 U2 r' U2 l F2 l' F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v2)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2
|
(25,15)
|
Alg.6(v3)
|
Y
|
|
[]
|
|
l2 F2 D2 l' D2 l B2 r' B2 D2 r' D2 r F2 l2
|
(25,15)
|
Mirror[Alg.6(v3)]
|
Y
|
|
[]
|
|
r2 F2 l D2 l' D2 B2 l' B2 r D2 r' D2 F2 r2
|
(25,15)
|
Inverse[Alg.6(v3)]
|
Y
|
|
[]
|
|
l2 U2 B2 l B2 l' D2 r D2 B2 r B2 r' U2 l2
|
(25,15)
|
Rotation[Alg.6(v3)]
|
Y
|
|
[]
|
|
l2 F2 r' D2 r D2 B2 r B2 l' D2 l D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v3)]]
|
Y
|
|
[]
|
|
r2 U2 B2 r' B2 r D2 l' D2 B2 l' B2 l U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v3)]]
|
Y
|
|
[]
|
|
l2 U2 r B2 r' B2 D2 r' D2 l B2 l' B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v3)]]
|
Y
|
|
[]
|
|
r2 U2 l' B2 l B2 D2 l D2 r' B2 r B2 U2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v3)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2
|
(25,15)
|
Alg.6(v4)
|
Y
|
|
[]
|
|
l2 F2 D2 l' D2 r D2 r' D2 F2 r' F2 l F2 l2
|
(25,15)
|
Mirror[Alg.6(v4)]
|
Y
|
|
[]
|
|
r2 F2 r F2 l' F2 D2 l' D2 l D2 r' D2 F2 r2
|
(25,15)
|
Inverse[Alg.6(v4)]
|
Y
|
|
[]
|
|
l2 U2 B2 l B2 r' B2 r B2 U2 r U2 l' U2 l2
|
(25,15)
|
Rotation[Alg.6(v4)]
|
Y
|
|
[]
|
|
l2 F2 l' F2 r F2 D2 r D2 r' D2 l D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v4)]]
|
Y
|
|
[]
|
|
r2 U2 B2 r' B2 l B2 l' B2 U2 l' U2 r U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v4)]]
|
Y
|
|
[]
|
|
l2 U2 l U2 r' U2 B2 r' B2 r B2 l' B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v4)]]
|
Y
|
|
[]
|
|
r2 U2 r' U2 l U2 B2 l B2 l' B2 r B2 U2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v4)]]]
|
Y
|
|
[]
|
|
r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2
|
(25,15)
|
Alg.6(v5)
|
Y
|
|
[]
|
|
l2 B2 U2 l F2 l' F2 r U2 B2 l B2 r' B2 l2
|
(25,15)
|
Mirror[Alg.6(v5)]
|
Y
|
|
[]
|
|
r2 B2 l' B2 r B2 U2 l F2 r' F2 r U2 B2 r2
|
(25,15)
|
Inverse[Alg.6(v5)]
|
Y
|
|
[]
|
|
l2 D2 F2 l' U2 l U2 r' F2 D2 l' D2 r D2 l2
|
(25,15)
|
Rotation[Alg.6(v5)]
|
Y
|
|
[]
|
|
l2 B2 r B2 l' B2 U2 r' F2 l F2 l' U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v5)]]
|
Y
|
|
[]
|
|
r2 D2 F2 r U2 r' U2 l F2 D2 r D2 l' D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v5)]]
|
Y
|
|
[]
|
|
l2 D2 r' D2 l D2 F2 r U2 l' U2 l F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v5)]]
|
Y
|
|
[]
|
|
r2 D2 l D2 r' D2 F2 l' U2 r U2 r' F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v5)]]]
|
Y
|
|
[]
|
|
r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2
|
(25,15)
|
Alg.6(v6)
|
Y
|
|
[]
|
|
l2 B2 U2 l F2 r' D2 l D2 F2 r U2 l' B2 l2
|
(25,15)
|
Mirror[Alg.6(v6)]
|
Y
|
|
[]
|
|
r2 B2 r' U2 l F2 D2 r D2 l' F2 r U2 B2 r2
|
(25,15)
|
Inverse[Alg.6(v6)]
|
Y
|
|
[]
|
|
l2 D2 F2 l' U2 r B2 l' B2 U2 r' F2 l D2 l2
|
(25,15)
|
Rotation[Alg.6(v6)]
|
Y
|
|
[]
|
|
l2 B2 l U2 r' F2 D2 l' D2 r F2 l' U2 B2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v6)]]
|
Y
|
|
[]
|
|
r2 D2 F2 r U2 l' B2 r B2 U2 l F2 r' D2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v6)]]
|
Y
|
|
[]
|
|
l2 D2 l' F2 r U2 B2 l B2 r' U2 l F2 D2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v6)]]
|
Y
|
|
[]
|
|
r2 D2 r F2 l' U2 B2 r' B2 l U2 r' F2 D2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v6)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2
|
(25,15)
|
Alg.6(v7)
|
Y
|
|
[]
|
|
l2 F2 D2 r' B2 l U2 r' U2 B2 l' D2 r F2 l2
|
(25,15)
|
Mirror[Alg.6(v7)]
|
Y
|
|
[]
|
|
r2 F2 l D2 r' B2 U2 l' U2 r B2 l' D2 F2 r2
|
(25,15)
|
Inverse[Alg.6(v7)]
|
Y
|
|
[]
|
|
l2 U2 B2 r D2 l' F2 r F2 D2 l B2 r' U2 l2
|
(25,15)
|
Rotation[Alg.6(v7)]
|
Y
|
|
[]
|
|
l2 F2 r' D2 l B2 U2 r U2 l' B2 r D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v7)]]
|
Y
|
|
[]
|
|
r2 U2 B2 l' D2 r F2 l' F2 D2 r' B2 l U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v7)]]
|
Y
|
|
[]
|
|
l2 U2 r B2 l' D2 F2 r' F2 l D2 r' B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v7)]]
|
Y
|
|
[]
|
|
r2 U2 l' B2 r D2 F2 l F2 r' D2 l B2 U2 r2
|
(25,15)
|
Mirror[Inverse[Rotation[Alg.6(v7)]]]
|
Y
|
|
[]
|
|
r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2
|
(25,15)
|
Alg.6(v8)
|
Y
|
|
[]
|
|
l2 F2 D2 r' B2 r B2 l' D2 F2 r' F2 l F2 l2
|
(25,15)
|
Mirror[Alg.6(v8)]
|
Y
|
|
[]
|
|
r2 F2 r F2 l' F2 D2 r' B2 l B2 l' D2 F2 r2
|
(25,15)
|
Inverse[Alg.6(v8)]
|
Y
|
|
[]
|
|
l2 U2 B2 r D2 r' D2 l B2 U2 r U2 l' U2 l2
|
(25,15)
|
Rotation[Alg.6(v8)]
|
Y
|
|
[]
|
|
l2 F2 l' F2 r F2 D2 l B2 r' B2 r D2 F2 l2
|
(25,15)
|
Mirror[Inverse[Alg.6(v8)]]
|
Y
|
|
[]
|
|
r2 U2 B2 l' D2 l D2 r' B2 U2 l' U2 r U2 r2
|
(25,15)
|
Mirror[Rotation[Alg.6(v8)]]
|
Y
|
|
[]
|
|
l2 U2 l U2 r' U2 B2 l' D2 r D2 r' B2 U2 l2
|
(25,15)
|
Inverse[Rotation[Alg.6(v8)]]
|
Y
|
|
[]
|
|
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
- Although not proven, the current upperbound in the single slice quarter turn metric is 23. This section contains over 100 of such algorithms.
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. As of yet, 23 is the current upperbound.
|
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 of the possible 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.)
|
x Rw2 U2 Rw U2 l' U2 Rw' F2 U' l' U F2 U' l U' Rw2 x'
|
(23,16)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
x Rw2 U2 Lw F2 l' F2 Lw' F2 U' l' U F2 U' l U' Rw2 x'
|
(23,16)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
x Rw2 U2 Rw U2 l' U2 Rw' F2 U l' U' F2 U l U Rw2 x'
|
(23,16)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
x Rw2 U2 Lw F2 l' F2 Lw' F2 U l' U' F2 U l U Rw2 x'
|
(23,16)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
x' Rw2 U2 Lw' U2 r U2 Lw F2 U r U' F2 U r' U Rw2 x
|
(23,16)
|
cmowlaparity
|
Y
|
Christopher Mowla
|
[104]
|
|
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
|
[]
|
|
x' Rw2 U2 Lw' U2 r U2 Lw F2 U' r U F2 U' r' U' Rw2 x
|
(23,16)
|
cmowlaparity
|
N
|
Christopher Mowla
|
[105]
|
|
x' Rw2 U2 Rw' F2 r F2 Rw F2 U' r U F2 U' r' U' Rw2 x
|
(23,16)
|
cmowlaparity(v2)
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw
|
(22,17)
|
v1
|
Y
|
Christopher Mowla
|
[106]
|
|
Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw
|
(22,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 B Rw
|
(22,17)
|
v1
|
N
|
Christopher Mowla
|
[107]
|
|
Rw' U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 B Rw
|
(22,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r' U' r' U B2 U' r U' r' U2 r' B2 l U2 l' U2 r2
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r' U r' U' B2 U r U r' U2 r' B2 l U2 l' U2 r2
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r B l B' D2 B l' B l B2 r F2 l' F2 l D2 r2
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
r B l B' D2 B l' B l B2 l D2 l' D2 r D2 r2
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
r B' l B D2 B' l' B' l B2 r F2 l' F2 l D2 r2
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
r B' l B D2 B' l' B' l B2 l D2 l' D2 r D2 r2
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
Rw D B2 D' l D B2 U2 Rw D2 l D2 Rw' D' l' U2 Rw'
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw D B2 D' l D B2 U2 Lw B2 l B2 Lw' D' l' U2 Rw'
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw D' B2 D l D' B2 U2 Rw D2 l D2 Rw' D l' U2 Rw'
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw D' B2 D l D' B2 U2 Lw B2 l B2 Lw' D l' U2 Rw'
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
Rw' F2 D2 B l B' D2 B l' B' Rw' B2 l B2 Rw F2 Rw
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' F2 D2 B l B' D2 B l' B' Lw' D2 l D2 Lw F2 Rw
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' F2 D2 B' l B D2 B' l' B Rw' B2 l B2 Rw F2 Rw
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw' F2 D2 B' l B D2 B' l' B Lw' D2 l D2 Lw F2 Rw
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 D2 r D2 l' D l D' F2 D l' D l D2 l F2 r
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 D2 r D2 l' D' l D F2 D' l' D' l D2 l F2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' B' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 Rw
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' B' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 Rw
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' B U2 B' r' B U2 F2 Lw' B2 r' B2 Lw B' r F2 Rw
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw' B U2 B' r' B U2 F2 Rw' U2 r' U2 Rw B' r F2 Rw
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
l' r' D' r D' B2 D r' D' B2 l' D2 l' F2 l F2 l2
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
l r U' r U' F2 U r' U' F2 l' U2 l' B2 l B2 r2
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
l' r' D r D B2 D' r' D B2 l' D2 l' F2 l F2 l2
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
l r U r U F2 U' r' U F2 l' U2 l' B2 l B2 r2
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
Rw U2 F2 D' r' D F2 D' r D Lw D2 r' D2 Lw' U2 Rw'
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw'
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 F2 D r' D' F2 D r D' Lw D2 r' D2 Lw' U2 Rw'
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw'
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 B' r B' U2 B r' B' U2 l' B2 Lw' D2 l D2 Lw r
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
l2 F' r F' D2 F r' F' D2 l' F2 l' U2 l U2 l' r'
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
r2 B r B U2 B' r' B U2 l' B2 Lw' D2 l D2 Lw r
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
l2 F r F D2 F' r' F D2 l' F2 l' U2 l U2 l' r'
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 U2 l' U2 l F' r' F U2 F' r F' r' F2 r' U2 r'
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
r2 U2 r' F2 l D' r' D F2 D' r D' r' D2 l' U2 r'
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
r2 U2 l' U2 l F r' F' U2 F r F r' F2 r' U2 r'
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
r2 U2 r' F2 l D r' D' F2 D r D r' D2 l' U2 r'
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 B2 D2 r D b' D F2 D' b D r' B2 l r F2 r
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 B2 D2 r D' f' D' F2 D f D' r' B2 l r F2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 F2 U2 l' U' f U' B2 U f' U' r' B2 r l F2 r
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 F2 U2 l' U b U B2 U' b' U r' B2 r l F2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 D f D' B2 D f' D r D2 F2 r' B2 l r F2 r
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 D' b D B2 D' b' D' r D2 F2 r' B2 l r F2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 U' b' U F2 U' b U' l' U2 B2 r' B2 r l F2 r
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 U f' U' F2 U f U l' U2 B2 r' B2 r l F2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 D2 r D b' D F2 D' b D r' B2 l B2 r F2 r
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
r2 D2 r D b' D F2 D' b D l' D2 l D2 l F2 r
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
r2 D2 r D' f' D' F2 D f D' r' B2 l B2 r F2 r
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
r2 D2 r D' f' D' F2 D f D' l' D2 l D2 l F2 r
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 F2 r' B2 l D f D' B2 D f' D r D2 r F2 r
|
(23,17)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
r2 F2 l' D2 l F u F' D2 F u' F r F2 l F2 r
|
(23,17)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
r2 B2 r U2 r' B' d' B U2 B' d B' r' U2 r' U2 r'
|
(23,17)
|
v3
|
Y
|
Christopher Mowla
|
[]
|
|
r2 F2 r' B2 l D' b D B2 D' b' D' r D2 r F2 r
|
(23,17)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
r2 F2 l' D2 l F' d F D2 F' d' F' r F2 l F2 r
|
(23,17)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 B2 r U2 r' B u' B' U2 B u B r' U2 r' U2 r'
|
(23,17)
|
v3
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 B r' U R' U r U' R U' r B U2 r U2 r' B2 Rw2
|
(23,18)
|
|
N
|
Christopher Mowla
|
[108]
|
|
Lw' B' r' B D2 B' r B' r' B2 r' D2 l B2 l' B2 r Lw
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Lw' B r' B' D2 B r B r' B2 r' D2 l B2 l' B2 r Lw
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
r Lw F2 l' F2 l D' r' D F2 D' r D' r' D2 r' F2 Lw'
|
(23,18)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw l F2 l' F2 r F' r' F U2 F' r F' r' F2 r' U2 Rw'
|
(23,18)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
r Lw F2 r' D2 l B' r' B D2 B' r B' r' B2 l' F2 Lw'
|
(23,18)
|
v3
|
Y
|
Christopher Mowla
|
[]
|
|
r Lw F2 l' F2 l D r' D' F2 D r D r' D2 r' F2 Lw'
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw l F2 l' F2 r F r' F' U2 F r F r' F2 r' U2 Rw'
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r Lw F2 r' D2 l B r' B' D2 B r B r' B2 l' F2 Lw'
|
(23,18)
|
v3
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U' r' U B2 U' r U' r' U2 l' D2 r D2 r' B2 Rw l
|
(23,18)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U' r' U B2 U' r U' r' U2 r' B2 r B2 l' B2 Rw l
|
(23,18)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U r' U' B2 U r U r' U2 l' D2 r D2 r' B2 Rw l
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U r' U' B2 U r U r' U2 r' B2 r B2 l' B2 Rw l
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
Rw' F2 D b' D l D2 l' D' b D Rw' B2 l B2 Rw F2 Rw
|
(23,18)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' F2 D b' D l D2 l' D' b D Lw' D2 l D2 Lw F2 Rw
|
(23,18)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' F2 D' f' D' l D2 l' D f D' Rw' B2 l B2 Rw F2 Rw
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw' F2 D' f' D' l D2 l' D f D' Lw' D2 l D2 Lw F2 Rw
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 B' D2 r D b' D F2 D' b D r' B2 l B' r F2 r
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 B D2 r D' f' D' F2 D f D' r' B2 l B r F2 r
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 B D2 r D b' D F2 D' b D r' B2 l B r F2 r
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r2 B' D2 r D' f' D' F2 D f D' r' B2 l B' r F2 r
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' Lw' B' d' B U2 B' d B' l' B2 D2 r' D2 r l U2 Lw
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r' Lw' B u' B' U2 B u B l' B2 D2 r' D2 r l U2 Lw
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw l D2 F2 l' F' d F' U2 F d' F' l D2 r' l' U2 Rw'
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw l D2 F2 l' F u F U2 F' u' F l D2 r' l' U2 Rw'
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw l F' u' F D2 F' u F' l' F2 U2 l D2 r' l' U2 Rw'
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw l F d' F' D2 F d F l' F2 U2 l D2 r' l' U2 Rw'
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw l F2 l' F' d F' U2 F d' F' Lw D2 r' D2 Lw' U2 Rw'
|
(23,18)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw l F2 l' F' d F' U2 F d' F' Rw F2 r' F2 Rw' U2 Rw'
|
(23,18)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw l F2 l' F u F U2 F' u' F Lw D2 r' D2 Lw' U2 Rw'
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw l F2 l' F u F U2 F' u' F Rw F2 r' F2 Rw' U2 Rw'
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r' Lw' U2 B2 l' B' u B' D2 B u' B' r' D2 r l U2 Lw
|
(23,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
r' Lw' U2 B2 l' B d B D2 B' d' B r' D2 r l U2 Lw
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw l U2 r F2 r' U' b' U F2 U' b U' l' U2 r' U2 Rw'
|
(23,18)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
r Lw U2 r F2 r' U' b' U F2 U' b U' r' F2 r' F2 Lw'
|
(23,18)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw l U2 r F2 r' U f' U' F2 U f U l' U2 r' U2 Rw'
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
r Lw U2 r F2 r' U f' U' F2 U f U r' F2 r' F2 Lw'
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
Rw U2 F' d F' r' F2 r F d' F' Lw D2 r' D2 Lw' U2 Rw'
|
(23,18)
|
v1
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 F' d F' r' F2 r F d' F' Rw F2 r' F2 Rw' U2 Rw'
|
(23,18)
|
v2
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 F u F r' F2 r F' u' F Lw D2 r' D2 Lw' U2 Rw'
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
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
- Most 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
|
Lw E Rw2 Uw r' Uw' Rw2 Dw R2 Uw r' Uw' Rw R Dw' E' Lw'
|
(20,17)
|
|
N
|
Christopher Mowla
|
[109]
|
|
Rw' E' Lw2 Uw' l Uw Lw2 Dw' L2 Uw' l Uw Lw' L' Dw E Rw
|
(20,17)
|
|
N
|
Christopher Mowla
|
[110]
|
|
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
|
[111]
|
|
Rw' 3Uw' u' Lw' r' Uw' r' Uw 3Lw r' Uw Lw' Uw' r' Uw Lw E' Rw
|
(18,18)
|
|
N
|
Christopher Mowla
|
[112]
|
|
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
|
[113]
|
|
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
|
[114]
|
|
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
|
[115]
|
|
Rw' E Uw2 Fw Uw Rw' r' Fw' r Fw Rw Uw' Fw' Uw r Uw E' Rw
|
(19,18)
|
|
N
|
Christopher Mowla
|
[116]
|
|
Lw' S Bw2 Dw r Dw' Bw Dw r' Dw' r' Bw' r Bw r Bw S' Lw
|
(19,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' F' b' Rw' Bw' Rw u Rw' Bw Rw u2 Bw' u Bw u b F Lw
|
(19,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Uw' Fw2 L' R' u Lw Rw Uw2 Rw d Lw' Bw2 Lw d' 3Rw Rw R Fw2 Uw
|
(23,18)
|
|
N
|
Christopher Mowla
|
[117]
|
|
Rw' E Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw E' Rw
|
(19,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' E Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw r Rw Fw' Uw Lw E' Rw
|
(19,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' D' u' Uw' Rw f Rw' Uw Rw f' Rw' f' Uw' f Uw f u D Rw
|
(19,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
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
|
[]
|
|
(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
|
[118]
|
|
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
|
[119]
|
|
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
|
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
|
[120]
|
|
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
|
[121]
|
|
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
|
[122]
|
|
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
|
[123]
|
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 algorithm which just uses the face turn U2.
|
r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r'
|
(27,18)
|
|
Y
|
|
[]
|
|
- No algorithms in this section are longer 27 single slice quarter turns and 18 single slice half turns, (27,18). In addition, 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.)
- Since this is a large set of algorithms,
- 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.
|
r' U2 r U2 l F2 l' r' F2 r' U2 r' U2 F2 r2 F2
|
(25,16)
|
|
Y
|
|
[]
|
|
r' U2 r U2 l' U2 l r U2 r U2 r' U2 F2 r2 F2
|
(25,16)
|
|
Y
|
|
[]
|
|
r' U2 l F2 l' F2 l r F2 r F2 l' U2 F2 r2 F2
|
(25,16)
|
|
Y
|
|
[]
|
|
r B2 r' U2 l B2 l2 B2 U2 r B2 l' B2 l' r' B2
|
(25,16)
|
|
Y
|
|
[]
|
|
l' r' B2 r' B2 l U2 B2 r2 B2 r U2 l' B2 l B2
|
(25,16)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r U2 r2 F2 l r2 F2 l' U2 F2 r2 F2
|
(27,16)
|
|
Y
|
|
[]
|
|
r' U2 l F2 r F2 l2 U2 l r2 U2 r' U2 F2 r2 F2
|
(27,16)
|
|
Y
|
|
[]
|
|
r' U2 r' U2 r2 U2 r U2 r2 B2 r U2 r U2 r2 B2
|
(27,16)
|
|
Y
|
|
[]
|
|
r' U2 l' B2 r2 B2 l U2 r2 B2 r U2 r U2 r2 B2
|
(27,16)
|
|
Y
|
|
[]
|
|
r U2 r U2 r' U2 l F2 l' F2 r F2 r' F2 r' U2 r'
|
(25,17)
|
|
Y
|
|
[]
|
|
r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r'
|
(25,17)
|
|
Y
|
|
[]
|
|
r U2 l F2 l' U2 r U2 r' F2 r F2 r' F2 r' U2 r'
|
(25,17)
|
|
Y
|
|
[]
|
|
r U2 l F2 r' F2 r F2 l' F2 r F2 r' F2 r' U2 r'
|
(25,17)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 r U2 r' F2 r F2 l' F2 l F2 l U2 l
|
(25,17)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 r U2 l' U2 r U2 r' F2 l F2 l U2 l
|
(25,17)
|
|
Y
|
|
[]
|
|
l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l' r'
|
(25,17)
|
|
Y
|
|
[]
|
|
l r U2 r F2 r' F2 U2 r' U2 l F2 l' F2 U2 l' r'
|
(25,17)
|
|
Y
|
|
[]
|
|
r' U2 r' U2 l F2 r' U2 r' U2 r2 F2 r' U2 l' U2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' F2 l r F2 l' r2 U2 r' U2 F2 r2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r U2 l' r' U2 l r2 U2 r' U2 F2 r2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 l F2 l' F2 r2 U2 l F2 r' F2 l' r F2 r2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 l F2 r F2 l' r' F2 l r2 F2 l' U2 F2 r2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 l F2 l2 r U2 l r U2 l F2 l' U2 F2 r2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 r2 U2 l' r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 r' U2 l F2 U2 r2 U2 r F2 l' U2 l U2 l' r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 r' F2 r F2 l' U2 l F2 r' U2 r' U2 r2 F2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 l' U2 l F2 r' F2 r F2 r' U2 r' U2 r2 F2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 l' U2 r U2 r' U2 l F2 r' U2 r' U2 r2 F2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 F2 r F2 l2 r U2 F2 l' F2 l F2 r' F2 U2 l r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 F2 r' U2 l F2 l' U2 r U2 r' F2 r' U2 r2 F2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 F2 r' U2 l F2 r' F2 r F2 l' F2 r' U2 r2 F2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 F2 r' U2 r U2 r' U2 l F2 l' F2 r' U2 r2 F2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 F2 r' U2 r U2 r' U2 r U2 l' U2 r U2 l2 F2 l'
|
(27,17)
|
|
Y
|
|
[]
|
|
l r2 F2 r F2 r F2 l' r' F2 r' U2 r' U2 F2 r2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
r B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2 U2 l r'
|
(27,17)
|
|
Y
|
|
[]
|
|
r B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2 U2 l r'
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' B2 r2 B2 U2 r' U2 l' r2 B2 l r B2
|
(27,17)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l2 U2 l' r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 r B2 r U2 r2 B2 r B2 r U2 l' B2 l U2 r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 l U2 l' r
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 r' U2 r' B2 r2 U2 r' U2 l' r' B2 r B2 l B2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 r' U2 r' B2 l' r' B2 r' B2 r2 B2 r B2 l B2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 l' U2 r U2 r' U2 r U2 r' B2 r' B2 r2 U2 l
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 U2 l' B2 r B2 l r' B2 r2 B2 r U2 l' B2 l B2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 U2 l' U2 r U2 r' U2 B2 l r2 U2 l U2 l' r'
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 U2 l' U2 r U2 r' U2 l r' U2 r' U2 r B2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 l' B2 l r' B2 r' B2 r B2 r' U2 B2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' B2 l' B2 l U2 l' B2 l U2 r2 U2 r'
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 B2 r' B2 r B2 l' B2 l r' B2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 l r' U2 l' B2 r B2 r' U2 B2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 l r' U2 r' U2 r U2 l' U2 B2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r2 B2 l' r B2 l' B2 l U2 r' U2 B2 r' B2 l B2 r2
|
(27,17)
|
|
Y
|
|
[]
|
|
r U r U' F2 U r' U' l F2 l' F2 U2 r' U2 r2 F2 r
|
(25,18)
|
|
Y
|
|
[]
|
|
r2 U2 l U2 r' U2 r F2 r F r' F U2 F' r F l' r2
|
(25,18)
|
|
Y
|
|
[]
|
|
r2 F2 r F2 l2 r U2 r' F2 U' l' U F2 U' l U' l r
|
(25,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 l F2 l' U' l' U F2 U' l U F2 l2 F2 r
|
(25,18)
|
|
Y
|
|
[]
|
|
r U2 r U2 r' U2 r B r B' U2 B r' B' U2 r2 U2 r'
|
(25,18)
|
|
Y
|
|
[]
|
|
r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' B2 l r2
|
(25,18)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 B r' B' l U2 l' U2 l' B' l B' r2
|
(25,18)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 B r' B' r B2 l' B2 r' B' l B' r2
|
(25,18)
|
|
Y
|
|
[]
|
|
r2 B' r B' U2 B r' B' U2 l' B2 l r2 U2 l U2 l' r'
|
(25,18)
|
|
Y
|
|
[]
|
|
(r2 U2)2 (r U2)2 r' U2 B2 U' r' U B2 U' r U'
|
(27,18)
|
|
N
|
Christopher Mowla
|
[124]
|
|
(r2 U2)2 (r U2)2 r' U2 B2 U r' U' B2 U r U
|
(27,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
r U2 r2 U2 r' U2 l F2 l' U2 l U2 r F2 r' U2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 l r2 F2 l'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 r U2 r' U2 r U2 r' F2 r F2 l' U2 l r2 U2 r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l F2 r' F2 l' r2 U2 l' U2 l F2 r' F2 r' U2 r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l F2 l' U2 r U2 l' U2 r U2 l r2 F2 r' U2 r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 l' r' U2 l r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' F2 r2 U2 r U2 r' U2 l' r U2 l r F2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' F2 l r F2 r F2 r' F2 l' r F2 r2 F2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 l' U2 l r U2 l F2 r' F2 l' r F2 r2 F2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 l F2 r' U2 r2 U2 F2 l' U2 r U2 l r U2 l' r
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 l F2 l' F2 r2 U2 l F2 l' U2 l' r U2 l r F2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 r2 U2 r U2 r F2 r' F2 r F2 r' F2 l F2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 r U2 l' U2 r U2 l' U2 l U2 l2 r' U2 l
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 r U2 l' U2 l F2 l' F2 r U2 l2 r' U2 l
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 r U2 l' U2 l F2 l' F2 l F2 l2 r' F2 r
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 l F2 l' F2 r F2 l' F2 r U2 l2 r' U2 l
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 l F2 l' F2 r F2 l' F2 l F2 l2 r' F2 r
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l' F2 l F2 l' F2 l' r2 U2 r' F2 l F2 l U2 l
|
(27,18)
|
|
Y
|
|
[]
|
|
r' F2 l2 F2 r U2 r' F2 r U2 r' U2 l' F2 l U2 l r
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r' U2 l' r' U2 l
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r F2 l r F2 l'
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 F2 U2 l' U2 l F' r' F U2 F' r F r2 U2 r2 F2 r
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r F2 l r F2 l'
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 F2 l' r F2 l' U2 l U2 l' U2 F2 l' F2 l U2 l r
|
(27,18)
|
|
Y
|
|
[]
|
|
l r' U2 l' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 r U2 l' B2 r B2 r' U2 r U2 r' U2 l r2 U2 r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 r U2 l' B2 r B2 l' B2 l U2 r' U2 r' B2 l r2
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' B2 l r2
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 l' B2 l' U2 l U2 l' U2 r B2 r' B2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 l' B2 l' U2 r B2 l' B2 l B2 r' B2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 l' B2 l' U2 r B2 r' U2 l U2 l' B2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 l' U2 l' B2 l B2 r' U2 r B2 l' U2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 l' U2 r' U2 l U2 l' U2 r B2 l' U2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 l' U2 r' U2 r B2 l' B2 l B2 l' U2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r U2 l2 B2 r' B2 l B2 r' B2 r B2 r' B2 r U2 l r
|
(27,18)
|
|
Y
|
|
[]
|
|
r B2 r' U2 r U2 l' r' U2 l' U2 r B2 U2 l2 U2 l r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r B2 r' U2 l B2 l2 B2 U2 r B2 r' U2 l' r' U2 l' r
|
(27,18)
|
|
Y
|
|
[]
|
|
r B2 l B2 r' U2 l B2 l B2 l2 U2 l B2 r B2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r B2 l' B2 r B2 l' r' B2 l' B2 l B2 U2 l2 U2 l r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r B2 l' B2 r' U2 l r U2 l B2 l B2 U2 l2 U2 l r'
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' B2 l r U2 l' r U2 r' U2 r U2 r2 B2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' B2 r2 B2 l' r B2 r' B2 r B2 l r B2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 l' r' B2 l r
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 l' r
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r' U2 l' r' B2 r B2 l r B2 r U2 r U2 r2 B2
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l r
|
(27,18)
|
|
Y
|
|
[]
|
|
r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 l r'
|
(27,18)
|
|
Y
|
|
[]
|
|
l r' U2 l' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l r
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 U2 l' B2 l U2 l r' U2 l' r' B2 r U2 l' B2 l B2
|
(27,18)
|
|
Y
|
|
[]
|
|
r2 B2 r U2 r' U2 B2 r' B2 r B2 r' U2 l r' U2 l' r'
|
(27,18)
|
|
Y
|
|
[]
|
|
Rw U2 Rw2 U L U r U' L' U2 L U r' U' L' U Rw' U2 r U2 Rw' U2 Rw'
|
(29,23)
|
|
Y
|
Christopher Mowla
|
[125]
|
|
Rw U2 Rw2 U L' U r U' L U2 L' U r' U' L U Rw' U2 r U2 Rw' U2 Rw'
|
(29,23)
|
|
N
|
Christopher Mowla
|
[]
|
2 Gen and "Semi 2 Gen" Algorithms
|
r U2 r' U2 r U2 r U r U r U2 r2 U2 r U2 r U r' U' r2 U2
|
(31,22)
|
|
N
|
Lucas Garron
|
[126]
|
|
r U2 r' U2 r U2 r U' r U' r U2 r2 U2 r U2 r U' r' U r2 U2
|
(31,22)
|
|
N
|
Lucas Garron
|
[127]
|
|
r2 U r' U' r U2 r U2 r2 U2 r U' r U' r U2 r U2 r' U2 r U2
|
(31,22)
|
|
N
|
Lucas Garron
|
[128]
|
|
r2 U' r' U r U2 r U2 r2 U2 r U r U r U2 r U2 r' U2 r U2
|
(31,22)
|
|
N
|
Lucas Garron
|
[129]
|
|
y' Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U' Rw U Rw' U' Rw U2 Rw' U2 y
|
(34,26)
|
|
Y
|
Bruce Norskog
|
[130]
|
|
y' Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U Rw U Rw' U' Rw U2 Rw' U2 y
|
(34,26)
|
|
Y
|
Bruce Norskog
|
[]
|
|
Rw U2 Rw U Rw U2 Rw U2 Rw' U2 Rw' U r' U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw' U2 Rw'
|
(37,27)
|
|
N
|
Christopher Mowla
|
[131]
|
|
Rw U2 Rw U' Rw U2 Rw U2 Rw' U2 Rw' U' r' U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw' U2 Rw'
|
(37,27)
|
|
N
|
Christopher Mowla
|
[]
|
|
y Rw U Rw2' U' Rw U' Rw' U Rw U' Rw2' U2' Rw' U2' Rw U2' Rw' U Rw2' U' Rw U Rw' U' Rw U2' Rw U2' Rw2' U Rw' U' Rw' y'
|
(42,33)
|
5x5 Alg
|
Y
|
Ben Whitmore
|
[]
|
4x4x4 Supercube Safe Algorithms
|
r' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U r//Safe
|
(27,23)
|
|
N
|
|
[132]
|
|
Rw2 U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw2 x'//Safe
|
(33,23)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
(Rw' U')(U' r2 U Rw (r2 u r2 u') U' r' U Rw')3 (U Rw)//Safe
|
(43,36)
|
|
N
|
Christopher Mowla
|
[133]
|
Opposite Double Parity
|
r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l y2
|
(21,14)
|
|
Y
|
Kenneth Gustavsson
|
[]
|
|
r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x
|
(25,15)
|
|
Y
|
Frédérick Badie
|
[]
|
|
x r F2 Lw' F r' F' U2 F r F' U2 Lw x' E2 l' U2 l y2
|
(21,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
x r F2 Lw' F' r' F U2 F' r F U2 Lw x' E2 l' U2 l y2
|
(21,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 r' U2 r2 U2 M' U2 r U2 r' U2 l U2 r' U2 Rw'
|
(26,17)
|
|
N
|
Jayden McNeill
|
[134]
|
|
Rw' U2 r' U2 l U2 Rw' U2 r U2 3Rw U2 r2 U2 r' U2 Rw
|
(26,17)
|
|
Y
|
|
[]
|
|
r2 U2 3Rw' U2 r' U2 Rw U2 l' U2 Rw U2 r U2 Rw' U2 r
|
(26,17)
|
|
Y
|
|
[]
|
|
Rw2 U2 r' U2 r' U2 r U2 M' U2 r U2 r' U2 M U2 Rw2
|
(27,17)
|
|
N
|
Thom Barlow
|
[135]
|
|
Rw2 U B2 U' r' U B2 U' Rw r U B2 U r' U' B2 U' Rw
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
Rw U2 Lw' U2 l U2 Lw U2 Rw' U2 l U2 l' U2 x U2 l2 U2 x' U2
|
(29,18)
|
|
Y
|
|
[]
|
|
Rw2 3Dw L2 3Dw' r' 3Dw L2 3Dw' Rw r 3Dw L2 3Dw l' 3Dw' L2 3Dw' Rw
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
r2 U' B2 U r' U' B2 U r2 U' B2 U' r' U B2 U r
|
(23,18)
|
v1
|
N
|
Christopher Mowla
|
[]
|
|
r2 3Dw' R2 3Dw r' 3Dw' R2 3Dw r2 3Dw' R2 3Dw' l' 3Dw R2 3Dw r
|
(23,18)
|
v2
|
N
|
Christopher Mowla
|
[]
|
|
U2 x' r' (F2 U' l' U)5 r x
|
(29,23)
|
|
Y
|
Christopher Mowla
|
[136]
|
|
U2 x' r' (U' l' U F2)5 r x
|
(29,23)
|
|
Y
|
Christopher Mowla
|
[138]
|
|
(F d' S r F Rw2 f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 Rw2 F' r' S' d F')
|
(31,23)
|
|
N
|
Christopher Mowla
|
[]
|
|
(B Lw2 U' L' U r u2 b' r2 Bw2 E) r' (E' Bw2 r2 b u2 r' U' L U Lw2 B')
|
(31,23)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2
|
(29,24)
|
|
N
|
Christopher Mowla
|
[140]
|
|
(z' Lw Uw2 U' Rw L2 U2 Lw' U' Lw R F2 U' R' U) r' (U' R U F2 R' Lw' U Lw U2 L2 Rw' U Uw2 Lw' z)
|
(33,29)
|
1 Slicer
|
N
|
Christopher Mowla
|
[]
|
|
(z' Lw Uw2 U' Rw L2 U2 Lw' U' Rw R U2 3Lw U' R2 U) r' (U' R2 U 3Lw' U2 R' Rw' U Lw U2 L2 Rw' U Uw2 Lw' z)
|
(37,31)
|
1 Slicer(2)
|
N
|
Christopher Mowla
|
[]
|
Adjacent Double Parity
|
(y' r2 F Rw' F') r2 U2 r' U2 r' U2 r' U2 (F Rw F' r2 y)
|
(23,16)
|
|
N
|
Christopher Mowla
|
[141]
|
|
(y Rw' z' L' U r F) r2 U2 r' U2 r' U2 r' U2 (F' r' U' L z Rw y')
|
(23,18)
|
|
N
|
Christopher Mowla
|
[142]
|
|
Dw2 D F2 U l' F2 l F2 U l D' U2 r' D F2 D' r Dw2
|
(23,18)
|
|
N
|
Clément Gallet
|
[]
|
|
Dw2 D F2 U l' F2 l F2 U l D U2 r' D' F2 D r d2
|
(23,18)
|
|
N
|
Clément Gallet
|
[]
|
|
(x' r2 U' Rw U) M' U2 r' U2 r' U2 r' U2 l r (U' Rw' U r2 x)
|
(24,18)
|
|
N
|
Christopher Mowla
|
[143]
|
|
u2 D' F2 U l' F2 l F2 U l D U2 r' D' F2 D r u2
|
(24,18)
|
|
N
|
Clément Gallet
|
[]
|
|
R B y2 r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l B' R'
|
(25,18)
|
|
N
|
Kenneth Gustavsson
|
[]
|
|
l2 U' B2 U l' U' l' B2 l U F2 U' B2 l B2 U F2 l'
|
(25,18)
|
|
N
|
Clément Gallet
|
[]
|
|
l2 U' B2 U l' F2 U' l' B2 l B2 l U F2 U' B2 U l'
|
(25,18)
|
|
N
|
Clément Gallet
|
[]
|
|
l2 U' B2 U l' F2 U' r' U2 l U2 r U F2 U' B2 U l'
|
(25,18)
|
|
N
|
Clément Gallet
|
[]
|
|
R B' r2 B2 r B2 r' B2 r B2 U2 r U2 r B2 r2 B' R'
|
(27,18)
|
|
N
|
|
[]
|
|
l2 F2 U' B2 U F2 l' F2 U' l' B2 l B2 l B2 U F2 l'
|
(27,18)
|
|
N
|
Clément Gallet
|
[]
|
|
l2 F2 U' B2 U F2 l' F2 U' r' U2 l U2 r B2 U F2 l'
|
(27,18)
|
|
N
|
Clément Gallet
|
[]
|
|
r2 B2 l2 U' r' B2 r U l U' B2 U l B2 D2 l' D2 r2
|
(27,18)
|
|
N
|
Clément Gallet
|
[]
|
|
(x Rw F2 U' R Rw) U' r U2 r U2 r U2 r2 U' (Rw' R' U F2 Rw' x')
|
(25,19)
|
|
N
|
Christopher Mowla
|
[144]
|
|
(y Rw2 U x') l U' L' U' l' U L U F2 l' F2 r U2 r' U2 (x U' Rw2 y')
|
(25,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
(r2 F') Rw' F' U2 F r F l D2 r' D2 F2 l' U2 F R (F r2)
|
(26,19)
|
|
N
|
Christopher Mowla
|
[145]
|
|
r' B L' B l' B' L B' l U l B2 l' F2 l' F2 l B2 U' M'
|
(24,20)
|
|
N
|
Christopher Mowla
|
[146]
|
|
(y Rw2 U x') l U' L' U' l' U L U M' U2 l' U2 l U2 r' U2 (x U' Rw2 y')
|
(26,20)
|
|
N
|
Christopher Mowla
|
[]
|
|
(y Rw2 F L) F U2 l F2 D2 r D2 l' F r' F U2 F' r (L' F' Rw2 y')
|
(27,20)
|
|
N
|
Christopher Mowla
|
[147]
|
|
(z' Rw' U' Rw' l' U L') U' r2 U2 r' U2 r' U2 r' U' (L U' l Rw U Rw z)
|
(25,21)
|
|
N
|
Christopher Mowla
|
[148]
|
|
(Lw2 B' R B l b2 u' l2 Uw2 S) l' (S' Uw2 l2 u b2 l' B' R' B Lw2)
|
(29,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
(y x' Lw2 F' L2 F r f2 u' r2 Uw2 S') r' (S Uw2 r2 u f2 r' F' L2 F Lw2 x y')
|
(31,21)
|
|
N
|
Christopher Mowla
|
[149]
|
|
(y Bw' R U b' R' Bw' Uw2 Rw' u2 l2 S') u (S l2 u2 Rw Uw2 Bw R b U' R' Bw y')
|
(29,23)
|
|
N
|
Christopher Mowla
|
[150]
|
|
(z Rw' Uw2 U Lw' R2 U2 Rw U Lw' U2 F' R2 F) l' (F' R2 F U2 Lw U' Rw' U2 R2 Lw U' Uw2 Rw z')
|
(33,27)
|
1 Slicer(1)
|
N
|
Christopher Mowla
|
[]
|
|
(Lw U Rw2 F Rw U' Rw U' F2 U Rw2 U' R' U') r (U R U Rw2 U' F2 U Rw' U Rw' F' Rw2 U' Lw')
|
(35,29)
|
1 Slicer(2)
|
N
|
Christopher Mowla
|
[151]
|
|
Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' B' L B U' L U l U' L' U B' L' B L Uw R Uw2 l2 Bw
|
(33,30)
|
|
N
|
Christopher Mowla
|
[152]
|
|
Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' U' B' L B L U l U' L' B' L' B U L Uw R Uw2 l2 Bw
|
(33,30)
|
|
N
|
Christopher Mowla
|
[153]
|
|
((Lw x) Uw2 Lw Rw Uw2 Rw2 U2 Rw U' Lw U2 F L2 U F' U') l' (U F U' L2 F' U2 Lw' U Rw' U2 Rw2 Uw2 Lw' Rw' Uw2 (Lw' x'))
|
(45,33)
|
5x5 1 Slicer
|
N
|
Christopher Mowla
|
[]
|
Three Dedge Flip
Single Parity
|
u2 f' U f2 Lw2 U2 f U2 B2 Lw2 f2 U f u2 Lw2 B2 Lw2
|
(29,17)
|
|
N
|
Clément Gallet
|
[]
|
|
R2 b' U' L2 f2 L2 f2 U b U f' U2 f M2 f M2 U R2
|
(27,18)
|
|
N
|
Clément Gallet
|
[]
|
|
R2 D' l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D' R2
|
(29,18)
|
|
N
|
Walter Randelshofer
|
[154]
|
|
y M U r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2 U' M' y'
|
(29,19)
|
|
N
|
|
[]
|
|
y M U r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2 U' M' y'
|
(29,19)
|
|
N
|
|
[]
|
|
M2' U' x' r2 U2 M r' U2 r F2 U2 r2 U2 M' r x U2 r U2 r' U' M2'
|
(31,20)
|
|
N
|
|
[]
|
|
y M U l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r' U' M' y'
|
(27,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M U l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r' U' M' y'
|
(27,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M U r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2 U' M' y'
|
(27,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M U r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2 U' M' y'
|
(27,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M U l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r U' M' y'
|
(27,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M U l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r U' M' y'
|
(27,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw U Rw U2 Rw U2 Rw U Rw' U2 r' U2 Rw' U Rw U2 Rw U2 Rw U Rw
|
(27,21)
|
v1
|
N
|
Kåre Krig
|
[]
|
|
Rw' U' Rw' U2 Rw' U2 Rw' U' Rw U2 r U2 Rw U' Rw' U2 Rw' U2 Rw' U' Rw'
|
(27,21)
|
v2
|
N
|
Kåre Krig
|
[]
|
|
Uw2 F2 Lw' U' L U Lw U2 Lw' U' L' U' l' U2 Lw' F2 l F2 Lw' U2 Lw' l' F2 Uw2
|
(33,24)
|
|
N
|
Christopher Mowla
|
[]
|
|
Uw2 B2 Lw U L' U' Lw' U2 Lw U L U l U2 Lw B2 l' B2 Lw U2 Lw l B2 Uw2
|
(33,24)
|
|
N
|
Christopher Mowla
|
[]
|
|
M2' U' l U2 r' F2 r D2 F2 r F2 r' Dw2 l r U' l' r' d2 l r U l M F2 l U' M2'//Safe
|
(38,28)
|
|
N
|
Christopher Mowla
|
[]
|
|
M2' U' r' U2 l F2 l' D2 F2 l' F2 l Dw2 l' r' U l r d2 l' r' U' r' M F2 r' U' M2'//Safe
|
(38,28)
|
|
N
|
Christopher Mowla
|
[]
|
|
L R U2 L' R' U' L R U2 L2 x' U B2 r2 U2 r D2 r' U2 x' U2 l2 U2 r' B2 r' U2 x l U' M' U'//Safe
|
(42,29)
|
|
N
|
François Courtès
|
[]
|
|
(Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw)(D' F2 D)(r' F2 r F2)(F2 r2 F2 r2 F2 r2 F2)(D' F2 D)
|
(39,29)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw U2 Rw U2 Rw U R U Rw U2 Rw' U' R' U' Rw' R' U R U Rw U2 Rw' U' R' U' Rw U2 Rw' U2 Rw'
|
(36,30)
|
|
Y
|
Christopher Mowla
|
[]
|
Double Parity
- Note that there are many possible types of last layer double parity that can exist. This case is probably just the first of many to come on this page, as fast algorithms for other cases are quite possible to achieve.
|
u2 f' U' f2 Lw2 U2 f' U2 B2 Lw2 f2 U' f u2 Lw2 B2 Lw2
|
(29,17)
|
|
N
|
Clément Gallet
|
[]
|
|
Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw R U2 x
|
(24,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
y M U r U2 r2 U2 r' U2 F2 r' F2 r2 U2 l F2 l' F2 r2 U' M' y'
|
(31,20)
|
|
N
|
|
[]
|
|
(y' r' U2 M l U) (r' U' F' R' F R2 U') r' (U R2 F' R F U r) r U2 r' U2 (U' M' l' U2 r y)
|
(33,27)
|
|
N
|
Christopher Mowla
|
[]
|
Eleven Dedge Flip (Single Parity)
|
Rw2 F2 l U2 x' l U2 l2 x' U2 r' U2 l D2 F2 l U2 L R E M S x
|
(30,20)
|
|
N
|
Herbert Kociemba &Christopher Mowla
|
[]
|
|
r D2 x U2 l D2 r' D2 l2 F2 l U2 l x' U2 r2 F2 R2 E L' R U' D y x R2
|
(31,20)
|
|
N
|
Herbert Kociemba
|
[155]
|
|
Lw2 F2 M r' F2 r' U2 r2 B2 r D2 l' B2 D2 r' F2 L2 E' M S' x2
|
(31,20)
|
|
N
|
Herbert Kociemba &Christopher Mowla
|
[]
|
|
Rw2 F2 l U2 r' x' U2 l2 F2 r D2 M l x U2 B2 r F2 R2 E M S x2
|
(31,20)
|
|
N
|
Herbert Kociemba &Christopher Mowla
|
[]
|
|
y d E M R D R' Bw f M d' M' Fw b M' F Uw M' R' S L F' U R D' R' E S2 R F' z'
|
(30,29)
|
|
N
|
Bruce Norskog &Christopher Mowla
|
[156]
|
OLL parity algorithms which don't preserve the last layer
- Some of the algorithms in this category are the most widely used speedsolving algorithms.
- None of these algorithms will result in a single dedge flip or the "pure form" of double parity if single slices are substituted for the wide turns.
Single Parity
1 Flip
- With the exception of Kåre Krig's 2 gen algorithms, all algorithms listed in this section can be derived from algorithms from the "Longer/Faster Algorithms" section by using 4x4x4 wide turn equivalencies such as r = (l x), l2 = (r2 x2), etc.
- Specifically, these algorithms were derived from the classic setup's solutions which are at most 18 single slice half turns. They only involve 2 face turns and thus they are additional transformations which are "legal" in wide turns, but "illegal" transformations to keep these algorithms pure dedge flips.
- Therefore we have more 15 BHTM solutions which preserve F3L in wide turns than we have for pure dedge flips, for example.
- Most of these algorithms need to be adjusted to work on 5x5x5.
It's interesting to note that the following algorithm cannot even be used to solve any form of OLL parity if all of its wide turns are converted into single slice turns!
|
Rw2 F2 U2 Rw' F' Uw L' U2 L Uw' F' Rw' U2 Rw2 F2 Rw
|
(23,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
|
Rw' U2 Rw U2 Rw U2 Rw2 F2 Rw' U2 Rw' U2 F2 Rw2 F2
|
(25,15)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2
|
(25,15)
|
|
Y
|
|
[]
|
|
Rw' U2 Lw F2 Rw' U2 Rw2 U2 F2 Lw' U2 Lw F2 Rw2 U2 x
|
(25,15)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Lw' B2 Lw U2 Rw2 B2
|
(25,15)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw U2 Rw2 B2
|
(25,15)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Lw' U2 Rw2 B2 Lw U2 Lw' B2 U2 Rw2 U2 x'
|
(25,15)
|
|
Y
|
|
[]
|
|
Rw2 U2 Rw' U2 Rw U2 B2 Rw2 B2 Rw U2 Rw' U2 Rw B2
|
(25,15)
|
|
Y
|
|
[]
|
|
x' Rw2 B2 Lw B2 Rw' U2 B2 Lw2 B2 Lw' U2 Lw U2 Lw' B2
|
(25,15)
|
|
Y
|
|
[]
|
|
Lw Rw U2 F2 Lw' F2 Rw F2 Rw' F2 U2 Rw' U2 Lw U2 Lw2 x'
|
(25,16)
|
|
Y
|
|
[]
|
|
Lw Rw U2 F2 Lw' F2 Rw F2 Rw' F2 U2 Rw' U2 Lw U2 Rw2 x
|
(25,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw U2 Lw Rw U2 x
|
(25,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw U2 Lw' Rw' U2 Rw' B2 Rw' B2 U2 Rw2 U2 x'
|
(25,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Lw Rw2 U2 Rw2 U2 F2 Lw' U2 Lw F2 Rw2 U2 x
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Lw Rw2 U2 Rw2 U2 F2 Lw' U2 Rw U2 Lw2 F2 x2
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Lw2 Rw B2 Lw2 U2 Rw U2 Lw' B2 U2 Rw2 U2 x'
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw' B2 Rw2 B2 U2 Rw' U2 Rw' B2 Rw2 U2 Rw2
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw U2 Lw2 B2 Lw Rw2 B2 Rw' B2 U2 Rw2 U2 x'
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw' U2 Rw2 U2 Rw' B2 Rw2 U2 Lw' B2 Lw U2 Rw2 B2
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw' U2 Rw2 U2 Rw' B2 Rw2 U2 Rw' U2 Rw U2 Rw2 B2
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw2 U2 B2 Rw B2 Rw B2 U2 Rw U2 Rw' U2 Rw' U2 Rw2 U2 B2
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw2 U2 Rw' U2 Rw' B2 Rw2 U2 Rw' U2 Rw2 U2 Rw U2 Lw U2 x
|
(27,16)
|
|
Y
|
|
[]
|
|
x' Rw2 B2 Lw2 Rw' U2 Lw' U2 B2 Lw2 B2 Lw' U2 Lw U2 Lw' B2
|
(27,16)
|
|
Y
|
|
[]
|
|
Rw' U' Rw' U B2 U' Rw U' Rw' U2 Rw' x' U2 Rw U2 Lw' U2 Rw2
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw2 U2 Lw' U2 Rw U' Rw' U B2 U' Rw U' Rw' U2 Rw' x' U2 Rw'
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Lw Rw U' Rw U' F2 U Rw' U' x U2 Rw' U2 Rw' U2 Lw U2 Rw2 x
|
(23,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
|
(25,17)
|
lucasparity
|
Y
|
Lucas Garron & Stefan Pochmann
|
[157]
|
|
Rw U2 Rw U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' Rw' U2 Rw'
|
(25,17)
|
lucasparity
|
Y
|
Lucas Garron & Stefan Pochmann
|
[]
|
|
Rw U2 Rw U2 Lw' B2 Lw U2 Lw' U2 Rw U2 Rw' U2 Rw' x' U2 Rw'
|
(25,17)
|
|
Y
|
|
[]
|
|
Rw U2 Rw U2 Rw' U2 Rw U2 Rw' F2 Rw F2 Rw' F2 Rw' U2 Rw'
|
(25,17)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw U2 Rw U2 Lw' Rw' U2 Lw2 Rw F2 Lw' U2 F2 Rw2 F2
|
(27,17)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw' U2 Rw2 U2 Rw U2 Lw Rw U2 Rw F2 Rw F2 Rw2 U2 x
|
(27,17)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw' U2 Rw U2 Rw' B2 Rw' B2 Rw2 U2 Rw' B2 Lw' B2 Lw2 x
|
(27,17)
|
|
Y
|
|
[]
|
|
Rw' U2 Rw' U2 Rw U2 Rw' B2 Rw' B2 Rw2 U2 Rw' B2 Rw' U2 Rw2
|
(27,17)
|
|
Y
|
|
[]
|
|
Rw2 U2 Lw' U2 Rw U2 Lw' B2 Lw U2 Rw' B2 Rw' B2 Rw2 U2 Lw
|
(27,17)
|
|
Y
|
|
[]
|
|
Lw Rw U2 Lw' Rw2 U2 Rw' U2 B2 Rw' B2 Lw U2 Lw' U2 B2 Rw2
|
(27,17)
|
|
Y
|
|
[]
|
|
Rw U2 Rw U2 Rw' U2 Lw U Rw U' F2 U Rw' U' x U2 Rw2 U2 Rw'
|
(25,18)
|
|
Y
|
Christopher Mowla
|
[]
|
|
R U r U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
|
(27,20)
|
|
N
|
Kåre Krig &xyzzy
|
[158]
|
|
Rw' U' Rw2 U' Rw' U Rw' U' Rw' U2 Rw U Rw U' Rw U Rw2 U Rw2 U2 Rw U2 Rw2 U2 Rw
|
(33,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U2 Rw' U2 Rw U Rw' U Rw' U2 Rw2 U Rw2 U' Rw2 U' Rw' U' Rw U Rw' U2 Rw2 U2 Rw
|
(34,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U2 Rw' U2 Rw U Rw' U Rw U' Rw2 U' Rw2 U2 Rw2 U' Rw U' Rw U Rw' U2 Rw2 U2 Rw
|
(34,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U2 Rw' U2 Rw U Rw' U Rw U Rw2 U2 Rw2 U' Rw2 U Rw U' Rw U Rw' U2 Rw2 U2 Rw
|
(34,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U' Rw U2 Rw U2 Rw' U2 Rw' U' Rw2 U Rw2 U Rw' U2 Rw
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U Rw U2 Rw U2 Rw' U2 Rw' U Rw2 U Rw2 U Rw' U2 Rw
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw' U' Rw' U2 Rw2 U2 Rw2 U Rw U2 Rw U2 Rw' U2 Rw U' Rw2 U' Rw2 U' Rw U2 Rw
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw' U' Rw U' Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U' Rw2 U Rw2 U Rw' U2 Rw
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw' U' Rw U Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw' U Rw2 U Rw2 U Rw' U2 Rw
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw' U' Rw U Rw2 U2 Rw2 U2 Rw' U2 Rw U2 Rw' U2 Rw U' Rw2 U' Rw2 U' Rw U2 Rw
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
3 Flip
|
Rw F U2 F' Rw U2 Rw U2 Rw U' L' U2 L F 3Lw' U' R U' x' U F Rw
|
(25,21)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' R' U2 R' U2 R U' Rw
|
(28,22)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw
|
(28,22)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U' Rw U2 R' U2 Rw' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw
|
(28,22)
|
|
Y
|
Kåre Krig
|
[]
|
Double Parity
1 Flip
|
Rw' U2 Rw' U2 Lw U2 Rw' U2 Rw U2 x U2 Rw2 U2 Rw' U2 Rw
|
(25,16)
|
v1
|
Y
|
|
[]
|
|
Lw U2 Lw U2 Rw' U2 Lw U2 Lw' U2 x U2 Lw2 U2 Lw U2 Lw'
|
(25,16)
|
v2
|
Y
|
|
[]
|
|
Rw U2 Rw' U2 Rw U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' U2 Rw2
|
(25,16)
|
v1
|
Y
|
|
[]
|
|
Lw' U2 Lw U2 Lw' U2 Lw' U2 Rw U2 Lw' U2 Lw U2 x' U2 Lw2
|
(25,16)
|
v2
|
Y
|
|
[]
|
|
Rw2 U2 x' U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw U2 Rw' U2 Rw
|
(25,16)
|
v1
|
Y
|
|
[]
|
|
Lw2 U2 x' U2 Lw U2 Lw' U2 Rw U2 Lw' U2 Lw' U2 Lw U2 Lw'
|
(25,16)
|
v2
|
Y
|
|
[]
|
|
Rw U2 Rw' U2 Rw2 U2 x U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw'
|
(25,16)
|
v1
|
Y
|
|
[]
|
|
Lw' U2 Lw U2 Lw2 U2 x U2 Lw' U2 Lw U2 Rw' U2 Lw U2 Lw
|
(25,16)
|
v2
|
Y
|
|
[]
|
|
Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U Rw2 R U Rw U' Rw
|
(23,19)
|
v1
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' Rw2 R' U' Rw' U Rw'
|
(23,19)
|
v2
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U2 Rw' U2 Rw R U Rw2 R' U2 Rw' R' U R U Rw' U2 Rw2 U' Rw2
|
(26,20)
|
|
Y
|
Kåre Krig
|
[]
|
|
z' U2 Lw' R2 x U' F2 U Lw' U2 r' U2 Rw F' L2 F r2 U2 x' U' F2 U x U2 Lw' U2 z
|
(32,22)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U' Rw' U' Rw U Rw U2 Rw2 U2 Rw U2 Rw U Rw' U Rw U Rw2 U2 Rw' U2 Rw U2 Rw'
|
(33,25)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U Rw2 U Rw2 U2 Rw U2 Rw' U2 Rw U Rw U Rw U2 Rw' U2 Rw' U2 Rw2 U' Rw2 U Rw'
|
(35,25)
|
|
Y
|
Kåre Krig
|
[]
|
3 Flip
|
Rw U' Rw U' Rw2 U Rw' U2 Rw U2 Rw' U Rw' U' Rw U2 Rw U2 Rw U2 Rw U' Rw' U2 Rw' U2 Rw
|
(35,27)
|
|
Y
|
Kåre Krig
|
[]
|
- One can make a 3 flip from a one flip, for example, by conjugating a 1 flip with B' R'.
|
(B' R') Rw U2' x Rw U2' Rw U2' Rw' U2 Lw U2' Rw' U2 Rw U2' Rw' U2 Rw' (R B)
|
(27,21)
|
|
Y
|
Lucas Garron
|
[159]
|
- For other algorithms for OLL + OLL parity (that is, using outer layer turn setup moves to algorithms like those in this section (and algorithms in the previous with wide turns), see Michael Fung's old page and this thread.
OLL parity algorithms which don't preserve F3L
- One advantage of having access to algorithms which don't preserve the first three layers of the 4x4x4 is that the shortest algorithms that this category of algorithms has to offer have fewer moves than algorithms which preserve the first three layers. (This is of interest to certain cubers.)
- Unlike algorithms which preserve the first three layers, which are at minimum 14 block half turns (double parity) and 18 block quarter turns (one dedge flip), some algorithms in this section are just 13 block half turns and some are just 15 block quarter turns.
Permute Corners Only
- Most of these algorithms are also just front right (FR) F3L slot destroyers.
Single Parity
|
r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r'
|
(21,15)
|
|
N
|
Christopher Mowla & Bruce Norskog
|
[160]
|
|
l U2 F' U2 F U2 l U2 l U2 l F' U2 F l
|
(21,15)
|
|
N
|
Christopher Mowla & Bruce Norskog
|
[161]
|
|
r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'
|
(21,17)
|
|
N
|
Christopher Mowla & Bruce Norskog
|
[]
|
|
l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l'
|
(21,17)
|
|
N
|
Christopher Mowla & Bruce Norskog
|
[]
|
|
r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2
|
(22,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw
|
(22,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw
|
(22,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw
|
(24,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2
|
(24,19)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2
|
(24,19)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw
|
(24,19)
|
|
N
|
Kåre Krig
|
[]
|
|
(r' U' R U r)(r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r)(r U R' U' r')
|
(31,21)
|
|
N
|
Christopher Mowla
|
[]
|
Front Right F3L Slot Destroyers
Single Parity
|
l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F
|
(22,17)
|
|
N
|
Christopher Mowla
|
[162]
|
|
Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F
|
(22,17)
|
|
N
|
Christopher Mowla
|
[163]
|
|
Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
|
(24,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r'
|
(24,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw
|
(24,19)
|
|
N
|
Kåre Krig
|
[]
|
Double Parity
|
Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw
|
(21,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2
|
(24,18)
|
|
N
|
Kåre Krig
|
[]
|
|
(r' U' R U r)(r2 F2 Uw2 r Uw2 F2 r2)(r U R' U' r')(Fw2 l' Uw2 l r Uw2 r' Fw2)
|
(31,23)
|
|
N
|
Christopher Mowla
|
[]
|
Petrus
- These algorithms "just" scramble two adjacent faces' worth of pieces.
Single Parity
|
Rw B' U2 B Rw B2 Lw B2 Rw B D2 B' Rw
|
(17,13)
|
v1
|
Y
|
Bruce Norskog
|
[]
|
|
x' Rw' U F2 U' Lw' U2 Rw' U2 Rw' F' U2 F Rw'
|
(17,13)
|
v2
|
Y
|
Bruce Norskog
|
[164]
|
|
x' Rw' U F2 U' Lw' U2 Rw' U2 Lw' U' B2 U Rw' x'
|
(17,13)
|
v3
|
Y
|
Bruce Norskog
|
[165]
|
|
x' Rw' U F2 U' Lw' U2 Rw' 3Dw2 Rw' U' F2 U Lw' x
|
(17,13)
|
v4
|
Y
|
Bruce Norskog
|
[166]
|
|
Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'
|
(20,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'
|
(20,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x'
|
(21,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'
|
(21,17)
|
|
Y
|
Kåre Krig, Bruce Norskog, & Christopher Mowla
|
[167]
|
|
Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw
|
(21,17)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw
|
(21,17)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw'
|
(21,17)
|
|
Y
|
Bruce Norskog & Christopher Mowla
|
[168]
|
|
Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F
|
(22,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw
|
(23,17)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'
|
(25,17)
|
|
Y
|
Kåre Krig & Christopher Mowla
|
[169]
|
|
Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw'
|
(25,17)
|
|
N
|
Kåre Krig & Christopher Mowla
|
[170]
|
|
Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw
|
(25,17)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw'
|
(21,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R' U' R U2 R' U Rw'
|
(22,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw
|
(23,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw
|
(23,18)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw
|
(23,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw'
|
(24,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw'
|
(24,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'
|
(24,18)
|
|
Y
|
Kåre Krig
|
[]
|
|
Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw
|
(22,19)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw
|
(22,19)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw
|
(22,19)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw
|
(23,19)
|
|
N
|
Kåre Krig
|
[]
|
|
Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw
|
(23,19)
|
|
N
|
Kåre Krig
|
[]
|
Double Parity
|
Lw' U2 F2 Lw' U' F R' F Lw2 U2 Rw U2 Lw2 U' x'
|
(20,14)
|
v1
|
Y
|
Bruce Norskog
|
[171]
|
|
Lw' U2 F2 Lw' U' F 3Lw' U Lw2 x' U2 Rw U2 Lw2 U' x'
|
(20,14)
|
v2
|
Y
|
Bruce Norskog
|
[172]
|
|
Rw U2 F2 Rw U' F R' F Rw2 U2 Lw' U2 Rw2 U' x'
|
(20,14)
|
v1
|
Y
|
Bruce Norskog
|
[173]
|
|
Rw U2 F2 Rw U' F 3Lw' U Rw2 x' U2 Lw' U2 Rw2 U' x'
|
(20,14)
|
v2
|
Y
|
Bruce Norskog
|
[174]
|
|
r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'
|
(24,19)
|
|
Y
|
Stefan Pochmann
|
[175]
|
Preserves X Cross
Single Parity
|
Rw' U2 F U2 F' U2 Rw' U2 Rw' U2 Rw' F U2 F' Rw'
|
(21,15)
|
|
Y
|
Bruce Norskog & Christopher Mowla
|
[]
|
|
Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw
|
(22,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r
|
(22,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z'
|
(20,17)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x'
|
(22,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R
|
(23,19)
|
|
Y
|
Christopher Mowla
|
[]
|
Algorithms which affect only the M layer
Single Parity (3 Dedge Flips)
|
r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2
|
(25,15)
|
|
N
|
|
[]
|
|
l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2
|
(25,15)
|
|
N
|
|
[]
|
|
B2 l2 U2 l' D2 l U2 B2 r2 B2 l D2 l B2 r'
|
(25,15)
|
|
N
|
|
[]
|
|
l D2 r' B2 r' D2 l2 D2 F2 r' B2 r F2 r2 D2
|
(25,15)
|
|
N
|
|
[]
|
|
B2 r2 U2 r D2 r' U2 B2 l2 B2 r' D2 r' B2 l
|
(25,15)
|
|
N
|
|
[]
|
|
r' D2 l B2 l D2 r2 D2 F2 l B2 l' F2 l2 D2
|
(25,15)
|
|
N
|
|
[]
|
|
D2 r2 F2 r' B2 r F2 D2 l2 D2 r B2 r D2 l'
|
(25,15)
|
|
N
|
|
[]
|
|
D2 l2 F2 l B2 l' F2 D2 r2 D2 l' B2 l' D2 r
|
(25,15)
|
|
N
|
|
[]
|
|
r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2
|
(25,15)
|
|
N
|
|
[]
|
|
l2 D2 l U2 l' D2 B2 r2 B2 l' U2 l' B2 r B2
|
(25,15)
|
|
N
|
|
[]
|
|
B2 l B2 r' U2 r' B2 l2 B2 D2 r' U2 r D2 r2
|
(25,15)
|
|
N
|
|
[]
|
|
l2 B2 l' F2 l B2 D2 r2 D2 l F2 l D2 r' D2
|
(25,15)
|
|
N
|
|
[]
|
|
B2 r' B2 l U2 l B2 r2 B2 D2 l U2 l' D2 l2
|
(25,15)
|
|
N
|
|
[]
|
|
r2 B2 r F2 r' B2 D2 l2 D2 r' F2 r' D2 l D2
|
(25,15)
|
|
N
|
|
[]
|
|
D2 r D2 l' F2 l' D2 r2 D2 B2 l' F2 l B2 l2
|
(25,15)
|
|
N
|
|
[]
|
|
D2 l' D2 r F2 r D2 l2 D2 B2 r F2 r' B2 r2
|
(25,15)
|
|
N
|
|
[]
|
|
l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r'
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r'
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2
|
(24,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2
|
(24,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2
|
(24,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2
|
(24,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' D2 l2 D2 F2 l' D b D' F2 D b' D M l D2 r2
|
(24,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' D2 l2 D2 F2 l' D' f D F2 D' f' D' M l D2 r2
|
(24,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 U2 M' r U2 r' B2 U2 r2 U2 M r' B2 r' B2 r B2
|
(27,17)
|
|
N
|
|
[]
|
|
r2 F2 r U2 r U2 F2 r2 U2 F2 r' U2 r U2 F2 r U2
|
(29,17)
|
|
N
|
|
[]
|
|
r2 U2 F2 r U2 F2 r U2 r2 U2 F2 r U2 r F2 r' U2
|
(29,17)
|
|
N
|
|
[]
|
|
(Rw' U' F' R' F R2 U' Lw' E' R2 E) r' (E' R2 E Lw U R2 F' R F U Rw) (r U2 r' U2) (U2 r2 U2 r2 U2 r2 U2)
|
(41,31)
|
|
N
|
Christopher Mowla
|
[]
|
|
(Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw) (D' U' F2 U D) (r' F2 r F2) (F2 r2 F2 r2 F2 r2 F2) (D' U' F2 U D)
|
(43,33)
|
|
N
|
Christopher Mowla
|
[]
|
Double Parity
|
r U2 r' U2 r' D2 r D2 r' B2 r B2 r'
|
(19,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l'
|
(20,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2
|
(23,15)
|
reParity(v2)
|
N
|
reThinking the Cube
|
[]
|
|
(r' U' F' R' F R2 U' Lw2 E L2 E') r' (E L2 E' Lw2 U R2 F' R F U r) (r U2 r' U2)
|
(35,26)
|
|
N
|
Christopher Mowla
|
[]
|
Complete 3x3x3 Scrambles
Single Parity
|
Rw B U2 B' r B2 l B2 r B' D2 B Rw
|
(17,13)
|
|
N
|
Bruce Norskog
|
[]
|
|
Rw U F2 U' Lw F2 r U2 Rw U B2 U' Rw
|
(17,13)
|
|
N
|
Bruce Norskog
|
[]
|
|
Rw U' F2 U Lw F2 r U2 Rw U' B2 U Rw
|
(17,13)
|
|
N
|
Bruce Norskog
|
[]
|
|
Uw M R D R' Bw f M d' M' Fw b M' F Uw
|
(15,15)
|
|
N
|
Bruce Norskog
|
[176]
|
|
Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'
|
(20,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'
|
(20,16)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U2 Rw' U2 Rw D2 Rw D2 Rw' F L' F' U' Rw' D2 Rw
|
(21,16)
|
|
Y
|
Christopher Mowla
|
[177]
|
|
r U' M' U M' U' M' U' M Uw2 r Uw2 U' M' U2 M' U M U2 M U M' U M U M' U' l'
|
(31,28)
|
|
N
|
Christopher Mowla
|
[178]
|
Double Parity
|
Rw F2 U2 Lw F U' R U' Rw2 B2 Rw' B2 Rw2
|
(19,13)
|
|
Y
|
Bruce Norskog
|
[]
|
|
Rw F2 U2 Lw F' U L' U Rw2 B2 Rw' B2 Rw2
|
(19,13)
|
|
Y
|
Bruce Norskog
|
[]
|
|
Rw F2 U2 Lw F U' (L' R) U' Rw2 B2 Rw' B2 Rw2
|
(19,13)
|
|
Y
|
Bruce Norskog
|
[]
|
|
Rw F2 U2 Lw F' U (L' R) U Rw2 B2 Rw' B2 Rw2
|
(19,13)
|
|
Y
|
Bruce Norskog
|
[]
|
|
Rw U2 Lw' U2 x' (Rw' U2 Lw U2)2 Lw'
|
(19,13)
|
reParity
|
Y
|
reThinking the Cube
|
[]
|
|
Rw U' b M r' D' b D l' b2 Lw E' B' Rw
|
(15,14)
|
|
N
|
Bruce Norskog
|
[179]
|
|
Uw M F R' B u d l' u d F R' B M Uw
|
(15,15)
|
|
N
|
Bruce Norskog
|
[180]
|
|
Uw M F' L B' u d l' u d F' L B' M Uw
|
(15,15)
|
|
N
|
Bruce Norskog
|
[181]
|
|
r' U M' U' M' U M' U M Uw2 l' Uw2 M' U M U' M' U M' U M U2 M' U2 r
|
(29,25)
|
|
N
|
Christopher Mowla
|
[182]
|
- It's interesting to note that the long (u,U,2R,2L,m) algorithms have the same structure as Bruce's (15,15) single parity solution.
- To see more detailed information on how most of the short algorithms were found, see Bruce Norskog's post.
- To see a large list of (U,r,R) solutions (several of the algorithms in this list are listed in this section already) that have been found by Kåre Krig, see this thread.
Non Dedge-Preserving Last Layer 2-Cycle Cases
- This section contains all of the 2-cycle cases that can occur in the last layer besides the one dedge flip.
- These are additional cases which arise in the K4 Method and other direct-solving methods.
- Algorithms marked as "Safe" are supercube safe.
In Opposite Dedges
Opposite
- All unique 8 (19,12) solutions are included. To obtain all 16, also consider their inverses.
|
r U2 r U2 F2 r F2 l' U2 l U2 r2
|
(19,12)
|
|
N
|
|
[]
|
|
r U2 l F2 D2 r D2 l' F2 r U2 r2
|
(19,12)
|
|
N
|
|
[]
|
|
r' U2 l' B2 D2 r' D2 l B2 r' U2 r2
|
(19,12)
|
|
N
|
|
[]
|
|
r' U2 r' U2 B2 r' B2 l U2 l' U2 r2
|
(19,12)
|
|
N
|
|
[]
|
|
l F2 r F2 D2 l B2 r' B2 r D2 l2
|
(19,12)
|
|
N
|
|
[]
|
|
l F2 r F2 D2 r D2 r' D2 l D2 l2
|
(19,12)
|
|
N
|
|
[]
|
|
l' B2 r' B2 D2 l' F2 r F2 r' D2 l2
|
(19,12)
|
|
N
|
|
[]
|
|
l' B2 r' B2 D2 r' D2 r D2 l' D2 l2
|
(19,12)
|
|
N
|
|
[]
|
|
r U2 r U2 M' U2 r U2 r' U2 l U2 r2
|
(20,13)
|
|
N
|
|
[]
|
|
Rw' U2 r' U2 3Rw' U2 r' U2 r U2 l' U2 Rw2
|
(20,13)
|
|
N
|
|
[]
|
|
z Rw' U l' Uw' Rw Uw l' Fw' l' Fw l2 Uw' Rw' u Rw z'
|
(16,15)
|
|
N
|
Christopher Mowla
|
[183]
|
|
l F2 r F2 l D f' D r D2 r' D' f D l2
|
(19,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b'
|
(17,16)
|
|
N
|
Christopher Mowla
|
[184]
|
|
Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F'
|
(23,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D'
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D'
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Dw' Fw l' Fw' Uw Fw l' Uw' u' R u l' u' R' Uw u l2 Fw' y'
|
(19,18)
|
|
N
|
Christopher Mowla
|
[185]
|
|
l U l U' l' U' l U l U l' D' b2 l b2 l' U2 D l' U//Safe
|
(23,20)
|
|
N
|
|
[186]
|
|
(y' L U') (r' F U2 F')4 r' (U L' y)
|
(25,21)
|
|
N
|
Floyd Newberry
|
[187]
|
|
(y' L U') (r F U2 F')4 r (U L' y)
|
(25,21)
|
|
N
|
Floyd Newberry
|
[188]
|
|
r' U' R U r' U R' U' r U R U2 R' U' r' U2 r' U2 r' U2 r'
|
(25,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
U2 l' U2 r U2 r' U2 x' U2 r' U2 r' U' l r u2 l' r' U l r u2 x//Safe
|
(29,21)
|
|
N
|
Per Kristen Fredlund
|
[]
|
Opposite/diagonal 2-Swap
- Note: The mirror case can also arise as well. One can simply apply the mirror image of this case's algorithms to get algorithms for its mirror case.
- All 36 unique (25,14) solutions are listed.
- To obtain all possible (25,14) solutions for the top/last layer, also take y2 cube rotations of all 36 and then also consider their inverses. (This gives a total of 144 algorithms.)
|
l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2
|
(21,14)
|
|
N
|
Kenneth Gustavsson
|
[]
|
|
l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2
|
(25,14)
|
|
N
|
Nicholas Ho
|
[]
|
|
r2 D2 r D2 F2 l2 F2 l' F2 D2 l2 D2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 U2 l' U2 l2 F2 l' U2 r2 U2 F2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 U2 l F2 D2 r2 D2 l' F2 r2 U2 r' F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 U2 l F2 D2 r2 D2 r F2 l2 U2 l F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 U2 r U2 r2 F2 r U2 r2 U2 F2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 U2 r U2 F2 r2 F2 r' F2 U2 r2 U2 r' F2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 B2 U2 r' U2 r2 B2 r' U2 l2 U2 B2 l B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 B2 U2 r B2 D2 l2 D2 l B2 r2 U2 r B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 B2 U2 r B2 D2 l2 D2 r' B2 l2 U2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 D2 l D2 B2 r2 B2 r' B2 D2 r2 D2 l B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 U2 l U2 B2 l2 B2 l' B2 U2 l2 U2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 U2 r' U2 F2 l2 F2 r' F2 D2 l2 D2 l' F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 B2 D2 l' D2 l2 B2 r' U2 r2 U2 B2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 U2 l' U2 B2 r2 B2 l' B2 D2 r2 D2 r' B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 F2 D2 r' D2 r2 F2 l' U2 l2 U2 F2 r' F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 U2 r B2 l2 D2 l D2 B2 r2 U2 F2 r' F2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 U2 l F2 r2 D2 r D2 F2 l2 U2 B2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 U2 l' B2 r2 D2 r' D2 B2 r2 U2 F2 r' F2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 U2 r' F2 l2 D2 l' D2 F2 l2 U2 B2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 F2 D2 l' F2 D2 l2 D2 r F2 r2 D2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 B2 D2 r' B2 D2 r2 D2 l B2 l2 D2 l B2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 B2 D2 r D2 r2 B2 l U2 r2 U2 B2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 F2 D2 l' F2 D2 l2 D2 l' F2 l2 D2 l' F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 B2 D2 r' B2 D2 r2 D2 r' B2 r2 D2 r' B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 F2 D2 l D2 l2 F2 r U2 l2 U2 F2 r' F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 U2 l B2 r2 U2 l U2 B2 r2 U2 F2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 U2 r' B2 l2 U2 r' U2 B2 r2 U2 F2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 U2 l' F2 r2 U2 l' U2 F2 l2 U2 B2 l B2
|
(25,14)
|
|
N
|
|
[]
|
|
l2 U2 r F2 l2 U2 r U2 F2 l2 U2 B2 l B2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 D2 l' D2 l2 F2 r U2 r2 U2 F2 l F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 D2 r' B2 U2 r2 U2 l' B2 r2 D2 l' F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 F2 D2 r' B2 U2 r2 U2 r B2 l2 D2 r F2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2
|
(25,14)
|
|
N
|
Nicholas Ho
|
[]
|
|
r2 B2 U2 l F2 U2 r2 U2 r' F2 r2 U2 l' B2
|
(25,14)
|
|
N
|
|
[]
|
|
r2 B2 U2 l F2 U2 r2 U2 l F2 l2 U2 r B2
|
(25,14)
|
|
N
|
|
[]
|
|
Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw'
|
(16,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw'
|
(16,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Uw Lw' Bw' r' Bw Lw2 Bw' Rw Fw' r' Fw R' Bw Lw' Uw'
|
(16,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Fw' L2 Uw b' Uw' Lw2 Uw L' Uw b' Uw' Lw Uw' l2 Fw
|
(18,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Fw' Uw B2 Rw' u Rw Bw2 Lw2 d Lw d' Lw b2 Uw' Fw
|
(19,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Uw Rw' F2 Rw' f Rw Bw2 Lw2 u Lw u' Rw u2 Rw Uw' y2
|
(19,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x'
|
(25,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Fw' L U' f Uw2 Lw2 Dw r Dw' Lw2 Uw f' Uw U L' Fw
|
(19,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r
|
(25,16)
|
|
N
|
|
[]
|
|
l' F2 D2 r' D2 F' l2 U2 l2 F' l F l2 U2 l2 F'
|
(25,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw
|
(26,17)
|
|
N
|
|
[]
|
|
Uw Rw Fw' L Fw d Fw' L' Fw Rw2 Fw2 Lw u Lw' Fw2 Rw b' Uw'
|
(21,18)
|
|
N
|
Christopher Mowla
|
[189]
|
|
x' l' Uw Rw' Uw' l Uw Fw Uw B' l2 B r' B' l2 B Uw' Fw' Rw Uw' x
|
(21,19)
|
|
N
|
Christopher Mowla
|
[190]
|
|
x' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U x//Safe
|
(25,21)
|
|
N
|
|
[193]
|
|
x l U2 l' U2 l U2 l2 U' l' U l U2 l U2 l2 U2 l U l U l U2 x'
|
(31,22)
|
|
N
|
Lucas Garron
|
[194]
|
|
x l U2 l' U2 l U2 l2 U l' U' l U2 l U2 l2 U2 l U' l U' l U2 x'
|
(31,22)
|
|
N
|
Lucas Garron
|
[195]
|
|
Rw2 U2 r' U R U r U2 r' U' R' U' r2 U R U r U2 r' U' R' U Rw2
|
(29,23)
|
|
N
|
Christopher Mowla
|
[196]
|
|
Lw' U2 l U2 l U l' r' u2 l r U' l' r' u2 x U2 r U2 l' U2 l U2 Lw x'//Safe
|
(31,23)
|
|
N
|
Per Kristen Fredlund
|
[]
|
|
Rw' U' Rw U2 Rw U2 Rw' U2 Rw' U' r U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw
|
(31,23)
|
|
N
|
Christopher Mowla
|
[197]
|
|
Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U'
|
(34,26)
|
|
Y
|
Bruce Norskog
|
[198]
|
|
Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U
|
(34,26)
|
|
Y
|
Bruce Norskog
|
[199]
|
In Adjacent Dedges
Close Unoriented
|
l2' U Lw U2 r' U2 Rw' U2 x U' r' U x' U2 x U' M' l'
|
(20,15)
|
|
N
|
Christopher Mowla
|
[200]
|
|
x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x
|
(23,15)
|
|
N
|
reThinking the Cube
|
[]
|
|
r U2 r U2 F' L F' r F L' F l' U2 l U2 r2
|
(21,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
x' l2 F U2 l U2 r' U2 r U2 3Rw U2 r U2 Rw' F' l2 x
|
(24,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
Bw l' Uw' r' Uw Lw Uw' Rw' r' Fw' r' Fw r' R Uw L' Bw'
|
(17,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
z F' Rw2 b' Uw Lw' Uw' b Uw b Lw b' Lw' b' Lw Uw' Rw2 F z'
|
(19,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
z F' Lw2 Uw Bw' l Bw Uw' Bw' Lw Uw l Uw' Lw' l' Bw Lw2 F z'
|
(19,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
z F' Rw2 z' Rw Bw' l Bw Rw' Bw' Lw Dw l Dw' Lw' l' Fw Rw2 F z'
|
(19,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' b Uw2 Lw Uw f' Uw' Lw' Uw f' Lw f' Lw' f2 Uw b' Lw
|
(19,17)
|
|
N
|
Christopher Mowla
|
[201]
|
|
r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2
|
(25,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(L U2)(r' F U2 F')4 r' (U2 L')
|
(27,21)
|
|
N
|
Floyd Newberry
|
[202]
|
|
l U l U l' U' l' U' l D f2 l' f2 l U2 D' l U' l' U' l2//Safe
|
(25,21)
|
|
N
|
|
[204]
|
|
x' l' Rw' U2 Rw U' L' U' r' U L U Rw' U2 Rw U' L' U' r2 U L U l x
|
(25,22)
|
|
N
|
Christopher Mowla
|
[]
|
|
z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R2 U r' U' R2 U Fw' L' Fw2 r2 Uw' z
|
(27,22)
|
|
N
|
Christopher Mowla
|
[205]
|
|
l' F2 l F2 U' Rw U2 l U2 Rw' B' M U' Lw2 F2 r2 F2 Lw2 U M' B U
|
(31,22)
|
|
N
|
Christopher Mowla
|
[]
|
Far Unoriented
|
l2' U' Lw U2 r' U2 Rw' U2 x U r' U' x' U2 x U M' l'
|
(20,15)
|
|
N
|
Christopher Mowla
|
[206]
|
|
x Rw2 F' U2 l U2 r' U2 r U2 F2 r F2 l' F Rw2 x'
|
(23,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
r U2 r U2 F R' F r F' R F' l' U2 l U2 r2
|
(21,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
x Rw2 F' U2 l U2 r' U2 r U2 3Rw U2 r U2 Rw' F Rw2 x'
|
(24,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw r z l Fw' Uw Fw l' Fw' l' Uw' l Uw l Uw' Fw z' Rw' r'
|
(17,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw r y Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Uw' Rw' r'
|
(17,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw r Uw' Fw l' Fw' Uw Fw Lw' Uw' l' Uw Lw l Fw' Lw' r'
|
(17,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw
|
(21,17)
|
|
N
|
Christopher Mowla
|
[207]
|
|
r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2
|
(23,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw2 U' M U2 l U2 r' U2 r U2 M' U2 r U2 l' U Lw2
|
(25,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
y z Dw' 3Rw' D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' 3Rw Uw y x
|
(19,18)
|
|
N
|
Christopher Mowla
|
[208]
|
|
x' U2 l' U2 l U2 r' U2 r B2 r' F D2 F' l' F D2 F' r B2 x
|
(27,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
z' Fw' Uw r' Uw' Fw Uw r' Fw2 U L U' Fw r' Fw' U L' U' Fw2 r2 Uw' z
|
(23,20)
|
|
N
|
Christopher Mowla
|
[211]
|
|
Rw' U R U r2 U' R' U' Rw' U2 Rw U R U r U' R' U' Rw' U2 Rw2
|
(25,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
l U' l U' l' U l' U l D' b2 l' b2 l U2 D l U l' U l2//Safe
|
(25,21)
|
|
N
|
|
[212]
|
|
z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R U r' U' R' U Fw' L' Fw2 r2 Uw' z
|
(25,22)
|
|
N
|
Christopher Mowla
|
[213]
|
|
Rw r U' R' U r' U' R U2 R' U r U2 r U2 r U2 r2 U R U' Rw'
|
(27,22)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 R U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw' U2 Rw' R'
|
(30,23)
|
|
N
|
Christopher Mowla
|
[]
|
Oriented
- Note: The mirror case can also arise as well. One can simply apply the mirror image of this case's algorithms to get algorithms for its mirror case.
|
y' Fw2 l Uw' Bw Uw l' Uw' l' Bw' l Bw l Bw' Uw Fw2 y
|
(17,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2
|
(17,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
y' z' Fw2 Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Dw' Fw2 z y
|
(17,15)
|
|
N
|
Christopher Mowla
|
[214]
|
|
Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2
|
(17,15)
|
|
N
|
Christopher Mowla
|
[215]
|
|
y' z' Fw' l' Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 l Fw z y
|
(19,15)
|
1st 15 Mover
|
N
|
Christopher Mowla
|
[216]
|
|
Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw'
|
(16,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
y' Bw' R Dw r' Dw' Rw' Bw Rw' R' Dw r' Dw' Rw2 Fw' u Fw y
|
(17,16)
|
|
N
|
Christopher Mowla
|
[217]
|
|
y' Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw' y
|
(19,16)
|
|
N
|
Christopher Mowla
|
[218]
|
|
r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw'
|
(19,16)
|
|
N
|
Christopher Mowla
|
[219]
|
|
z x2 Rw' Uw l' Uw' Rw Uw l' Fw2 R Fw l' Fw' R' Fw2 l2 Uw' x2 z'
|
(19,16)
|
|
N
|
Christopher Mowla
|
[220]
|
|
y' Bw' Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r Bw y
|
(19,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
y' l' r' U Rw U2 l' U2 Lw' U2 x' U' l' U F2 U' M' l' y
|
(20,16)
|
|
N
|
Christopher Mowla
|
[221]
|
|
z Uw' Rw Uw2 l' Uw r' Uw' l Uw2 R' Uw Bw2 Uw' r' Uw Bw2 z'
|
(20,16)
|
|
N
|
Christopher Mowla
|
[]
|
|
x l' U L U l' U' L' U' F2 l' F2 r U2 r' U2 l2 x'
|
(21,16)
|
|
N
|
Christopher Mowla
|
[222]
|
|
(L' B') l' U2 l' U2 x U2 l' U2 x' r U2 r' U2 l2 (B L)
|
(23,16)
|
|
N
|
|
[]
|
|
x l' U L U l' U' L' U' x U2 l' U2 l U2 r' U2 l r x2
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
x l' U L U l' U' L' U' M' U2 l' U2 l U2 r' U2 l2 x'
|
(22,17)
|
|
N
|
Christopher Mowla
|
[223]
|
|
x l U2 l U2 M U L U l U' L' U' l' U2 r U2 l2 x'
|
(22,17)
|
|
N
|
Christopher Mowla
|
[224]
|
|
Rw U2 l U2 3Lw U L' U l U' L U' l' U2 r U2 Lw2 x'
|
(22,17)
|
|
N
|
Christopher Mowla
|
[225]
|
|
x' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' r' Fw Rw Uw' r2 x
|
(19,18)
|
|
N
|
Christopher Mowla
|
[226]
|
|
y' l U F2 U' l U F2 l F L F l F' L' F' l' U' l2 y
|
(21,18)
|
|
N
|
Christopher Mowla
|
[]
|
|
x Lw' L' U L' U l' U' L U' M' U2 l' U2 l U2 r' U2 Lw2 x'
|
(23,18)
|
|
N
|
Christopher Mowla
|
[227]
|
|
z' r' Uw Bw Uw' Bw L Bw r Bw' L' Bw' Uw Bw' Lw Uw' r Uw Lw' Uw' z
|
(19,19)
|
|
N
|
Christopher Mowla
|
[228]
|
|
r Uw' Lw Uw r' Uw' Fw' Uw' B Rw2 B' l B Rw2 B' Uw Fw Lw' Uw
|
(21,19)
|
|
N
|
Christopher Mowla
|
[]
|
|
y' x Lw' U' R' U' l2 U R U Lw' U2 Lw U' R' U' l U R U Lw' U2 Lw2 x' y
|
(25,21)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U' r U' r' D b2 r b2 r' U2 D' r' U' r U' r U r' U r2//Safe
|
(25,21)
|
|
N
|
|
[229]
|
|
x l2 U2 Lw U l U' Lw' U2 Lw' U2 Lw U2 Lw U l2 U' Lw' U2 Lw' U2 Lw' L2 x'
|
(30,22)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U Rw' U Rw' U Rw U2 Rw U2 Rw' U Rw U' Rw' U' Rw' U2 Rw' U2 Rw U2 Rw' U Rw2 U2
|
(34,26)
|
|
Y
|
Bruce Norskog
|
[]
|
|
y Rw' U2 r' Rw2 U2 Rw U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw r U2 Rw y'
|
(37,27)
|
|
N
|
Christopher Mowla
|
[]
|
|
U' Rw' U Rw U' Rw2 U2 Rw' U2 Rw U2 Rw' U Rw2 U' Rw U Rw' U' Rw U2 Rw U2 Rw2 U Rw U' Rw
|
(36,28)
|
5x5 Alg
|
Y
|
Ben Whitmore
|
[]
|
Non Dedge-Preserving Last Layer 4-Cycle Cases in Two Dedges
- These are all of the other 4-cycles that can occur in two dedges in the last layer besides double parity and adjacent double parity.
- These are additional cases which arise in the K4 Method and other direct-solving methods.
In Opposite Dedges
Checkerboard
|
Rw2 U2 r' E2 r E2 r' U2 Rw2
|
(15,9)
|
|
N
|
Tom Rokicki & Ed Trice
|
[230]
|
|
(f2 u' r2 Uw2 S') r (S Uw2 r2 u f2)
|
(17,11)
|
|
N
|
Christopher Mowla
|
[231]
|
|
(f2 u r2 Uw2 S') r (S Uw2 r2 u' f2)
|
(17,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 U2 r S2 r S2 r' U2 l2 f2 M2 f2
|
(21,12)
|
|
N
|
Christopher Mowla
|
[232]
|
|
r2 U2 r S2 r S2 r' U2 l2 b2 M2 b2
|
(21,12)
|
|
N
|
|
[]
|
|
r S' L2 S r U2 r U2 r S' L2 S r
|
(17,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
r S R2 S' r U2 r U2 r S R2 S' r
|
(17,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
(Rw2 Uw U S Lw2 u2) r (u2 Lw2 S' U' Uw' Rw2)
|
(19,13)
|
|
N
|
Christopher Mowla
|
[233]
|
|
(Rw2 Uw' U' S Lw2 u2) r (u2 Lw2 S' U Uw Rw2)
|
(19,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 S r' U2 r' U2 r' U2 r' U2 r' S' Rw2
|
(19,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 S' r' U2 r' U2 r' U2 r' U2 r' S Rw2
|
(19,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'
|
(21,13)
|
Alg(v1a)
|
N
|
|
[]
|
|
Rw' U2 r2 U2 Rw U2 r' U2 Rw U2 r2 U2 Rw'
|
(21,13)
|
Alg(v1b)
|
N
|
|
[]
|
|
r' U2 Rw2 U2 r U2 r' U2 r U2 Rw2 U2 r'
|
(21,13)
|
Alg(v1c)
|
N
|
|
[]
|
|
Rw' U2 r2 U2 r U2 r' U2 Rw U2 r2 U2 r'
|
(21,13)
|
Alg(v1d)
|
N
|
|
[]
|
|
l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l'
|
(21,13)
|
Alg(v2a)
|
N
|
|
[]
|
|
Lw' U2 l2 U2 Lw U2 l' U2 Lw U2 l2 U2 Lw'
|
(21,13)
|
Alg(v2b)
|
N
|
|
[]
|
|
l' U2 Lw2 U2 l U2 l' U2 l U2 Lw2 U2 l'
|
(21,13)
|
Alg(v2c)
|
N
|
|
[]
|
|
Lw' U2 l2 U2 l U2 l' U2 Lw U2 l2 U2 l'
|
(21,13)
|
Alg(v2d)
|
N
|
|
[]
|
Bowtie/Hourglass
|
r2 U2 r B2 r B2 E2 l' B2 l B2 D2 l' y2
|
(21,13)
|
|
N
|
Oscar Roth Andersen
|
[234]
|
|
r U2 r U2 M' U2 r U2 r' U2 M r' Uw2 r2 u2
|
(23,15)
|
|
N
|
|
[]
|
|
r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2
|
(25,15)
|
|
N
|
|
[]
|
|
r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2
|
(25,16)
|
|
N
|
|
[]
|
|
(B' R Uw' u' r' f2 Rw2 E) f' (E' Rw2 f2 r u Uw R' B)
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
(B' R Uw' u' r f2 Rw2 E) f' (E' Rw2 f2 r' u Uw R' B)
|
(21,17)
|
|
N
|
Christopher Mowla
|
[]
|
|
r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r'
|
(26,17)
|
|
N
|
|
[]
|
In Adjacent Dedges
Checkboard
|
F2 Uw' F2 Rw2 Uw2 R2 z' S u F' B' Uw2 Rw2 Uw' F2
|
(22,14)
|
|
N
|
Tom Rokicki
|
[]
|
|
(F U' F' Rw2 U2) r' E2 r E2 r' (U2 Rw2 F U F')
|
(21,15)
|
|
N
|
Tom Rokicki & Ed Trice
|
[]
|
|
(R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2)
|
(21,15)
|
|
N
|
Christopher Mowla
|
[236]
|
|
(R2 Uw' u' r f2 Rw2 E) f (E' Rw2 f2 r' u Uw R2)
|
(21,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
(Rw' F2 M2 F) U2 l U2 l2 U2 l U2 l (F' M2 F2 Rw)
|
(25,16)
|
|
N
|
Christopher Mowla
|
[237]
|
|
(Lw' U2 M2 U) M U2 l U2 l2 U2 l U2 r (U' M2 U2 Lw)
|
(26,17)
|
|
N
|
Christopher Mowla
|
[238]
|
|
(R B) r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' (B' R')
|
(30,21)
|
|
N
|
|
[]
|
Bowtie/Hourglass
|
(R B) Rw2 U2 r' E2 r E2 r' U2 Rw2 (B' R')
|
(19,13)
|
|
N
|
Tom Rokicki & Ed Trice
|
[]
|
|
(R Fw f r u2 Rw2 S) u' (S' Rw2 u2 r' Fw' f' R')
|
(19,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
(R Fw f r' u2 Rw2 S) u' (S' Rw2 u2 r Fw' f' R')
|
(19,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
F' Lw U D Lw2 Bw2 Rw' R' U' D B2 Lw2 Fw2 D2 Lw' F
|
(21,15)
|
|
Y
|
Tom Rokicki
|
[]
|
|
(Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw)
|
(25,16)
|
|
N
|
Christopher Mowla
|
[239]
|
|
R B r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r B' R'
|
(25,17)
|
|
N
|
|
[]
|
|
(r U2 M2 U') M' U2 l' U2 l2 U2 l' U2 r' (U M2 U2 r')
|
(26,17)
|
|
N
|
Christopher Mowla
|
[240]
|
|
y2 Fw' r2 Uw2 L' Uw' U' R U F' R' F r' F' R F U' R' Uw U L Uw2 r' Fw Uw Fw' r' Fw Uw' y2
|
(31,28)
|
|
N
|
Christopher Mowla
|
[241]
|
Move count comparison of all last layer 2-cycles and 2 dedge 4-cycles
- Since there is disagreement among cubers about whether lowest slice quarter turn moves (BQTM) or lowest slice half turn moves (BHTM) defines the "optimal algorithm", the table below categorizes all 2-cycle and 4-cycle cases (in two dedges) on the 4x4x4 by the average of the two.
- Algorithms optimal in BHTM need not be the algorithm with the lowest average of BQTM and BHTM, and algorithms optimal in BQTM turns need not be the algorithm with the lowest average of BQTM and BHTM. Therefore the average for a given case might be from an algorithm optimal in BQTM moves, optimal in BHTM moves or optimal in both.
- Of course this ranking is based off of required moves. It is not based off of the amount of time it takes to solve a case.
- These results will change in the future if shorter algorithms are found for any of these cases.
- The term optimal average below does not necessarily mean the average of the minimum BQTM and BHTM (if an algorithm has both the fewest BQTM and BHTM, then yes). It's an average of the BQTM and BHTM of one algorithm. Should one algorithm have the least BQTM but not the least BHTM, we do not average the shortest numbers from two different algorithms.
- The table shows that the "worst case" is Adjacent Double Parity, and that the "easiest case" is the Checkerboard (in two opposite edges).
Algorithms which do not preserve the centers
- These algorithms are for fixing the wing edges, but they do not preserve the centers. Many of these algorithms can be used in solving methods such as the Cage Method.
One Dedge Flip
|
Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2
|
(17,12)
|
|
N
|
Michael Gottlieb
|
[242]
|
|
Rw2 U r' U' B2 U r U r' U2 B2 Rw2
|
(17,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 3Dw l U' R2 U l' U y r U2 F2 Rw2
|
(17,12)
|
|
N
|
Christopher Mowla
|
[243]
|
|
Rw2 F r F' Uw2 B l' B l B2 Uw2 Rw2
|
(17,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2
|
(21,13)
|
|
N
|
|
[]
|
|
Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2
|
(21,13)
|
|
N
|
|
[]
|
|
l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2
|
(21,13)
|
|
N
|
|
[]
|
|
r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r
|
(15,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r
|
(21,14)
|
|
N
|
Lucas Garron
|
[]
|
|
r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r
|
(21,14)
|
|
N
|
Nicholas Ho
|
[]
|
|
Rw' l' Uw Rw' Uw' l Uw y Lw Dw r' Dw' Lw' y' Rw Uw' Rw
|
(15,15)
|
|
N
|
Christopher Mowla
|
[244]
|
|
x r R' U' Rw U' r U Rw' r' U R U' r U r' x'
|
(15,15)
|
|
N
|
|
[]
|
Opposite Double Parity
- Most of these algorithms are exactly the same as the one dedge flip ones except that the extra quarter turn is inverted.
|
Rw' F' u F' D2 F u' F' l D2 F2 Rw
|
(15,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U r' U' B2 U r U r U2 B2 Rw2
|
(17,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U' r' U B2 U' r U' r U2 B2 Rw2
|
(17,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 3Dw l U' R2 U l' U y r' U2 F2 Rw2
|
(17,12)
|
|
N
|
Christopher Mowla
|
[245]
|
|
x' Rw2 F2 r F2 r U2 l' U2 l U2 r' U2 Rw2 x
|
(21,13)
|
|
N
|
|
[]
|
|
l' y' Uw2 Rw2 Uw' l' Uw Rw2 Uw' l Uw' y U2 l U2 l'
|
(18,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 b2 D' f' D B2 D' f U' f U D Bw2 Rw2
|
(19,14)
|
|
N
|
Christopher Mowla
|
[]
|
|
l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2
|
(21,14)
|
|
N
|
Nicholas Ho
|
[]
|
Adjacent Double Parity
|
(r2 U' Rw U' R' U') r' (U R U Rw' U r2)
|
(15,13)
|
|
N
|
Christopher Mowla
|
[246]
|
|
(r2 U F2 U' r' F2) r (F2 r U F2 U' r2)
|
(19,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw
|
(16,14)
|
|
N
|
Christopher Mowla
|
[247]
|
|
(x Uw F U r' U R' U) r (U' R U' r U' F' Uw' x')
|
(15,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
x' r2 U' Rw U' l' U2 l' U2 l' U2 l2 U' Rw' U r2 x
|
(21,15)
|
|
N
|
Christopher Mowla
|
[]
|
Three Flips
Single Parity
|
(r2 F2 U) r U2 r' U2 r U2 r' U2 r (U' F2 r2)
|
(23,15)
|
|
N
|
Christopher Mowla
|
[]
|
|
(r2 U2 F' M' U) r U2 r' U2 r U2 r' U2 r (U' M F U2 r2)
|
(27,19)
|
|
N
|
Christopher Mowla
|
[]
|
Double Parity
|
(r' U' F' R' F R2 U') r' (U R2 F' R F U r) (r U2 r' U2)
|
(23,18)
|
|
N
|
Christopher Mowla
|
[]
|
2-Cycles In Two Adjacent Edges (in the M ring)
Opposite
|
l U' l' U' F2 U l U' F2 U2
|
(13,10)
|
|
N
|
|
[]
|
|
l U l' U F2 U' l U F2 U2
|
(13,10)
|
|
N
|
|
[]
|
|
z2 y' U2 R2 U l U' R2 U l' U y r z2
|
(13,10)
|
|
N
|
|
[]
|
|
l F2 r' U2 l U2 l' U2 r U2 F2
|
(17,11)
|
|
N
|
|
[]
|
|
l' U Lw' U L U' l' U L' U' Lw l U'
|
(13,13)
|
|
N
|
|
[]
|
Diagonal
- Some of these are nearly the same as the one dedge flip algorithms.
|
Lw' U' l U B2 U' l' U' l U2 B2 Lw
|
(15,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' U l U' B2 U l' U l U2 B2 Lw
|
(15,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' 3Dw' r' U L2 U' r U' y' l' U2 F2 Lw
|
(17,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
x' U Rw' U r' U' Rw r U' R' U r' U' R x
|
(13,13)
|
|
N
|
Marc Waterman
|
[]
|
|
x' R U Rw' U r' U' Rwr U' R' U r' U' x
|
(13,13)
|
|
N
|
Marc Waterman
|
[]
|
|
x' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' x
|
(13,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' 3Dw' r' U L2 U' r D' r' U D L2 y' Lw
|
(15,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' U l U' B2 U l' U' B2 D2 r' D2 Lw
|
(17,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
Lw' 3Dw' r' U L2 U' r U D2 y' r' D2 F2 Lw
|
(17,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
(x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x)
|
(19,13)
|
|
N
|
|
[]
|
|
Lw' U2 l' U2 r U2 r' U2 l F2 l' F2 Lw
|
(19,13)
|
|
N
|
|
[]
|
|
Lw' U2 l' U2 r U2 r' U2 l B2 r' B2 Lw
|
(21,13)
|
|
N
|
|
[]
|
|
M' l' U2 l' U2 l U2 r' U2 l U2 l' U2 l
|
(20,14)
|
|
N
|
Nicholas Ho
|
[]
|
2-Cycles In Two Opposite Edges (in the M Ring)
Directly Opposite
|
y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw
|
(13,12)
|
|
N
|
Christopher Mowla
|
[]
|
|
U' Rw' U r' U' Rw r U' R' U r' U' R U2
|
(15,14)
|
|
N
|
François Courtès
|
[]
|
Opposite/Diagonal 2-Swap
- These are the same as the one dedge flips but without first and last moves.
|
U r' U' B2 U r U r' U2 B2
|
(13,10)
|
|
N
|
Christopher Mowla
|
[]
|
|
U' r' U B2 U' r U' r' U2 B2
|
(13,10)
|
|
N
|
Christopher Mowla
|
[]
|
|
3Dw l U' R2 U l' D l U' D' R2 y
|
(13,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
U' r' U B2 U' r U B2 D2 l D2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
3Dw l U' R2 U l' U' D2 y l D2 F2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
x' U2 l U2 r' U2 r U2 l' F2 r F2 x
|
(17,11)
|
|
N
|
|
[]
|
|
U2 r U2 l' U2 l U2 r' F2 r F2
|
(17,11)
|
|
N
|
|
[]
|
|
U2 r U2 l' U2 l U2 r' B2 l B2
|
(17,11)
|
|
N
|
|
[]
|
4-Cycles in Adjacent Edges (in the M ring)
Checkboard
|
Rw2 U2 r U2 Rw2
|
(9,5)
|
|
N
|
Marc Waterman
|
[]
|
Bowtie/Hourglass
|
(y L' U B' Rw2 U2) r' (U2 Rw2 B U' L y')
|
(15,11)
|
|
N
|
|
[]
|
|
(y L F' U Rw2 F2) r (F2 Rw2 U' F L' y')
|
(15,11)
|
|
N
|
|
[]
|
|
r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x
|
(19,12)
|
|
N
|
Nicholas Ho
|
[]
|
|
r2 U2 r U2 x' D2 r' U2 r D2 r' U2 r' x
|
(19,12)
|
|
N
|
Kenneth Gustavsson
|
[]
|
Algorithms which do not preserve F3L OR the centers
- These algorithms are least practical when it comes to use of parity algorithms, and therefore they are mentioned here for theoretical purposes only. They have fewer moves than any other OLL parity algorithm forms.
Single Parity
|
Rw2 U r' U' B2 U r U r' B2 Rw2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U' r' U B2 U' r U' r' B2 Rw2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U f U' B2 U f' U l B2 Rw2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[248]
|
|
r' U' R U' r U2 r U2 r U' R' U' r'
|
(15,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U' R U r' U2 r' U2 r' U R' U' r'
|
(15,13)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U' R U r' F2 U2 r U2 F2 r' U R' U' r'
|
(19,15)
|
|
N
|
Christopher Mowla
|
[]
|
Double Parity
|
r 3Dw r' 3Dw F2 3Dw' r 3Dw l' F2 l
|
(13,11)
|
|
N
|
Christopher Mowla
|
[249]
|
|
Rw U R B R' l Fw2 r' Fw2 U' Rw2 x
|
(14,11)
|
|
N
|
Bruce Norskog
|
[250]
|
|
Rw U R B l Fw2 r' Fw2 R' U' Rw2 x
|
(14,11)
|
|
N
|
Bruce Norskog
|
[251]
|
|
Rw2 U r' U' B2 U r U r B2 Rw2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U' r' U B2 U' r U' r B2 Rw2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw2 U f U' B2 U f' U l' B2 Rw2
|
(15,11)
|
|
N
|
Christopher Mowla
|
[252]
|
|
Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2
|
(21,15)
|
|
Y
|
Christopher Mowla
|
[253]
|
|
Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw'
|
(21,15)
|
|
Y
|
Kåre Krig & Christopher Mowla
|
[254]
|
Either single parity or double parity
- The following list of algorithms can be considered either single parity or double parity. Just exchange the last move Rw' with Lw', Rw with Lw, and so forth.
|
Rw' U' R' U' Rw F' R' F' Rw'
|
(9,9)
|
|
Y
|
Christopher Mowla
|
[255]
|
|
Rw' U' R U' Rw F' R F' Rw'
|
(9,9)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U' R U' r' D' R D' Rw
|
(9,9)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U R' U Rw U F2 U Rw'
|
(10,9)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw U' R U' Rw' D' R2 D' Lw
|
(10,9)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U' F2 U' r B' R B' Lw'
|
(10,9)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw U' L U' F2 Lw U' R U' Rw'
|
(11,10)
|
|
Y
|
Christopher Mowla
|
[257]
|
|
Rw U' L' U' F2 l U L U Rw'
|
(11,10)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw' U' L' U' Rw F2 U L U Rw
|
(11,10)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U' L' U' B2 Rw' B R B Rw
|
(11,10)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U R2 U Rw F2 U L' U Rw
|
(12,10)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U F' U l U2 F' U2 F Rw'
|
(12,10)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw U' R' U' Rw' D' L D L' D' Lw
|
(11,11)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw B U F' R b' M R E' R Bw
|
(11,11)
|
|
N
|
Bruce Norskog & Christopher Mowla
|
[258]
|
|
Rw U R' U R r' U2 B' L' B' Rw'
|
(12,11)
|
|
N
|
Christopher Mowla
|
[259]
|
|
l' B' u B' D2 B u' B' l D2 l'
|
(13,11)
|
|
N
|
Christopher Mowla
|
[]
|
|
Rw F U' R U Rw' F U R F' U Rw
|
(12,12)
|
|
Y
|
Christopher Mowla
|
[]
|
|
Rw' U F' L F Rw F R B' E y B Rw'
|
(12,12)
|
|
Y
|
Christopher Mowla
|
[260]
|
|
Rw S' F L F' U b' U E M U Bw
|
(12,12)
|
|
N
|
Bruce Norskog & Christopher Mowla
|
[261]
|
|
Rw' U' F R' F' Rw F' U' F2 R U Rw'
|
(13,12)
|
|
Y
|
Christopher Mowla
|
[262]
|
2-Cycles
- Although the following list of algorithms is not "OLL parity", where dedge preservation is important, they are the briefest 2-cycle algorithms yet to be found. They do not preserve F3L or the centers.
- These algorithms are nothing more than 2-cycle algorithms which don't preserve centers with beginning and ending outer layer turns omitted.
|
r' U' B2 U r U r'
|
(8,7)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U B2 U' r U' r'
|
(8,7)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U L2 U' r D' r'
|
(8,7)
|
|
N
|
Christopher Mowla
|
[]
|
|
r' U' R2 U r D r'
|
(8,7)
|
|
N
|
Christopher Mowla
|
[]
|
External Links
PLL Parity Algorithms
OLL Parity Algorithms
SuperCube Parity Algorithms
OLL parity algorithms which do not preserve F3L
K4 Method Parity Algorithms
Cage Method Parity Algorithms
Comprehending and making your own parity algorithms
General Parity Theory
Preventing/Avoiding Parity
Miscellaneous