PLL

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Revision as of 07:43, 27 July 2012 by Cmowla (talk | contribs) (I have changed the format of all 2-cycles. The 1st version of each alg. and their decompositions correspond to the case images exactly. For sym. cases J, N and R Perms, all algorithms are now evenly distributed between the a and b versions of each.)
PLL method
Information about the method
Proposer(s):
Proposed:
Alt Names:
Variants:
No. Steps: 1
No. Algs: 21
Avg Moves: 12.3 HTM
Purpose(s):

PLL is the Permutation of the Last Layer, 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. Make sure to 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.


PLL (edit)
Permutations of corners only
Permutations of edges only
Permutations of corners and edges

See also

External links

PLL algorithms

Note that all of these algorithms assume that you are right-hand dominant and know 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
Used in: EPLL, CPLL, PLL, ELL, ZBLL, ZZLL
Optimal moves: 10 HTM, 7 STM
X-PLL is H-PLL + U2.

Speedsolving Algorithms

PLL M2' U M2' U2 M2' U M2'
PLL M2' U' M2' U2' M2' U' M2' [1]
PLL M2' U2 M2' U M2' U2 M2'
PLL M2' U2 M2' U' M2' U' M2'

Note that the last two algorithms should only be used as Post-AUF tricks, as it saves having to do a U or U' after the PLL if necessary.

Optimal Algorithms

HTM 9 R2 F2 B2 L2 D' R2 F2 B2 L2
STM 7 M2 D S2 D2 S2 D M2
QTM 12 R L U U R' L' F' B' U U F B
QSTM 12 R L U U R' L' F' B' U U F B

Ua Permutation

Name: U-PLL a
Used in: EPLL, PLL, ELL, ZBLL, BLD
Optimal moves: 9 HTM, 7 STM

Speedsolving Algorithms

PLL R U R' U R' U' R2 U' R' U R' U R [2]
PLL (U2) M2' U M U2 M' U M2' [3]
PLL (U2) R U' R U R U R U' R' U' R2 [4]
PLL (U) R2 U' S' U2' S U' R2

Optimal Algorithms

HTM 9 B2 U' R L' B2 R' L U' B2
STM 7 B2 U' M U2 M' U' B2
QTM 12 R U B U' B' R' L' B' U' B U L
QSTM 10 R' F' M' F U F' M F U' R

Ub Permutation

Name: U-PLL b
Used in: EPLL, PLL, ELL, ZBLL, BLD
Optimal moves: 9 HTM, 7 STM

Speedsolving Algorithms

PLL R' U R' U' R3 U' R' U R U R2 [5]
PLL (U2) M2 U' M U2 M' U' M2 [6]
PLL (U2) R2' U R U R' U' R3 U' R' U R'
PLL (U) R2 U' S R2' S' R2 U R2'
PLL (U) R2' U R2 S R2' S' U' R2


Optimal Algorithms

HTM 9 B2' U L' R B2' L R' U B2'
STM 7 B2' U M U2' M' U B2'
QTM 12 L' U' B' U B L R B U B' U' R'
QSTM 10 L F M' F' U' F M F' U L'

Z Permutation

Name: Z-PLL
Used in: EPLL, PLL, ELL, ZBLL, ZZLL
Optimal moves: 12 HTM, 7 STM

Speedsolving Algorithms

PLL (U) M' U M2' U M2' U M' U2 M2'
PLL M2' U M2' U M' U2 M2' U2 M'
PLL M2' U2 M U M2' U M2' U M
PLL R' U' R U' R U R U' R' U R U R2 U' R'

Optimal Algorithms

HTM 12 R L' U2 D2 R L' D' R2 L2 U F2 B2
STM 7 M S2 M' D' M2 D S2
QTM 13 R B' R' F B R' F B' R' B R F F
QSTM 10 M S' S' M' D M' M' D' S' S'


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
Used in: CPLL, PLL, L3C, L4C, ZBLL, BLD
Optimal moves: 9 HTM

Speedsolving Algorithms

PLL (U') x R' U R' D2 R U' R' D2 R2 x' [7]
PLL x' R2 D2 R' U' R D2 R' U R' x
PLL (U2) x L2 D2' L' U' L D2' L' U L' x'
PLL (U) R' D R U' R' D' R U' R' D R U2 R' D' R

Optimal Algorithms

HTM 9 R2 F2 R' B' R F2 R' B R'
STM 9 R2 F2 R' B' R F2 R' B R'
QTM 12 R B' D F' D' B' D F D' B B R'
QSTM 12 R B' D F' D' B' D F D' B B R'

Ab Permutation

Name: Ab-PLL
Used in: CPLL, PLL, L3C, L4C, ZBLL, BLD
Optimal moves: 9 HTM

Speedsolving Algorithms

PLL (U') x R2' D2 R U R' D2 R U' R x' [8]
PLL x' R U' R D2 R' U R D2 R2' x
PLL (U2) x L U' L D2' L' U L D2' L2' x'
PLL (U) R' D R U2 R' D' R U R' D R U R' D' R
PLL (U') R' U' D' R U R' D R U' R' U R


Optimal Algorithms

HTM 9 (y) L2 F2 L B L' F2 L B' L
STM 9 (y) L2 F2 L B L' F2 L B' L
QTM 12 (y) L' B D' F D B D' F' D B' B' L
QSTM 12 (y) L' B D' F D B D' F' D B' B' L

E Permutation

Name: E-PLL
Used in: CPLL, PLL, L4C, ZBLL, ZZLL
Optimal moves: 14 HTM

Speedsolving Algorithms

PLL (U) x' R U' R' D R U R' D' R U R' D R U' R' D' x [9]
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 R2 U R' d' (R U R' U')2 R U R' F U' F2
PLL F' (r U R' U' r' F R) U2 (r U R' U' r' F R F')

Optimal Algorithms

HTM 14 F R B R' F' R L F L' B' L F' R' L'
STM 14 F R B R' F' R L F L' B' L F' R' L'
QTM 14 F R B R' F' R L F L' B' L F' R' L'
QSTM 14 F R B R' F' R L F L' B' L F' R' L'


Permutations of Edges and Corners

F Permutation

Name: F-PLL
Used in: PLL, ZBLL, ZZLL
Optimal moves: 14 HTM

Alg.1 R' U R U' R2 F' U' F U R F R' F' R2 U'
Alg.1(v2) R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')

Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')

Alg.2 L' U2 L' U' F' L' F2 U' F' U F' L F U' L
Alg.2(v2) (y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F [10]

Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]

Alg.3 L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'
Alg.3(v2) (y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')

Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]

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

Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]

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) L' U' L U L2 (x')

Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)

Alg.6 R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R

Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]

Alg.7 L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'

Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]

Alg.8 L R' F2 R' D L' F2 R U' L2 R B2 L2 U
Alg.8(v2) (y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')

Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]

Alg.9 L F R' F' L' F' D2 B' L' B D2 F' R F2
Alg.9(v2) (r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)

Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]

Alg.10 R B2 D B2 R' B' R B' D2 F L' F' D B2 R'
Alg.10(v2) (y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')

Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]

Alg.11 B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'
Alg.11(v2) (y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')

Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']

Alg.12 F2 B2 D F2 B2 R U R' U' R' F R2 U' R' U' R U R' F B2 D' F2 B2
Alg.12(v2) (y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2

Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]

Alg.13 R U' F R F' U F' U' F2 R' F' U' R' U2 R'
Alg.13(v2) (y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'

Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]


G Permutation : a

Name: G-PLL a
Used in: PLL, ZBLL
Optimal moves: 12 HTM

PLL (y) R2' u R' U R' U' R u' R2 (y') R' U R
PLL (y) R2 D B' U B' U' B D' R2 F' U F
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


G Permutation : b

Name: G-PLL b
Used in: PLL, ZBLL
Optimal moves: 12 HTM

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 (y2) R' U2 R U' F R U R' U' R' F' U' R U R U' R'


G Permutation : c

Name: G-PLL c
Used in: PLL, ZBLL
Optimal moves: 12 HTM

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 (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


G Permutation : d

Name: G-PLL d
Used in: PLL, ZBLL
Optimal moves: 12 HTM

PLL (y2) R U R' (y') R2 u' R U' R' U R' u R2
PLL (y2) R U R' F (y') R 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) L U' R U2 L' U R' (y') L' R' U2 L R
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


J Permutation : a

Name: J-PLL a
Used in: PLL, ZBLL, BLD
Optimal moves: 10 HTM

Alg.1 B' U F' U2 B U' B' U2 F B U'
Alg.1(v2) (y) R' U L' U2 R U' R' U2 R L
Alg.1(v3) (y') L' U R' U2 L U' L' U2 R L
Alg.1(v4) (y') L' U R' (z) R2 U R' U' R2 U D (z')

Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]

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.2(v4) (y x') R2 u' R' u R2 (x' y') R' U R' U' l2'
Alg.2(v5) (y2 x) U2 r' U' r U2 l' U R' U' l2
Alg.2(v6):Inv(Alg.2(v5)) (y2) l2 U R U' l U2 r' U r U2 (x')

Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]

Alg.3 L' U R' U2 L U' R U L' U R' U2 L U' R

Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]

Alg.4 L' U' L F L' U' L U L F' L2 U L U

Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)

Alg.5 B2 R2 U' R2 D B2 D' B2 U B2 U'
Alg.5(v2) B2' R2 U' R2' u R2 D' R2' U R2

Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]

Alg.6 B2 U' D B2 U' B2 U B2 D' B2 U B2 U'
Alg.6(v2) (y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'

Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]

Alg.7 L' U2 L U L' U2 R U' L U R'
Alg.7(v2) (y2) R' U2 R U R' U2' L U' R U L'
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.7(v7):Inv(Alg.7(v2)) (y2) L U' R' U L' U2 R U' R' U2 R [11]

Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]

Alg.8 R' L' U2 L U L' U2 R U' L U
Alg.8(v2) (y2) L' R' U2 R U R' U2 L U' R
Alg.8(v3) R' L' d2 R U R' d2 R U' L
Alg.8(v4) (z) U' D' R2 U R U' R2 (z') R U' L
Alg.8(v5):Inv(Alg.8) (y') L' U R' U2 L U' L' U2 L R
Alg.8(v6):Inv(Alg.8(v4)) (y') L' U R' (z) R2 U R' U' R2 U D (z')

Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]

Alg.9 B U' L' B L2 U' L' U' L U L' B' L U L' B'
Alg.9(v2) (y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'

Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]

Alg.10 B' U B' R2 F D' F D F2 R2 B2
Alg.10(v2) (y) R' U l' U2 r U' L U r2 F2 R2

Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]


J Permutation : b

Name: J-PLL b
Used in: PLL, ZBLL, BLD
Optimal moves: 10 HTM

Alg.1 B U' F U2 B' U B U2 F' B' U
Alg.1(v2) (y') L U' R U2 L' U L U2 R' L'
Alg.1(v3) (y) R U' L U2 R' U R U2 L' R'
Alg.1(v4) (y) R U' L (z') L2 U' L U L2 D' U' (z)

Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]

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.2(v6):Inv(Alg.2(v5)) (y2) r2 U' L' U r' U2 l U' l' U2 (x')

Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]

Alg.3 R U' L U2 R' U L' U' R U' L U2 R' U L'

Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]

Alg.4 R U R' F' R U R' U' R' F R2 U' R' U'

Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')

Alg.5 B2 L2 U L2 D' B2 D B2 U' B2 U
Alg.5(v2) B2 L2 U L2 u' L2 D L2 U' L2

Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]

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.7(v2) (y2) L U2 L' U' L U2' R' U L' U' R
Alg.7(v3) (y2) L U2 L' U' L (z') L2' U' L D' L' U (z)
Alg.7(v4) (y2) L U2' L' U' L (z') L2' U' L D' L' U (z)
Alg.7(v5) (z') D' L U L' D L' (L' U' L U) L2' U' (z)
Alg.7(v6):Inv(Alg.7) L' U R U' L U2 R' U R U2' R'
Alg.7(v7):Inv(Alg.7(v2)) (y2) R' U L U' R U2 L' U L U2 L'

Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]

Alg.8 L R U2 R' U' R U2 L' U R' U'
Alg.8(v2) (y2) R L U2 L' U' L U2 R' U L'
Alg.8(v3) L R d2 L' U' L d2 L' U R'
Alg.8(v4) (z') U D L2 U' L' U L2 (z) L' U R'
Alg.8(v5):Inv(Alg.8) (y) R U' L U2 R' U R U2 R' L'
Alg.8(v6):Inv(Alg.8(v4)) (y) R U' L (z') L2 U' L U L2 U' D' (z)

Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]

Alg.9 B' U R B' R2 U R U R' U' R B R' U' R B
Alg.9(v2) (y2) F' U L F' L2 U L U L' U' L F L' U' L F

Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]

Alg.10 B U' B L2 F' D F' D' F2 L2 B2
Alg.10(v2) (y') L U' r U2 l' U R' U' l2 F2 L2

Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]


N Permutation : a

Name: N-PLL a
Used in: PLL, ZBLL, ZZLL
Optimal moves: 14 HTM

Alg.1 (L U' R U2 L' U R')2 U'
Alg.1(v2) (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'

Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')

Alg.2 L U' L' U L F U F' L' U' L F' L F L' U L'
Alg.2(v2) (z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')
Alg.2(v3):Inv(Alg.2) (L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'

Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]

Alg.3 R U' R' U R B U B' R' U' R B' R B R' U R'
Alg.3(v2) R U' R' U l U F U' R' F' R U' R U l' U R'

Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]

Alg.4 R' U R2 B2 U R' B2' R U' B2 R2' U' R U'

Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')

Alg.5 F' R U R' U' R' F R2 F U' R' U' R U F' R'

Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]

Alg.6 R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'

Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]

Alg.7 R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'
Alg.7(v2) L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'

Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]

Alg.8 L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2
Alg.8(v2) (z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')

Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]

Alg.9 R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'
Alg.9(v2) (R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)

Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]

Alg.10 L' U L2 F2 U L' F2 L U' F2 L2 U' L U'

Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')

Alg.11 L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'

Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')

Alg.12 (L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')

Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]


N Permutation : b

Name: N-PLL b
Used in: PLL, ZBLL, ZZLL
Optimal moves: 14 HTM

Alg.1 (R' U L' U2 R U' L)2 U
Alg.1(v2) (z) (D' R U' R2' D R' U)2 (z')
Alg.1(v3) (y' z') L (U' L D' L2 U L' D)2 (z)
Alg.1(v4) (L' U R' U2' L U' R)2
Alg.1(v5) (z) (U' R D' R2' U R' D)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) L' U R' d2 R U' L R' U L' U2 l F' r

Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)

Alg.2 R' U R U' R' F' U' F R U R' F R' F' R U' R
Alg.2(v2) (z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)
Alg.2(v3):Inv(Alg.2) (R' U R' F) R F' (R U' R') F' U (F R U R' U') R

Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]

Alg.3 L' U L U' L' B' U' B L U L' B L' B' L U' L
Alg.3(v2) L' U L U' r' U' F' U L F L' U L' U' r U' L

Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]

Alg.4 L U' L2 B2 U' L B2 L' U B2 L2 U L' U

Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

Alg.5 F L' U' L U L F' L2 F' U L U L' U' F L

Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]

Alg.6 L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L

Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]

Alg.7 L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L
Alg.7(v2) R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L

Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]

Alg.8 R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2
Alg.8(v2) (z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')

Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]

Alg.9 L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L
Alg.9(v2) (L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')

Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]

Alg.10 R U' R2' F2 U' R F2' R' U F2 R2 U R' U

Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)

Alg.11 R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U

Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)

Alg.12 (R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)

Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]


R Permutation : a

Name: R-PLL a
Used in: PLL, ZBLL
Optimal moves: 14 HTM

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
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'

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'

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

Name: R-PLL b
Used in: PLL, ZBLL
Optimal moves: 14 HTM

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')


T Permutation

Name: T-PLL
Used in: PLL, ZBLL, ZZLL, BLD
Optimal moves: 11 HTM

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] ]


V Permutation

Name: V-PLL
Used in: PLL, ZBLL
Optimal moves: 14 HTM

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']] ] ]


Y Permutation

Name: Y-PLL
Used in: PLL, ZBLL, BLD
Optimal moves: 13 HTM

Alg.1 F R U' R' U' R U R' F' R U R' U' R' F R F' [12]

Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]

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']


PLL (edit)
Permutations of corners only
Permutations of edges only
Permutations of corners and edges


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