Difference between revisions of "PLL"
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===R Permutation : a=== | ===R Permutation : a=== |
Revision as of 02:52, 21 September 2018
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PLL is the acronym for Permutation of the Last Layer. Permutation of the Last Layer is the last step of many speedsolving methods. In this step, the pieces on the top layer have already been oriented (OLL) so that the top face has all the same color, and they can now be moved into their solved positions. There are 21 PLLs (13 if you count mirrors and inverses as being the same) and each one is named after a letter. The following page gives a list of all of the PLLs, along with a picture and a list of common algorithms for each one. The diagrams below are top views of where you want the pieces to go. For example, the T Permutation (or 'T perm') swaps the UL and UR edges, as well as the UFR and UBR corners. If you like, try out all of the available algorithms for a case to see which one feels the fastest to you - the same algorithm may not be the fastest for everyone, and shorter algorithms are not always faster than longer ones. PLL is a subgroup of ZBLL.
Permutations of corners only |
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Permutations of edges only |
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Permutations of corners and edges |
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See also
External links
- AlgDB PLL Page
- "PLL 2SR: A guide to recognizing PLLs by looking at only two sides (V2.0)" (Comparative pattern analysis of PLLs from all angles, by Parity Case)
- Recognize PLLs by patterns (PLL patterns and Algs by RiDo)
- PLL Cheat Sheet (Printable PDF of all PLL algorithms on a single page)
- Speedsolving.com: Recognizing PLLs from only 2 sides
- Recognizing PLLs from only 2 sides - Improved version
- YouTube series
PLL algorithms
Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. (how to add algorithms) Click on an algorithm (not the camera icon) to watch an animation of it. |
Permutations of Edges Only
This subgroup, EPLL is used as a substep for many speedsolving methods, for example in the VH method (COLL).
H Permutation
Name: H-PLL, X-PLL |
PLL | M2' U M2' U2 M2' U M2' | [1] |
PLL | M2' U' M2' U2' M2' U' M2' | [2] |
PLL | R2' S2 R2 U' R2' S2 R2 |
PLL | R2' U2 R' U2 R2' U2' R2' U2 R' U2 R2' | [3] |
PLL | M2' U2 M2' U' M2' U2 M2' |
PLL | M2' U2 M2' U M2' U2 M2' |
PLL | R2 U2 R U2 R2 U2 R2 U2 R U2 R2 |
PLL | L2 U2 L' U2 L2 U2 L2 U2 L' U2 L2 |
PLL | L R U2 L' R' F' B' U2 F B |
PLL | L R U2 L' R' (y) L' R' U2 L R |
PLL | S R U2 R2 U2 R2 U2 R S' |
PLL | F2 M2' F2 U' F2 M2' F2 |
PLL | M2' u M2' u2 M2' u M2' |
PLL | M2' u' M2' u2' M2' u' M2' |
PLL | (M2' U)5 M2' |
PLL | x2 (R U R' U' D)30 x2 |
U Permutation : a
Name: U-PLL a |
PLL | M2 U M' U2 M U M2 |
PLL | (y2) M2' U M U2 M' U M2' | [4] |
PLL | (y2) R U' R U R U R U' R' U' R2 | [5] |
PLL | (y) R2 U' S' U2' S U' R2 |
PLL | (y) R2 U' R2 S R2 S' U R2 |
PLL | R2 U' R' U' R U R U R U' R |
PLL | R U R' U R' U' R2 U' R' U R' U R | [6] |
PLL | (y') M2 u' M u2 M u' M2 |
PLL | (y) M2 u' M' u2 M' u' M2 |
PLL | (y2) F2 U' (L R') F2 (L' R) U' F2 |
PLL | (y2) F2 U' M' U2 M U' F2 |
PLL | R U R' U' L' U' L U2 R U' R' U' L' U L |
PLL | (R' E' R) U (R' E R) U (R' E' R) U2 (R' E R) |
PLL | (R U R' U')(L' U' L) U2 (R U' R')(U' L' U L) |
U Permutation : b
Name: U-PLL b |
PLL | M2 U' M' U2 M U' M2 |
PLL | (y2) M2 U' M U2 M' U' M2 | [7] |
PLL | R' U R' U' R3 U' R' U R U R2 | [8] |
PLL | (y2) R2 U R U R' U' R' U' R' U R' |
PLL | (y) R2 U' S R2 S' R2 U R2 |
PLL | R' U R' U' R' U' R' U R U R2 |
PLL | (y2) L' U L' U' L' U' L' U L U L2 |
PLL | (y') M2 u M' u2 M' u M2 |
PLL | (y2) R' U' R U' R U R2 U R U' R U' R' |
PLL | (y2) L' U' L U R U R' U2 L' U L U R U' R' |
PLL | (z) U2' R U R U' R' U' R' U' R U' (z') |
PLL | (y2 z) U' R U' R' U' R' U' R U R U2' (z') |
PLL | (y2) F2 U M' U2 M U F2 |
PLL | (R' E' R) U2 (R' E R) U' (R' E' R) U' (R' E R) |
PLL | (L' U' L U)(R U R') U2' (L' U L)(U R U' R') |
Z Permutation
Name: Z-PLL |
PLL | (y) M2' U2 M U M2' U M2' U M |
PLL | M2' U2 M U' M2' U' M2' U' M | [9] |
PLL | M2' U M2' U M' U2 M2' U2 M' |
PLL | (y) M2' U' M2' U' M' U2 M2' U2 M' |
PLL | M2' U M2' U M U2 M2' U2 M |
PLL | (y) M2' U' M2' U' M U2 M2' U2 M |
PLL | M2' u M2' u' S M2' S' |
PLL | M' U' M2' U' M2' U' M' U2 M2' |
PLL | (y) M' U M2' U M2' U M' U2 M2' |
PLL | M U' M2' U' M2' U' M U2 M2' |
PLL | (y) M U M2' U M2' U M U2 M2' |
PLL | M2' U' M U2 M2' U2 M U M2' |
PLL | R' U' R2 U R U R' U' R U R U' R U' R' |
PLL | R U R' U R' U' R' U R U' R' U' R2 U R |
PLL | (y) R' U' R U' R U R U' R' U R U R2 U' R' |
PLL | R B' R' B F R' F B' R' B R F2 |
PLL | M2' U2 M' U' M2' U' M2' U' M' |
PLL | (y) M2' U2 M' U M2' U M2' U M' |
PLL | M' U2 M2' U2 M' U' M2' U' M2' |
PLL | (y) M' U2 M2' U2 M' U M2' U M2' |
PLL | M U2 M2' U2 M U' M2' U' M2' |
PLL | (y) M U2 M2 U2 M U M2 U M2 |
PLL | M2' U M2' U' E2 M' E2 M' |
PLL | (y) M2' U' M2' U E2 M' E2 M' |
PLL | M2' U M' E2 M' E2 U' M2' |
PLL | M2' U M2' U' M E2 M D2 |
PLL | E2 M' E2 M' U M2 U' M2 |
PLL | M2' U M2' U M2' F2 M2' F2 |
Permutations of Corners Only
This is also known as CPLL (Corner Permute Last Layer). There is one more case in this group, the X-PLL but that is the same alg as H-PLL + U2, see EPLL.
Aa Permutation
Name: A-PLL a |
Alg.01(v1) | (x) R' U R' D2 R U' R' D2 R2 (x') | [10] |
Alg.01(v2) | l' U R' D2 R U' R' D2 R2 (x') | [11] |
Alg.01(v3) | (x') R' D R' U2 R D' R' U2 R2 (x) |
Alg.02(v2) | (y x') R2 D2 R' U' R D2 R' U R' |
Alg.02(v3) | (y' x) L2 D2 L' U' L D2 L' U L' (x') |
Alg.04(v1) | R' U2 R2 U' L' U R' U' L U R' U2 R |
Alg.05(v1) | R U' L' U' L2 U' R2 U L2 U' R2 U2 L U R' |
Alg.06(v1) | (y') R U R' F' r U R' U' r' F R2 U' R' |
Alg.07(v1) | (y') r U r' U' r' F r2 U' r' U' r U r' F' | [12] |
Alg.08(v1) | (y) R L D2 R' U' R D2 R' U L' |
Alg.09(v1) | (y') R U R' U' R' F R U R' U' R' F' R U R2 U' R' |
Alg.10(v1) | (y') R U R' U R2 D' R U' R' D R U R U' R U' R' |
Alg.11 | x L2 D2 L' U' L D2 L' U L' x' |
Alg.12 | R' F R' B2 R F' R' B2 R2 |
Ab Permutation
Name: Ab-PLL |
PLL | (x) R D' R U2 R' D R U2 R2 (x') |
PLL | (y')(L' U' L F) (l' U' L U l) F' L2 U L |
PLL | (x') R U' R D2 R' U R D2 R2 (x) |
PLL | (y' x) R2 D2 R U R' D2 R U' R (x') | [13] |
PLL | (y2 x) L U' L D2 L' U L D2 L2 (x') |
PLL | R B' R F2 R' B R F2 R2 |
PLL | R U2 R' U2 (R' F R F')(r U R' U R U2 r') |
PLL | (y z) U2 L' U2 L F2 U2 R U2 R' F2 (z') |
PLL | (z') F2 L' U2 L U2 F2 R U2 R' U2 (z) |
PLL | (y') R' U2 R U' L' U R U' L U R2 U2 R |
PLL | (y') R2 B2 R F R' B2 R F' R |
PLL | (y' x') R2 U2 R D R' U2 R D' R |
PLL | (y2) L F' L B2 L' F L B2 L2 |
PLL | (y) R U R' U R' D' R U R' D R U2 R U' R' (y') |
PLL | R' D' R U R' D R U2 R' D' R U R' D R |
PLL | (y') R U2 R U2 R D R' U2 R D' R2 U2 R' |
PLL | (y x') L2 D2 L U L' D2 L U' L |
E Permutation
Name: E-PLL |
PLL | (y x') (R U' R' D) (R U R' D') (R U R' D) (R U' R' D') (x) | [14] |
PLL | R2 U F' (R' U R U')3 F U' R2 |
PLL | (y x') R' D R U' R' U2 R' U R D' R' U' R U2 R U x |
PLL | R2 U R' U' (y) (R U R' U')2 R U R' (y') R U' R2' | [15] |
PLL | R2 U R' d' (R U R' U')2 R U R' F U' F2 |
PLL | (x) U R' U' L U R U' r2 U' R U L U' R' U (x) |
PLL | (y x') R U' R' D R U R' u2 R' U R D R' U' R (x') |
PLL | (y x') R U' R' D R U R' D2 L' U L D L' U' L (x) |
PLL | (x) U R' U' L U R U' L' U R U' L U R' U' L' (x') |
PLL | (x') U' R U L' U' R' U r2 U R' U' r' F R F' |
PLL | (y) R U R' U R' U' R F' R U R' U' R' F R2 U' R2 U R |
PLL | L R' U' R U L' U' R' U R r U R' U' r' F R F' |
PLL | l' U' L' U R U' l U R' U' L U R U' l' U (x') |
PLL | (y) r' R' U' L D' L' U L R U' R' D R U (x) |
PLL | (y) l L U R' D R U' R' r' F r D' L' U' |
PLL | r2 U r2 D (x') (R U' R' U)3 (x) D' r2 U' r2 |
PLL | L' U' L' U R U' L U L (R' l') U' L U R U' L' U (x' y) |
PLL | R2 U R' (y) (R U' R' U)3 (y') R U' R2 |
PLL | (y' z') R' F R2 U R' B' R U' R2 F' R (z) R B R' |
PLL | R' U L' D2 L U' R L' U R' D2 R U' L |
PLL | R B L B' R' (y) R L (y) L B' R' B L' (y') R' L' |
PLL | (y) l U' R' D R U R' D' R U R' D R U' R' D' x |
PLL | l' U' r' F R F' R U R' U' L U R U' R' F |
PLL | F' R U R' U' L' U R U' l' U R' U' r B R (x2) |
PLL | (z) U2 R2 F (R U R' U')3 F' R2 U2 (z') |
PLL | R' D' R U' R' D R U R' D' R U2 R' D R U' R' D' R U R' D R |
PLL | (y x') R' D R U' R' D' R U2 L D' L' U' L D L' (x) |
PLL | F R' F' r U R U' r' F R F' r U R' U' r' |
PLL | (x) R U' R' D R U R' D' R U R' D R U' R' D' |
PLL | D R' D2 F' D L D' F D2 R D' F' L' F |
PLL | l' U' L' U R U' L U R' U' L U R U' L' U (x') |
PLL | (y) R U R D R' U R D' R' U' R D R' U' R D' R2 |
Permutations of Edges and Corners
F Permutation
PLL | (y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R |
PLL | y2 R' U2 R' d' R' F' R2 U' R' U R' F R U' F |
PLL | R' U R U' R2 F' U' F U R F R' F' R2 |
Alg.1 | M' U2 L F' R U2 r' U r' R2 U2 R2 |
Alg.1 | (R' U R U') R2 (F' U' F U) (R F R' F') R2 U' |
Alg.1(svn) | y2 R U' R' U R U F R U R' U' x' D' R2 D R D' |
Alg.1(svn1) | y2 R U' R' U R U F R U R' U' x U' R2 U R U' |
Alg.1(v2) | R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x') |
Alg.2(v2) | (y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F | [16] |
Alg.3(v2) | (y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z') |
Alg.4 | B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B |
Alg.4(v2) | (y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R |
Alg.5 | L U' L' U L2 F U F' U' L' F' L F L2 U |
Alg.5(v2) | (y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x') |
Alg.5(v3) | (y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x) |
Alg.9 | L F R' F' L' F' D2 B' L' B D2 F' R F2 |
G Permutation : a
PLL | (y) R2 U (R' U R' U') R U' R2 (D U' R' U) R D' | [17] |
PLL | (y) R2' u (R' U R' U' R) u' R2 (y') R' U R |
PLL | (y) R2 U (R' U R' U' R) U' R2 D (U' R' U R) D' |
PLL | (y2) F2' D (R' U R' U' R) D' F2 L' U L |
PLL | R L U2 R' L' (y') R' U L' U2 R U' L |
PLL | (R U R' U' R') U F (R U R U' R') F' U R' U2 R |
PLL | (y) L F2 R (F' L' F U) R' U' (F' L F' L') |
PLL | (y) R2' S2 U l2' U' l2' u R2 U' r2' F2 |
G Permutation : b
PLL | R' U' R U D' R2 U R' U R U' R U' R2 D | [18] |
PLL | R' U' R (y) R2 u (R' U R U' R) u' R2 |
PLL | (y) F' U' F R2 u (R' U R U' R) u' R2' |
PLL | R' U' R B2 D (L' U L U' L) D' B2 |
PLL | (y2) L' U' L (y') R2' u (R' U R U' R) u' R2 |
PLL | (y') R' U L' U2 R U' L (y) R L U2 L' R' |
PLL | R2 D L2 D F2 L D R' D2 L D' R' U2 |
G Permutation : c
PLL | (y) R2' u' (R U' R U R') u R2 (y) R U' R' |
PLL | (y) R2' u' (R U' R U R') u R2 B U' B' |
PLL | (y) R2' U' (R U' R U R') U R2 (D' U R U' R' D) |
PLL | (y) R2' D' F U' F U F' D R2 B U' B' |
PLL | (y2) F2' D' L U' L U L' D F2 R U' R' |
PLL | L' U' L U L U' F' L' U' L' U L F U' L U2 L' |
PLL | L' R' U2 L R (y) L U' R U2 L' U R' |
PLL | B2 L2 U' B2 D B2 D' R2 U M2 F2 (x2) |
PLL | (y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2 |
PLL | (y') l' U2' L' U l F' U' L U F R' F R |
PLL | (y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U' |
G Permutation : d
PLL | (y2) R U R' (y') R2 u' (R U' R' U R') u R2 |
PLL | (y2) R U R' F2 D' (L U' L' U L') D F2 |
PLL | (y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L) |
PLL | (y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x') |
PLL | (y) L U' R U2 L' U R' (y) R' L' U2 R L |
PLL | (y) f R f' R2 u' R U' R' U R' u R2 |
PLL | (y') R' F' R F' U' L' U F R' F' L F2 R |
PLL | (y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2 |
PLL | (y2) (R U R') F2 D' L U' L' U L' D F2 U2 |
J Permutation : a
Name: J-PLL a, L-perm |
Alg.7 | (y2) L U' R' U L' U2 R U' R' U2 R | [19] |
Alg.7(v2) | (y2) R' U2 R U R' U2' L U' R U L' | [20] |
Alg.3 | L' U R' U2 L U' R U L' U R' U2 L U' R |
Alg.1(v4) | y2 R' U2 R U R' U2 L U' R U L' |
Alg.1(v3) | y2 x R2 F R F' R U2 r' U r U2 x' |
Alg.1(v2) | (y) (R' U L') U2 (R U' R') U2 R L |
Alg.2 | (y2) F U' R U' R' U' R U R' F' R U R' U' R' F R U F' |
Alg.2 | B2 R' U' R B2 L' D L' D' L2 |
Alg.2(v2) | (y2) F2 L' U' L F2 R' D R' D' R2 |
Alg.2(v3) | (y2) F2 L' U' L b2 L' U L' U' r2 |
Alg.7(v3) | (y2) R' U2 R U R' (z) R2' U R' D R U' (z') |
Alg.7(v4) | (y2) R' U2' R U R' (z) R2 U R' D R U' (z') |
Alg.7(v5) | (z) D R' U' R D' R (R U R' U') R2 U (z') |
Alg.7(v6):Inv(Alg.7) | R U' L' U R' U2 L U' L' U2' L |
Alg.8 | R' L' U2 L U L' U2 R U' L U |
J Permutation : b
Alg.4 | R U R' F' R U R' U' R' F R2 U' R' U' | [21] |
Alg.1 | R U2 R' U' R U2 L' U R' U' r x |
Alg.2 | R U2 (R' U' R) U2 L' (U R' U') L |
Alg.1(v3) | (y) (R U' L) U2 (R' U R) U2 L' R' |
Alg.1(v4) | L' U R U' L U2 R' U R U2 R' |
Alg.2 | B2 (L U L') B2 (R D' R D) R2 |
Alg.2(v2) | (y2) F2 (R U R') F2 (L D' L D) L2 |
Alg.2(v3) | (y2) F2 (R U R') b2 (R U' R U) l2' |
Alg.2(v4) | (y' x') L2 u L u' L2 (x' y) (L U' L U) r2 |
Alg.2(v5) | (y2 x) U2 l U l' U2 r (U' L U) r2 |
Alg.3 | R U' L U2 R' U L' U' R U' L U2 R' U L' |
Alg.6 | B2 U D' B2 U B2 U' B2 D B2 U' B2 U |
Alg.6(v2) | (y') L2 (U D') L2 U L2 U' L2 D L2 U' L2 |
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
Alg.7 | R U2 R' U' R U2 L' U R' U' L |
Alg.13 | R2 U F U F' R2 F U' F' R2 U' R2 U' |
N Permutation : a
Name: N-PLL a |
PLL | r' D r U2 r' D r U2 r' D r U2 r' D r U2 r' D r |
PLL | R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R' |
PLL | L U' R U2 L' U R' L U' R U2 L' U R' |
PLL | (z) (U R' D R2 U' R D')2 (z') |
Alg.1(v3) | (y z) R' (U R' D R2 U' R D')2 (z') |
Alg.1(v4) | (R U' L U2 R' U L')2 |
Alg.1(v5) | (z) (D R' U R2 D' R U')2 (z') |
Alg.1(v6) | (z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R' |
Alg.1(v7) | R U' L d2 L' U L R' U' R U2 r' F l' |
N Permutation : b
Name: N-PLL b |
PLL | (R' U L' U2 R U' L)2 U |
PLL | (z) (D' R U' R2' D R' U)2 (z') |
PLL | R' U R U' R' F' U' F R U R' F R' F' R U' R |
PLL | z D' R U' R2 D R' U D' R U' R2 D R' U z' |
PLL | (z) (U' R D' R2' U R' D)2 (z') |
PLL | z U' R D' R2 U R' D U' R D' R2 U R' D z' |
PLL | L' U R' d2 R U' L R' U L' U2 l F' r |
R Permutation : a
Alg.1 | R U2 R' U2 R B' R' U' R U R B R2 U |
Alg.1(v2) | R U2 R' U2 R B' R' U' R U l U R2 (x) |
Alg.1(v3) | (y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z') |
Alg.1(v4) | (y2) L U2 L' U2 L F' L' U' L U L F L2 |
Alg.1(v5):Inv(Alg.1) | (y') R2 B' R' U' R' U R B R' U2 R U2 R' |
Alg.1(v6):Inv(Alg.1(v4)) | (y) L2 F' L' U' L' U L F L' U2 L U2 L' |
Alg.1(v7) | F2 R' F' U' F' U F R F' U2 F U2 F' |
Alg.1(v8) | (y' x') R2 U' l' U' R' U l U l' U2 R U2 R' |
Alg.1(v9) | (y') R l U' l' U' R' U l U l' U2 R U2' R' |
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
Alg.2 | F2 L2 U F U F' U' F' U' L2 F' U F' U' |
Alg.2(v2) | R U' R F2 U R U R U' R' U' F2 R2 U |
Alg.2(v3):Inv(Alg.2) | (y') R2 F2 U R U R' U' R' U' F2 R' U R' |
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
Alg.3 | F U F' L' F U2 F' U2 F' L F U F U2 F' U' |
Alg.3(v2) | (y') R U R' F' R U2 R' U2 R' F R U R U2 R' U' |
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
Alg.4 | R U2 R' U' R' F' R U2 R U2 R' F R U' R' U |
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
Alg.5 | L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2 |
Alg.5(v2) | (y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2 |
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
Alg.6 | R U2 R D R' U R D' R' U' R' U R U R' U |
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
Alg.7 | F U' F' U' F U F D F' U' F D' F' U2 F' U' |
Alg.7(v2) | (y') R U' R' U' R U R D R' U' R D' R' U2 R' |
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
Alg.8 | B' L' U' L B' L' U B' U' B' U B L B2 |
Alg.8(v2) | (y x') R' U' F' U R' U' (x) U R' U' R' U R B R2 |
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
Alg.9 | R U2 R' U B L' B' R B L B' U R' U |
Alg.9(v2) | R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z') |
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
Alg.10 | L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F |
Alg.10(v2) | (y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B |
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
Alg.11 | R U2 R D R' U R D' R' U' R' U R U R' U |
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)
R Permutation : b
Alg.1 | R' U2 R U2 R' F (R U R' U') R' F' R2' U' |
Alg.1(v2) | R' U2 R U2 R' F (R U R' U') l' U' R2 (x') |
Alg.1(v3) | (z') U' L2 U L2 U' F U L U' L' U' F' U2 (z) |
Alg.1(v4) | R' U2 R U2 R' F R U R' U' R' F' R2 |
Alg.1(v5):Inv(Alg.1) | (y) R2 F R U R U' R' F' R U2 R' U2 R |
Alg.1(v6):Inv(Alg.1(v4)) | (y) R2 F R U R U' R' F' R U2 R' U2 R |
Alg.1(v7) | B2 R B U B U' B' R' B U2 B' U2 B |
Alg.1(v8) | (y x) R2 U l U R U' l' U' l U2 R' U2 R |
Alg.1(v9) | (y') r' L' U r U L U' r' U' r U2 L' U2 L |
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
Alg.2 | B2 L2 U' B' U' B U B U L2 B U' B U |
Alg.2(v2) | R' U R' B2 U' R' U' R' U R U B2 R2 |
Alg.2(v3):Inv(Alg.2) | (y) R2 B2 U' R' U' R U R U B2 R U' R |
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
Alg.3 | B' U' B L B' U2 B U2 B L' B' U' B' U2 B U |
Alg.3(v2) | (y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R |
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
Alg.4 | R' U2 R U R B R' U2 R' U2 R B' R' U R U' |
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
Alg.5 | L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2 |
Alg.5(v2) | (y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R |
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
Alg.6 | R' U2 R' D' R U' R' D R U R U' R' U' R U' |
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
Alg.7 | B' U B U B' U' B' D' B U B' D B U2 B U |
Alg.7(v2) | (y) R' U R U R' U' R' D' R U R' D R U2 R |
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
Alg.8 | F L U L' F L U' F U F U' F' L' F2 |
Alg.8(v2) | (y' x) R U B U' R U (x') U' R U R U' R' F' R2 |
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
Alg.9 | R' U2 R U' F' L F R' F' L' F U' R U' |
Alg.9(v2) | R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z') |
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
Alg.10 | L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B' |
Alg.10(v2) | (y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F' |
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
Alg.11 | R' U2 R' D' R U' R' D R U R U' R' U' R U' |
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
Alg.12 | (y') (R U2 R' U' R U' R')(R U R' U' R' F R2 U' R' U' R U R' F')(R U R' U R U2 R') |
T Permutation
Name: T-PLL |
Alg.1 | R U R' U' R' F R2 U' R' U' R U R' F' |
Alg.1(v2):Inv(Alg.1) | F R U' R' U R U R2 F' R U R U' R' |
Alg.1(v3):Inv(Alg.1) | (y2) B L U' L' U L U L2 B' L U L U' L' |
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
Alg.2 | R' U' R U R B' R2 U R U R' U' R B |
Alg.2(v2) | (y2) L' U' L U L F' L2 U L U L' U' L F |
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
Alg.3 | R2 U R2 U' R2' U' D R2 U' R2' U R2 D' |
Alg.3(v2) | R2 U R2' U' R2 U' D R2' U' R2 U R2' D' |
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
Alg.4 | R2 U' R2 D B2 L2 U L2 D' B2 U |
Alg.4(v2) | (y2) L2 U' L2 D F2 R2 U R2 D' F2 |
Alg.4(v3) | R2 U' R2 D B2 L2 U L2 D' B2 |
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
Alg.5 | R2 D' F2 U F2 R2 D B2 U' B2 U |
Alg.5(v2) | R2' u' R2 U R2' (y) R2 u R2' U' R2 |
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
Alg.6 | R2 D' F2 D R2 B2 D L2 D' B2 U |
Alg.6(v2) | (y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z') |
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
Alg.7 | R U R' U' R2 D R' U' R' U' R U R2 D' R |
Alg.7(v2) | R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z) |
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
Alg.8 | R2 U R2 U' R2 F2 U' F2 D R2 D' |
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
Alg.9 | F' U F' L2 B D' B' L2 F2 U' S' U2 S U2 |
Alg.9(v1):Mirr(Alg9) | y' L U' r U2 l' U l U2 x r2' (U M U2 M') |
Alg.9(v2) | y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M | [22] |
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]
Alg.10 | R U R' U' R' F R F' R' F R F' U' F' U F U' |
Alg.10(v1) | (R U R' U') (R' F R F')2 (y') (x') F' (R' F R F') (x) (y) |
V Permutation
Alg.1 | R' U R' U' B' R' B2 U' B' U B' R B R |
Alg.1(v2) | R' U R' d' R' F' R2 U' R' U R' F R F |
Alg.1(v3) | R' U R' (y) U' R' F' R2 U' R' U R' F R F |
Alg.1(v4) | R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x') |
Alg.1(v5) | R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F |
Alg.1(v6) | R' U R' U' (y) R' F' R2 U' R' U R' F R F |
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
Alg.2 | R' U R' U' B' D B' D' B2 R' B' R B R |
Alg.2(v2) | R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x') |
Alg.2(v3) | R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x') |
Alg.2(v4) | R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x) |
Alg.2(v5) | R' U R' U' (y) R' D R' D' R2 F' R' F R F |
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
Alg.3 | R' U2 R U2 L U' R' U L' U L U' R U L' |
Alg.3(v2) | R' U2 R U2 L U' R' U r' F r U' R U L' |
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
Alg.4 | R2 U' (B2 U B2) (R D') (R D) R' U R U' R |
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
Alg.5 | F' U B U' F U F' U B' U' F U2 B U2 B' |
Alg.5(v2) | (y') R' U L U' R U R' U L' U' R U2 L U2 L' |
Alg.5(v3) | (y) r' F R F' r U r' F R' F' r U2 R U2 R' |
Alg.5(v4) | (y) L' U R U' L U L' U R' U' L U2 R U2 R' |
Alg.5(v5) | (y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z') |
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
Alg.6 | L U' R' U L' U' L U' R U L' U2 R' U2 R |
Alg.6(v2) | (y2) R U' L' U R' U' R U' L U R' U2 L' U2 L |
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
Alg.7 | R U2 R' D R U' R U' R U R2 D R' U' R D2 |
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
Alg.8 | (y) R U' R U (y) L D' L D L2 (y') R F R' F' R' |
Y Permutation
Alg.1 | F R U' R' U' R U R' F' R U R' U' R' F R F' | [23] |
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
Alg.1(vns) | R2 U' R' U R U' x D' R' U R' U' R' D R |
Alg.2 | R' U' R F2 R' U R U F2 U' F2 U' F2 |
Alg.2(v2) | R' U' R F2 R' U R d R2 U' R2' U' R2 |
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
Alg.3 | R2 U' R2 U' R2 U F U F' R2 F U' F' |
Alg.3(v2) | R2 U' R2 U' R2 d R U R' B2 R U' R' |
Alg.3(v3) | (y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z') |
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
Alg.4 | F2 D R2 U R2 D' R' U' R F2 R' U R |
Alg.4(v2) | (y') R2 u R2' U R2 D' R' U' R F2' R' U R |
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
Alg.5 | F R' F R2 U' R' U' R U R' F' R U R' U' F' |
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
Alg.6 | F R' F' R U R U' R2 U' R U R B' R' B U |
Alg.6(v2) | F R' F' R U R U' R2 U' R U l U' R' U (x) |
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
Alg.7 | F R U' R' U' R U F U F' R' F U' F2 |
Alg.7(v2) | F R U' R' U' R d R U R' B' R U' R2 |
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
Alg.8 | R' F R F' U' F' U F2 U F' U' F' L F L' U' |
Alg.8(v2) | R' F R F' (y') U' R' U R2 U R' U' R' F R F' |
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
Alg.9 | R' F' U F U F' U' F R F' U' F U F R' F' R |
Alg.9(v2) | (y) F' L' U L U L' U' L F L' U' L U L F' L' F |
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
Alg.10 | F2 U F U' F' U L F R' F R F L' F' |
Alg.10(v2) | (y z) U2 R U R' U' R (y) R U L' U L U R' U' (x) |
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
Alg.11 | R2 U' R' U R U' B' R' F R' F' R' B R |
Alg.11(v2) | (z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x) |
Alg.11(v3) | R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z) |
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
Alg.12 | F R U' R' F D R' B' R' B R2 D' F2 |
Alg.12(v2) | F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z) |
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
Alg.13 | R' U' R2 U' L U2 R' U R U2 L' R' U R' U R |
Alg.13(v2) | (y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z') |
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
Alg.14 | F R F' U' F R' F' R B' R2 B R' U' R2 U |
Alg.14(v2) | (y) r U r' U' r U' r' (y') l U' R2 U l' U' R2 |
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
Alg.15 | U F' L F L' U' L' U L U2 R U R' U' R' F R F' |
Permutations of corners only |
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Permutations of edges only |
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Permutations of corners and edges |
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