Speedsolving.com Wiki - User contributions [en]

Template:Z-PLL

2016-05-02T12:54:55Z

Addons zz: /* Z Permutation */

===Z Permutation===
{{case
|image=z.gif
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=12 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|(M2' U)2 M' (U2 M2' U2) M' U2|PLL}}
{{Alg|(y) (M2' U')2 M' (U2' M2' U2') M'|PLL}}
{{Alg|M2' U2 M' U' M2' U' M2' U' M'|PLL}}
{{Alg|(y) M2' U2 M' U M2' U M2' U M'|PLL}}
{{Alg|M' U' M2' U' M2' U' M' U2 M2'|PLL}}
{{Alg|(y) M' U M2' U M2' U M' U2 M2'|PLL}}
{{Alg|M' U2 M2 U2 M' U' M2 U' M2|PLL}}
{{Alg|M2' U M2' U' E2 M' E2 M'|PLL}}
{{Alg|(y) M2' U' M2' U E2 M' E2 M'|PLL}}
{{Alg|M2' U M' E2 M' E2 U' M2'|PLL}}
{{Alg|M2' U M2' U M2 B2 M2 B2|PLL}}
{{Alg|U R' U' R U' R U R U' R' U R U R2 U' R' U|PLL}}
{{Alg|R' U' R2 U R U R' U' R U R U' R U' R'|PLL|vidurl=http://www.youtube.com/watch?v=n8fJFo6SofY}}
{{Alg|R U R' U R' U' R' U R U' R' U' R2 U R|PLL}}
{{Alg|(y) R U R2 U' R' U' R U R' U' R' U R' U R|PLL}}
{{Alg|(x') R U' R' (U D) R' (D U') R' U R D2' (x)|PLL}}
{{Alg|M2' D S2 D' S' M2' S|PLL}}
{{Alg|M2' u M2' D' M S2 M'|PLL}}
{{Alg|(y) F2 M2' F2 M2' U M2' U M2'|PLL}}
{{Alg|(y) M2' U (F2 M2' F2 M2') U' M2'|PLL}}
{{Alg|(y) R2 U R2 U' R2 F2 R2 U' F2 U R2 F2|PLL}}
{{Alg|R' U L' E2 L U' R L' U R' E2 R U' L|PLL}}
{{Alg|R2 U' R2 U R2 (x') U2 R2 F U2 F' R2 U2 (x)|PLL}}
{{Alg|(y') l' U R U' D' R U D' R U' R' D2 (x')|PLL}}
{{Alg|R' U' R' F R F' U R F' U' L' U L F|PLL}}
{{Alg|R' U' R' F R F' U R U' R' U' F' U F R|PLL}}
{{Alg|R U R2 U' R' F R U R U' R U' R' U' R U R' F'|PLL}}

PLL

2016-03-21T11:34:56Z

Addons zz: /* J Permutation : b */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL|vidurl=http://www.youtube.com/watch?v=4hxXyedEvoE}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U (R' U R' U' R) U' R2 D (U' R' U R) D'|PLL}}
{{Alg|(y2) F2' D (R' U R' U' R) D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|(R U R' U' R') U F (R U R U' R') F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R (F' L' F U) R' U' (F' L F' L')|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D (L' U L U' L) D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u (R' U R U' R) u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}
{{Alg|R' U' R U D' R2 U R' U R U' R U' R2 D|PLL|vidurl=http://www.youtube.com/watch?v=M6RDFenst9g}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B' U F') U2 (B U' B') U2 (F B U')|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R' U L') U2 (R U' R') U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') U2 (L U' L') U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') (z) R2 (U R' U') R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B U' F) U2 (B' U B) U2 (F' B' U)|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L U' R) U2 (L' U L) U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) U2 (R' U R) U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) (z') L2 (U' L U) L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 (R' U' R) U2 L' (U R' U') L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 (L U L') B2 (R D' R D) R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 (R U R') F2 (L D' L D) L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 (R U R') b2 (R U' R U) l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) (L U' L U) r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r (U' L U) r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 (U' L' U) r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-03-21T11:33:04Z

Addons zz: /* J Permutation : b */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL|vidurl=http://www.youtube.com/watch?v=4hxXyedEvoE}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U (R' U R' U' R) U' R2 D (U' R' U R) D'|PLL}}
{{Alg|(y2) F2' D (R' U R' U' R) D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|(R U R' U' R') U F (R U R U' R') F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R (F' L' F U) R' U' (F' L F' L')|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D (L' U L U' L) D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u (R' U R U' R) u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}
{{Alg|R' U' R U D' R2 U R' U R U' R U' R2 D|PLL|vidurl=http://www.youtube.com/watch?v=M6RDFenst9g}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B' U F') U2 (B U' B') U2 (F B U')|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R' U L') U2 (R U' R') U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') U2 (L U' L') U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') (z) R2 (U R' U') R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B U' F) U2 (B' U B) U2 (F' B' U)|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L U' R) U2 (L' U L) U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) U2 (R' U R) U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) (z') L2 (U' L U) L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 (R' U' R) U2 L' (U R' U') L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 (R U R') F2 (L D' L D) L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 (R U R') b2 (R U' R U) l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) (L U' L U) r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 (U' L' U) r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-03-13T13:01:41Z

Addons zz: /* J Permutation : a */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U (R' U R' U' R) U' R2 D (U' R' U R) D'|PLL}}
{{Alg|(y2) F2' D (R' U R' U' R) D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|(R U R' U' R') U F (R U R U' R') F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R (F' L' F U) R' U' (F' L F' L')|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D (L' U L U' L) D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u (R' U R U' R) u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(B' U F') U2 (B U' B') U2 (F B U')|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R' U L') U2 (R U' R') U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') U2 (L U' L') U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') (L' U R') (z) R2 (U R' U') R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-23T04:08:55Z

Addons zz: /* G Permutation : a */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U (R' U R' U' R) U' R2 D (U' R' U R) D'|PLL}}
{{Alg|(y2) F2' D (R' U R' U' R) D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|(R U R' U' R') U F (R U R U' R') F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R (F' L' F U) R' U' (F' L F' L')|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D (L' U L U' L) D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u (R' U R U' R) u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-23T03:50:06Z

Addons zz: /* G Permutation : b */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D (L' U L U' L) D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u (R' U R U' R) u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-23T03:48:43Z

Addons zz: /* G Permutation : b */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u (R' U R U' R) u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-23T03:47:35Z

Addons zz: /* G Permutation : d */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' (R U' R' U R') u R2|PLL}}
{{Alg|(y2) R U R' F2 D' (L U' L' U L') D F2|PLL}}
{{Alg|(y2) L U2 L' U F' (L' U' L U L) F U (L' U' L' U L)|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-23T03:45:51Z

Addons zz: /* G Permutation : c */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' (R U' R U R') u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' (R U' R U R') u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' (R U' R U R') U R2 (D' U R U' R' D)|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-21T14:39:35Z

Addons zz: /* G Permutation : a */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U' R) u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-21T14:36:51Z

Addons zz: /* G Permutation : b */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U') R u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U' R) u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-20T16:33:14Z

Addons zz: /* G Permutation : a */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u (R' U R' U') R u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U') R u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-20T16:31:17Z

Addons zz: /* G Permutation : b */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u R' U R' U' R u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u (R' U R U') R u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-20T16:29:44Z

Addons zz: /* G Permutation : a */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 (D U' R' U) R D'|PLL}}
{{Alg|(y) R2' u R' U R' U' R u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u R' U R U' R u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

Template:Z-PLL

2016-02-20T15:44:24Z

Addons zz: /* Z Permutation */

===Z Permutation===
{{case
|image=z.gif
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=12 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|(M2' U)2 M' U2 M2' U2 M' U2|PLL}}
{{Alg|(y) M2' U' M2' U' M' U2' M2' U2' M'|PLL}}
{{Alg|M2' U2 M' U' M2' U' M2' U' M'|PLL}}
{{Alg|(y) M2' U2 M' U M2' U M2' U M'|PLL}}
{{Alg|M' U' M2' U' M2' U' M' U2 M2'|PLL}}
{{Alg|(y) M' U M2' U M2' U M' U2 M2'|PLL}}
{{Alg|M' U2 M2 U2 M' U' M2 U' M2|PLL}}
{{Alg|M2' U M2' U' E2 M' E2 M'|PLL}}
{{Alg|(y) M2' U' M2' U E2 M' E2 M'|PLL}}
{{Alg|M2' U M' E2 M' E2 U' M2'|PLL}}
{{Alg|M2' U M2' U M2 B2 M2 B2|PLL}}
{{Alg|U R' U' R U' R U R U' R' U R U R2 U' R' U|PLL}}
{{Alg|R' U' R2 U R U R' U' R U R U' R U' R'|PLL|vidurl=http://www.youtube.com/watch?v=n8fJFo6SofY}}
{{Alg|R U R' U R' U' R' U R U' R' U' R2 U R|PLL}}
{{Alg|(y) R U R2 U' R' U' R U R' U' R' U R' U R|PLL}}
{{Alg|(x') R U' R' (U D) R' (D U') R' U R D2' (x)|PLL}}
{{Alg|M2' D S2 D' S' M2' S|PLL}}
{{Alg|M2' u M2' D' M S2 M'|PLL}}
{{Alg|(y) F2 M2' F2 M2' U M2' U M2'|PLL}}
{{Alg|(y) M2' U (F2 M2' F2 M2') U' M2'|PLL}}
{{Alg|(y) R2 U R2 U' R2 F2 R2 U' F2 U R2 F2|PLL}}
{{Alg|R' U L' E2 L U' R L' U R' E2 R U' L|PLL}}
{{Alg|R2 U' R2 U R2 (x') U2 R2 F U2 F' R2 U2 (x)|PLL}}
{{Alg|(y') l' U R U' D' R U D' R U' R' D2 (x')|PLL}}
{{Alg|R' U' R' F R F' U R F' U' L' U L F|PLL}}
{{Alg|R' U' R' F R F' U R U' R' U' F' U F R|PLL}}
{{Alg|R U R2 U' R' F R U R U' R U' R' U' R U R' F'|PLL}}

First Two Layers

2016-02-18T03:18:01Z

Addons zz: /* F2L 33 */

{{Substep Infobox
|name=F2L
|image=F2Linfo.png
|proposers=[[René Schoof]]
|year=1981
|anames=First Two Layers
|variants=[[ZBLS]], [[VHF2L]], [[WV]], [[MGLS]], possibly others
|subgroup=<nowiki><U,R,L,F,B></nowiki>
|algs=42
|moves=6.7 [[HTM]] a slot
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[Cross cube state]]
|next=[[F2L cube state]]
|previousimage=[[Image:VisualCube_3_Egell.png|120px|left|link=Cross cube state]]
|nextimage=[[Image:F2L_higlight.jpg|120px|right|link=F2L cube state]]

}}
'''First Two Layers''', or '''F2L''' are normally the first two bottom layers of the [[3x3x3 cube]], or essentially all layers up until the last layer on larger cubes.

The definition is a little different depending on the subject or who you are talking to. Normally it is as above but it may also refer to the part of the [[Fridrich method]] that solves the [[pair]]s without counting the [[cross]] part.

[[2-gen]] F2L, most pairs (30:42) have the edge sitting in the U-layer having two orientations, it shows R or F colour at the side. If it is the R colour you can solve the pair using only RU and if it is the F colour you can turn the cube (y') and sovle the pair to the back slot using only RU. The only pairs that needs both R and F turns are the six ones with the edge unoriented in the slot, if the edge is oriented in the slot both ways works.

 
== Approaches ==

=== Petrus F2L ===

Another way to solve the 'F2L' is by building blocks, common during the first two layers of the [[Petrus]] method.

=== Fridrich F2L ===
There are many ways to solve the 'F2L' on a cube. A common system is using the [[Fridrich]] method first two layer approach. After solving the cross, a corner-edge pair is paired up, and then inserted into the correct slot. A total of four corner edge (or 'CE') pairs are made and inserted to solve the first two layers.

The concept of pairing up four corner/edge pairs was first proposed by [[René Schoof]] in 1981.

{{F2L}}

==Easy Cases==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 1 ===
[[Image:F2L01.png]]

{{Alg|U (R U' R')|F2L}}
{{Alg|R' F R F'|F2L}}
{{Alg|U2 (R U2 R')|F2L}}

|

=== F2L 2 ===
[[Image:F2L02.png]]

{{Alg|y' U' (R' U R)|F2L}}
{{Alg|U' (F' U F)|F2L}}
{{Alg|F R' F' R|F2L}}
{{Alg|d' L' U L|F2L}}
{{Alg|r U R' U' M|F2L}}
{{Alg|(U2) l R U' R' U l'|F2L}}
{{Alg|(U2) l2 F' l' U l'|F2L}}
{{Alg|(U') F R' F' R2 U' R'|F2L}}

|-valign="top"
|

=== F2L 3 ===
[[Image:F2L03.png]]

{{Alg|y' (R' U' R)|F2L}}
{{Alg|y (L' U' L)|F2L}}
{{alg|F' U' F|F2L}}
{{Alg|U M R U' R' U M'|F2L}}
{{Alg|U r' R2 U' R' U M'|F2L}}

|

=== F2L 4 ===
[[Image:F2L04.png]]

{{Alg|(R U R')|F2L}}
{{Alg|(U2) L (R U' R') U L'|F2L}}

|-valign="top"
|}

==Reposition Edge==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 5 ===
[[Image:F2L05.png]]

{{Alg|(U' R U R') U2 (R U' R')|F2L}}
{{Alg|(U' R U R') U (R' F R F')|F2L}}
{{Alg|F2 (L' U' L U) F2|F2L}}
{{Alg|L U' R U L' R' U2 R U' R'|F2L}}
{{Alg|U' (R U R') U' R U2 R'|F2L}}

|

=== F2L 6 ===
[[Image:F2L06.png]]

{{Alg|d (R' U' R) U2' (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U2 (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U' y (F R' F' R)|F2L}}
{{Alg|U' (r U' R' U) (R U r')|F2L}}
{{Alg|R2 (B U B' U') R2|F2L}}
{{Alg|y F2 (R U R' U') F2|F2L}}

|-valign="top"
|

=== F2L 7 ===
[[Image:F2L07.png]]

{{Alg|U' (R U2' R') U2 (R U' R')|F2L}}
{{Alg|U' R U2 R' U' R U2 R'|F2L}}
{{Alg|M' U' M U2 r U' r'|F2L}}
{{Alg|R U B U2 B' U R'|F2L}}

|

=== F2L 8 ===
[[Image:F2L08.png]]

{{Alg|d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|y' U (R' U2 R) U2 (R' U R)|F2L}}
{{Alg|(r' U2) (R2 U R2 U r)|F2L}}
{{Alg|y' R' U' F' U2 F U' R|F2L}}

|-valign="top"
|}

==Reposition Edge and Flip Corner==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 9 ===
[[Image:F2L09.png]]

{{Alg|U' R U' R' d R' U' R |F2L}}
{{Alg|d (R' U' R U') (R' U' R)|F2L}}
{{Alg|y2 U' (L U' L') d (L' U' L)|F2L}}
{{Alg|U r U R' U' R2 r' U' R'|F2L}}
{{Alg|U' R U' R' U2 M R U' R' U M'|F2L}}
{{Alg|F (R U R' U') F' R U' R'|F2L}}
{{Alg|(U F' U' F) U' (F' U' F)|F2L}}
{{Alg|y F2 (U R U' R') F2|F2L}}

|

=== F2L 10 ===
[[Image:F2L10.png]]

{{Alg|U' (R U R' U)(R U R')|F2L}}
{{Alg|R d' R U R' U2 F'|F2L}}
{{Alg|U F' U F U' R U R'|F2L}}
{{Alg|d R' U R d' R U R'|F2L}}
{{Alg|y2 B2 (U' R' U R) B2|F2L}}

Back Right Slot Open: R' U R2 U R'

|-valign="top"
|

=== F2L 11 ===
[[Image:F2L11.png]]

{{Alg|U' (R U2' R') d (R' U' R)|F2L}}
{{Alg|(y) L' d L' U2 L U2 F|F2L}}
{{Alg|U' R U2 R' U2 M R U' R' U M'|F2L}}
{{Alg|U (F R' F' R)2 U' R U R'|F2L}}
{{Alg|(y') R U2 R2 U' R2 U' R'|F2L}}
{{Alg|U' l F U' R U l' U R'|F2L}}
|

=== F2L 12 ===
[[Image:F2L12.png]]

{{Alg|R U' R' U R U' R' U2 R U' R'|F2L}}
{{Alg|d (R' U2 R) d' (R U R')|F2L}}
{{Alg|R U2 R' U2' R U2' R' U2' R U' R'|F2L}}
{{Alg|R' U2 R2 U R2 U R|F2L}}
{{Alg|y (F U') (R U2 R' U2') F'|F2L}}
{{Alg|(U R U' R') U' (R U R' U') (R U R')|F2L}}
Back right slot open: R' U2 R2 U R'

|-valign="top"
|

=== F2L 13 ===
[[Image:F2L13.png]]

{{Alg|d (R' U R U') (R' U' R)|F2L}}
{{Alg|y' U (R' U R U') (R' U' R)|F2L}}
{{Alg|(U F' U F) U' (F' U' F)|F2L}}
{{Alg|M' U' (R U R') U' (R U2 r')|F2L}}
{{Alg|(R U' R') U (R' F R F') (R U' R')|F2L}}
{{Alg|(R U R') d' (L' U' L U) (L' U' L)|F2L}}
{{Alg|(R U' R' U2) (R U' l U' R' U l')|F2L}}
Back right slot open : R' U R F' U' F

|

=== F2L 14 ===
[[Image:F2L14.png]]

{{Alg|U' (R U' R' U) (R U R')|F2L}}
{{Alg|d' F U' F' d R U R'|F2L}}

|-valign="top"
|}

==Split Pair by Going Over==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 15 ===
[[Image:F2L15.png]]

{{Alg|M U L F' L' U' M'|F2L}}
{{Alg|U (R' F R F') U (R U R')|F2L}}
{{Alg|y' (R' U R U') d' (R U R')|F2L}}
{{Alg|y (L' U L) U2 y' (R U R')|F2L}}
{{Alg|R U2 R' U R U R' U R U' R'|F2L}}
{{Alg|R U R' U2 R U' R' U R U' R'|F2L}}
{{Alg|R U' R U2' R2' U' R2 U' R2'|F2L}}
{{Alg|U' R2 U2 R U' R' U R' U2 R2|F2L}}
{{Alg|U2 (R U R' U') R U2 R' U R U R'|F2L}}
Front left slot open: U (R U' R') D (R U' R') D'

Back right slot open: U' (R' U R U') (R U R')

=== F2L 16 ===
[[Image:F2L16.png]]

{{Alg|(R U' R' U) d (R' U' R)|F2L}}
{{Alg|(R U' R') U2 (F' U' F)|F2L}}
{{Alg|(U') (R U2 M' U' R' U) (R U r')|F2L}}
{{Alg|(U) R (F R U R' U' F') R'|F2L}}
{{Alg|(U) M' (U R U' r') (U' R U R')|F2L}}
{{Alg|y' U R U2 R U' R U R' U2 R'|F2L}}
{{Alg|y M U' R' F R U M' y'|F2L}}

|-valign="top"
|

=== F2L 17 ===
[[Image:F2L17.png]]

{{Alg|(R U2 R') U' (R U R')|F2L}}

|

=== F2L 18 ===
[[Image:F2L18.png]]

{{Alg|y' (R' U2 R) U (R' U' R)|F2L}}
{{Alg|y (L' U2 L) U (L' U' L)|F2L}}
{{Alg|(R U R' U') R U2 R' U y (L' U L)|F2L}}
{{Alg|(R U R' U') (R U R' U') F R' F' R |F2L}}
{{Alg|F' U2 F U F' U' F|F2L}}
{{Alg|(R' F R F') (R U' R' U) (R U' R')|F2L}}

|-valign="top"
|}

==Pair Made on Side==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 19 ===
[[Image:F2L19.png]]

{{Alg|U R U2 R2 (F R F')|F2L}}
{{Alg|U (R U2 R') U (R U' R')|F2L}}
{{Alg|(R U2 R' U') U' (R U' R' U)(R U R')|F2L}}
|

=== F2L 20 ===
[[Image:F2L20.png]]

{{Alg|U' F' U2 F2 (R' F' R)|F2L}}
{{Alg|y' U' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|y2 d' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|U' (R U R' U) (F' L' U2 L F)|F2L}}
{{Alg|U' (R U' R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U' R' U) (R U') (l U' R' U l')|F2L}}
{{Alg|d' L' U2 L U' L' U L|F2L}}

|-valign="top"
|

=== F2L 21 ===
[[Image:F2L21.png]]
{{Alg|(R U' R') U2 (R U R')|F2L}}
{{Alg|U2 (R U R' U)(R U' R')|F2L}}
{{Alg|R B U2 B' R'|F2L}}
{{Alg|U2 R x' U' R U x R2'|F2L}}
{{Alg|U F R U R' U' R' F' R|F2L}}
|

=== F2L 22 ===
[[Image:F2L22.png]]
{{Alg|y' (R' U R) U2 (R' U' R)|F2L}}
{{Alg|F' L' U2 L F|F2L}}
{{Alg|y' U2 (R' U' R U') (R' U R)|F2L}}
{{Alg|y2 U' d' (R' U' R U') (R' U R)|F2L}}
{{Alg| r U' r' U2 r U r'|F2L}}
{{Alg|U F R U R' U' F' R U R' U2'|F2L}}
{{Alg|d2 y' R' U' R U' R' U R|F2L}}

|-valign="top"
|}

==Weird==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 23 ===
[[Image:F2L23.png]]

{{Alg|U2 R2 U2 (R' U' R U') R2|F2L}}
{{Alg|U (F R' F' R) U (R U R')|F2L}}
{{Alg|U R U' R' U' R U' R' U R U' R'|F2L}}
{{Alg|(R U R' U') U' (R U R' U')(R U R')|F2L}}
{{Alg|(R U2 R') (F' U F) U' (R U R')|F2L}}

|

=== F2L 24 ===
[[Image:F2L24.png]]

{{Alg|U F' L' U L F R U R'|F2L}}
{{Alg|(R U R') d (R' U R U') (R' U R)|F2L}}
{{Alg|y' (R' U' R U) U (R' U' R U)(R' U' R)|F2L}}
{{Alg|y' U2 R2 U2 (R U R' U) R2|F2L}}
{{Alg|U' (R U) (R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U R' U) (R U') (l U' R' U l') |F2L}}
{{Alg|U2 F2 U2 (F U F' U) F2|F2L}}
{{Alg|F U (R U' R' F')(R U' R')|F2L}}
{{Alg|d' (F' L F L') U' (L' U' L)|F2L}}
{{Alg|y (L' U' L U) U (L' U' L U)(L' U' L )|F2L}}

|-valign="top"
|}

==Corner in Place, Edge in U Face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 25 ===
[[Image:F2L25.png]]

{{Alg|d' (L' U L) d (R U' R')|F2L}}
{{Alg|d' (L' U L) (F' L F L')|F2L}}
{{Alg|y U' (L' U' L) U (F U F')|F2L}}
{{Alg|U' (F' U F) U (R U' R')|F2L}}
{{Alg|U' M' U R U' r' (R U R')|F2L}}
{{Alg|R U2 R' U R U2 R' U2 R U' R'|F2L}}
{{Alg|R U R' U2 R U R' U2 R U' R'|F2L}}
{{Alg|R' F' R U R U' R' F|F2L}}
{{Alg|(U') F' R U R' U' R' F R|F2L}}
{{Alg|(R U' R' U') (R U' R' U) (R U R')|F2L}}
{{Alg|y' (l' U' l U) (l F' l' F)|F2L}}
{{Alg|(U) (R' U' R' U') R2 (U R U R)|F2L}}
{{Alg|y U R' u' R U' R' U u R|F2L}}
If the back right slot is open:
{{Alg|R2 U' R' U R2|F2L}}
{{Alg|U D' R U' R' D|F2L}}

|

=== F2L 26 ===
[[Image:F2L26.png]]

{{Alg|U (R U' R') d' (L' U L)|F2L}}
{{Alg|U (R U' R') U' (F' U F)|F2L}}
{{Alg|U (R U' R') (F R' F' R)|F2L}}
{{Alg|U R U (r' R U' R' U M')|F2L}}
{{Alg|U R U' M' U R' U' M|F2L}}
{{Alg|r U r' U2 r U r' U2 r U' r'|F2L}}
{{Alg|y (r U r' U') (r' F r F')|F2L}}

|-valign="top"
|

=== F2L 27 ===
[[Image:F2L27.png]]

{{Alg|(R U' R' U)(R U' R')|F2L}}
{{Alg|(R U' R2)(F R F')|F2L}}
{{Alg|F' U' F U2 (R U' R')|F2L}}

|

=== F2L 28 ===
[[Image:F2L28.png]]

{{Alg|(R U R' U') F R' F' R |F2L}}
{{Alg|(R U R') d (R' U2 R) |F2L}}
{{Alg|y' (R' U R U')(R' U R)|F2L}}
{{Alg|(R U R') U (F' U2 F)|F2L}}
{{Alg|R U2 l U' R' U l'|F2L}}
{{Alg|(R U R') U l2 F' l' U l'|F2L}}
{{Alg|(F' U F2)(R' F' R)|F2L}}
{{Alg|(U2) R' F R F2 L' U2 L F|F2L}}

|-valign="top"
|

=== F2L 29 ===
[[Image:F2L29.png]]

{{Alg|y' (R' U' R U)(R' U' R)|F2L}}
{{Alg|U2 (R U' R') y' (R' U' R)|F2L}}
{{Alg|(R' F R F')(R' F R F')|F2L}}
{{Alg|M' U R U' r' U (R U' R')|F2L}}

|

=== F2L 30 ===
[[Image:F2L30.png]]

{{Alg|(R U R' U')(R U R')|F2L}}
{{Alg|U2 (F' U F)(R U R')|F2L}}
{{Alg|U' (R U2 R')U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge in Place, Corner in U face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 31 ===
[[Image:F2L31.png]]

{{Alg|(R U' R') d (R' U R)|F2L}}
{{Alg|(R U' R' U)(F' U F)|F2L}}
{{Alg|U' R' F R F' R U' R'|F2L}}
{{Alg|R U' l U' R' U l'|F2L}}
{{Alg|F2 r U r' F R U' R'|F2L}}
{{Alg|R U2 R' U' F R' F' R|F2L}}
{{Alg|R U' R B' R' B R'|F2L}}
|

=== F2L 32 ===
[[Image:F2L32.png]]

{{Alg|(R U R' U')(R U R' U')(R U R')|F2L}}
{{Alg|(U R U' R')(U R U' R')(U R U' R')|F2L}}
{{Alg|U2 R d' R U R' d R'|F2L}}
{{Alg|U R d' R U2 R' d R'|F2L}}
{{Alg|R2 U R2 U R2 U2 R2|F2L}}
{{Alg|U2 R2 U2 R2 U' R2 U' R2|F2L}}
{{Alg|(R U2 R') (F' U2 F) U' (R U R')|F2L}}

|-valign="top"
|

=== F2L 33 ===
[[Image:F2L33.png]]

{{Alg|U' (R U' R') U2' (R U' R')|F2L}}
{{Alg|y U' L' U' R' U L U' R|F2L}}
{{Alg|(U' R U' R') U2 (R U' R')|F2L}}
{{Alg|y U' (L' U' L) U2 (L' U' L)|F2L}}
{{Alg|U y F U R U R' U' R U' R' F'|F2L}}
{{Alg|(U' F' U' F) U2 (F' U' F)|F2L}}
{{Alg|y' U' R D R' U R D' R'|F2L}}

|

=== F2L 34 ===
[[Image:F2L34.png]]

{{Alg|U (F' U F) U2 (F' U F)|F2L}}
{{Alg|U' (R U2' R') U (R U R')|F2L}}
{{Alg|U (R U R') U2 (R U R')|F2L}}
{{Alg|d (R' U R) U2 (R' U R)|F2L}}
{{Alg|y (U L' U L) U2 (L' U L)|F2L}}
{{Alg|U y F U2 R U2 R' F'|F2L}}
Back right slot open:
{{Alg|E' R U R' E|F2L}}
{{Alg|E' U' F' U F E|F2L}}

|-valign="top"
|

=== F2L 35 ===
[[Image:F2L35.png]]

{{Alg|(U' R U R') d (R' U' R)|F2L}}
{{Alg|U2 (R U' R') U' (F' U' F)|F2L}}
{{Alg|U M' U R U' r' R U' R'|F2L}}
{{Alg|U' l U' R U l' U R'|F2L}}

|

=== F2L 36 ===
[[Image:F2L36.png]]

{{Alg|d (R' U' R) d' (R U R')|F2L}}
{{Alg|y U2 (L' U L) U (F U F')|F2L}}
{{Alg|U F' U' F U' (R U R')|F2L}}
{{Alg|U2 (R' F R F') U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge and Corner in Place==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 37 ===
[[Image:F2L37.png]]

Solved

|

=== F2L 38 ===
[[Image:F2L38.png]]

{{Alg|(R' F R F') (R U' R' U) (R U' R' U2) (R U' R')|F2L}}
{{Alg|(R U' R') d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|(R U R') U2 (R U2 R') d (R' U' R)|F2L}}
{{Alg|(R2 U2) (F R2 F') (U2 R' U R')|F2L}}

Back right corner free- D' R U R' F R' F' R
|-valign="top"
|

=== F2L 39 ===
[[Image:F2L39.png]]

{{Alg|(R U' R') U' (R U R') U2 (R U' R')|F2L}}
{{Alg|y' (R' U' R) U2 (R' U R U') (R' U' R)|F2L}}
{{Alg|y (L' U' L) U2 (L' U L U')(L' U' L)|F2L}}
{{Alg|(R U R' U') (R U2 R') U' (R U R')|F2L}}
{{Alg|(R U2 R' U2) (R U2 R' U') R U R'|F2L}}
{{Alg|R U' R' F2 L' U' L U F2|F2L}}
{{Alg|(R2 U2) (R' U' R U') (R' U2 R')|F2L}}

=== F2L 40 ===
[[Image:F2L40.png]]

{{Alg|(R U' R' U)(R U2' R') U (R U' R')|F2L}}
{{Alg|(R U R') U2 (R U' R' U)(R U R')|F2L}}
{{Alg|(R U2) (R U R' U) (R U2 R2')|F2L}}

|-valign="top"
|

=== F2L 41 ===
[[Image:F2L41.png]]

{{Alg|(R U' R') d (R' U' R U') (R' U' R)|F2L}}
{{Alg|R U' R' U' R U' R' d R' U' R|F2L}}
{{Alg|y (L' U' L U)(L' U L) U2 (F U F')|F2L}}
{{Alg|(R U' R) y (U R U' R') y' R2|F2L}}
{{Alg|F2 (L' U' L U) y (L U' L)|F2L}}
{{Alg|R F (U R U' R' F') U' R'|F2L}}
|

=== F2L 42 ===
[[Image:F2L42.png]]

{{Alg|(R U' R' U) d (R' U' R U') (R' U R)|F2L}}
{{Alg|(R U' R' U2) y' (R' U' R U' R' U R)|F2L}}
{{Alg|(R U R' U') (R U' R') U2 (F' U' F)|F2L}}
{{Alg|y (L' U L) d' (L U L' U) (L U L')|F2L}}
{{Alg|R2 y (R U R' U') y' (R' U R')|F2L}}
{{Alg|(R U' R')(F' L' U2 L F)|F2L}}
{{Alg| R U (F R U R' U' F') R'|F2L}}
|-valign="top"
|}

== See also ==
* [[Keyhole First Two Layers]]
* [[Intuitive solving]]
* [[Advanced F2L]]
* [[ZBLS]]
* [[Fridrich Method]]
* [[Petrus Method]]

== External Resources ==
=== Beginner ===
* [http://rishidoshi.blogspot.com/ RiDo's Hunting Story] - Simple analogy method for F2L

=== Standard ===
* [http://erikku.er.funpic.org/rubik/F2L.html Erik Akkersdijk's F2L Cases (from his old site)]
* [http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l Dan Harris's F2L Cases]
* [http://www.opticubes.com/cubing/f2l/ Opticubes.com Optimal F2L Cases]
* [http://jmbaum.110mb.com/f2l.htm Jason Baum's F2L Cases]
* [http://www.kungfoomanchu.com/#333speedcubing Andy Klise's Printable F2L PDF]
* [http://www.cubeloop.com/php/cube/advanced.php?chapter=f2l CubeLoop F2L Algs]
* [http://www.cubewhiz.com/pll.php Bob Burton's F2L Cases]
* [http://cubefreak.net/speed/advancedf2l/standard.php F2L algs for every case from all angles by Shotaro Makisumi]
* Youtube: [http://www.youtube.com/watch?v=J8Yl3lioY8c How to get faster at the 3x3 Rubik's cube - F2L] - by Feliks Zemdegs
* Youtube: [http://www.youtube.com/watch?v=k-xbcAMfWwM Rubik's Cube: Fridrich F2L explained] - by Badmephisto

=== Advanced ===
* Youtube: [https://www.youtube.com/playlist?list=PL83bqDZwr97mik_tbQrCJQQcXsb-wzC53 Expert F2L (Russian language)] - by Viktor Danilov
* [http://www.speedsolving.com/forum/showthread.php?t=15050 Erik Expert F2L tutorial]
* [http://cubefreak.net/advancedf2l/ Cubefreak Advanced F2L]
* [http://pagesperso-orange.fr/absolutemind/ms-angl.html Multislotting Tutorial]

== F2L Trainers ==
[http://expertcuber.by/ ExpertCuber.by]

[[Category:3x3x3 other substeps]]

__NOTOC__

First Two Layers

2016-02-18T03:15:37Z

Addons zz: /* F2L 33 */

{{Substep Infobox
|name=F2L
|image=F2Linfo.png
|proposers=[[René Schoof]]
|year=1981
|anames=First Two Layers
|variants=[[ZBLS]], [[VHF2L]], [[WV]], [[MGLS]], possibly others
|subgroup=<nowiki><U,R,L,F,B></nowiki>
|algs=42
|moves=6.7 [[HTM]] a slot
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[Cross cube state]]
|next=[[F2L cube state]]
|previousimage=[[Image:VisualCube_3_Egell.png|120px|left|link=Cross cube state]]
|nextimage=[[Image:F2L_higlight.jpg|120px|right|link=F2L cube state]]

}}
'''First Two Layers''', or '''F2L''' are normally the first two bottom layers of the [[3x3x3 cube]], or essentially all layers up until the last layer on larger cubes.

The definition is a little different depending on the subject or who you are talking to. Normally it is as above but it may also refer to the part of the [[Fridrich method]] that solves the [[pair]]s without counting the [[cross]] part.

[[2-gen]] F2L, most pairs (30:42) have the edge sitting in the U-layer having two orientations, it shows R or F colour at the side. If it is the R colour you can solve the pair using only RU and if it is the F colour you can turn the cube (y') and sovle the pair to the back slot using only RU. The only pairs that needs both R and F turns are the six ones with the edge unoriented in the slot, if the edge is oriented in the slot both ways works.

 
== Approaches ==

=== Petrus F2L ===

Another way to solve the 'F2L' is by building blocks, common during the first two layers of the [[Petrus]] method.

=== Fridrich F2L ===
There are many ways to solve the 'F2L' on a cube. A common system is using the [[Fridrich]] method first two layer approach. After solving the cross, a corner-edge pair is paired up, and then inserted into the correct slot. A total of four corner edge (or 'CE') pairs are made and inserted to solve the first two layers.

The concept of pairing up four corner/edge pairs was first proposed by [[René Schoof]] in 1981.

{{F2L}}

==Easy Cases==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 1 ===
[[Image:F2L01.png]]

{{Alg|U (R U' R')|F2L}}
{{Alg|R' F R F'|F2L}}
{{Alg|U2 (R U2 R')|F2L}}

|

=== F2L 2 ===
[[Image:F2L02.png]]

{{Alg|y' U' (R' U R)|F2L}}
{{Alg|U' (F' U F)|F2L}}
{{Alg|F R' F' R|F2L}}
{{Alg|d' L' U L|F2L}}
{{Alg|r U R' U' M|F2L}}
{{Alg|(U2) l R U' R' U l'|F2L}}
{{Alg|(U2) l2 F' l' U l'|F2L}}
{{Alg|(U') F R' F' R2 U' R'|F2L}}

|-valign="top"
|

=== F2L 3 ===
[[Image:F2L03.png]]

{{Alg|y' (R' U' R)|F2L}}
{{Alg|y (L' U' L)|F2L}}
{{alg|F' U' F|F2L}}
{{Alg|U M R U' R' U M'|F2L}}
{{Alg|U r' R2 U' R' U M'|F2L}}

|

=== F2L 4 ===
[[Image:F2L04.png]]

{{Alg|(R U R')|F2L}}
{{Alg|(U2) L (R U' R') U L'|F2L}}

|-valign="top"
|}

==Reposition Edge==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 5 ===
[[Image:F2L05.png]]

{{Alg|(U' R U R') U2 (R U' R')|F2L}}
{{Alg|(U' R U R') U (R' F R F')|F2L}}
{{Alg|F2 (L' U' L U) F2|F2L}}
{{Alg|L U' R U L' R' U2 R U' R'|F2L}}
{{Alg|U' (R U R') U' R U2 R'|F2L}}

|

=== F2L 6 ===
[[Image:F2L06.png]]

{{Alg|d (R' U' R) U2' (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U2 (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U' y (F R' F' R)|F2L}}
{{Alg|U' (r U' R' U) (R U r')|F2L}}
{{Alg|R2 (B U B' U') R2|F2L}}
{{Alg|y F2 (R U R' U') F2|F2L}}

|-valign="top"
|

=== F2L 7 ===
[[Image:F2L07.png]]

{{Alg|U' (R U2' R') U2 (R U' R')|F2L}}
{{Alg|U' R U2 R' U' R U2 R'|F2L}}
{{Alg|M' U' M U2 r U' r'|F2L}}
{{Alg|R U B U2 B' U R'|F2L}}

|

=== F2L 8 ===
[[Image:F2L08.png]]

{{Alg|d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|y' U (R' U2 R) U2 (R' U R)|F2L}}
{{Alg|(r' U2) (R2 U R2 U r)|F2L}}
{{Alg|y' R' U' F' U2 F U' R|F2L}}

|-valign="top"
|}

==Reposition Edge and Flip Corner==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 9 ===
[[Image:F2L09.png]]

{{Alg|U' R U' R' d R' U' R |F2L}}
{{Alg|d (R' U' R U') (R' U' R)|F2L}}
{{Alg|y2 U' (L U' L') d (L' U' L)|F2L}}
{{Alg|U r U R' U' R2 r' U' R'|F2L}}
{{Alg|U' R U' R' U2 M R U' R' U M'|F2L}}
{{Alg|F (R U R' U') F' R U' R'|F2L}}
{{Alg|(U F' U' F) U' (F' U' F)|F2L}}
{{Alg|y F2 (U R U' R') F2|F2L}}

|

=== F2L 10 ===
[[Image:F2L10.png]]

{{Alg|U' (R U R' U)(R U R')|F2L}}
{{Alg|R d' R U R' U2 F'|F2L}}
{{Alg|U F' U F U' R U R'|F2L}}
{{Alg|d R' U R d' R U R'|F2L}}
{{Alg|y2 B2 (U' R' U R) B2|F2L}}

Back Right Slot Open: R' U R2 U R'

|-valign="top"
|

=== F2L 11 ===
[[Image:F2L11.png]]

{{Alg|U' (R U2' R') d (R' U' R)|F2L}}
{{Alg|(y) L' d L' U2 L U2 F|F2L}}
{{Alg|U' R U2 R' U2 M R U' R' U M'|F2L}}
{{Alg|U (F R' F' R)2 U' R U R'|F2L}}
{{Alg|(y') R U2 R2 U' R2 U' R'|F2L}}
{{Alg|U' l F U' R U l' U R'|F2L}}
|

=== F2L 12 ===
[[Image:F2L12.png]]

{{Alg|R U' R' U R U' R' U2 R U' R'|F2L}}
{{Alg|d (R' U2 R) d' (R U R')|F2L}}
{{Alg|R U2 R' U2' R U2' R' U2' R U' R'|F2L}}
{{Alg|R' U2 R2 U R2 U R|F2L}}
{{Alg|y (F U') (R U2 R' U2') F'|F2L}}
{{Alg|(U R U' R') U' (R U R' U') (R U R')|F2L}}
Back right slot open: R' U2 R2 U R'

|-valign="top"
|

=== F2L 13 ===
[[Image:F2L13.png]]

{{Alg|d (R' U R U') (R' U' R)|F2L}}
{{Alg|y' U (R' U R U') (R' U' R)|F2L}}
{{Alg|(U F' U F) U' (F' U' F)|F2L}}
{{Alg|M' U' (R U R') U' (R U2 r')|F2L}}
{{Alg|(R U' R') U (R' F R F') (R U' R')|F2L}}
{{Alg|(R U R') d' (L' U' L U) (L' U' L)|F2L}}
{{Alg|(R U' R' U2) (R U' l U' R' U l')|F2L}}
Back right slot open : R' U R F' U' F

|

=== F2L 14 ===
[[Image:F2L14.png]]

{{Alg|U' (R U' R' U) (R U R')|F2L}}
{{Alg|d' F U' F' d R U R'|F2L}}

|-valign="top"
|}

==Split Pair by Going Over==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 15 ===
[[Image:F2L15.png]]

{{Alg|M U L F' L' U' M'|F2L}}
{{Alg|U (R' F R F') U (R U R')|F2L}}
{{Alg|y' (R' U R U') d' (R U R')|F2L}}
{{Alg|y (L' U L) U2 y' (R U R')|F2L}}
{{Alg|R U2 R' U R U R' U R U' R'|F2L}}
{{Alg|R U R' U2 R U' R' U R U' R'|F2L}}
{{Alg|R U' R U2' R2' U' R2 U' R2'|F2L}}
{{Alg|U' R2 U2 R U' R' U R' U2 R2|F2L}}
{{Alg|U2 (R U R' U') R U2 R' U R U R'|F2L}}
Front left slot open: U (R U' R') D (R U' R') D'

Back right slot open: U' (R' U R U') (R U R')

=== F2L 16 ===
[[Image:F2L16.png]]

{{Alg|(R U' R' U) d (R' U' R)|F2L}}
{{Alg|(R U' R') U2 (F' U' F)|F2L}}
{{Alg|(U') (R U2 M' U' R' U) (R U r')|F2L}}
{{Alg|(U) R (F R U R' U' F') R'|F2L}}
{{Alg|(U) M' (U R U' r') (U' R U R')|F2L}}
{{Alg|y' U R U2 R U' R U R' U2 R'|F2L}}
{{Alg|y M U' R' F R U M' y'|F2L}}

|-valign="top"
|

=== F2L 17 ===
[[Image:F2L17.png]]

{{Alg|(R U2 R') U' (R U R')|F2L}}

|

=== F2L 18 ===
[[Image:F2L18.png]]

{{Alg|y' (R' U2 R) U (R' U' R)|F2L}}
{{Alg|y (L' U2 L) U (L' U' L)|F2L}}
{{Alg|(R U R' U') R U2 R' U y (L' U L)|F2L}}
{{Alg|(R U R' U') (R U R' U') F R' F' R |F2L}}
{{Alg|F' U2 F U F' U' F|F2L}}
{{Alg|(R' F R F') (R U' R' U) (R U' R')|F2L}}

|-valign="top"
|}

==Pair Made on Side==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 19 ===
[[Image:F2L19.png]]

{{Alg|U R U2 R2 (F R F')|F2L}}
{{Alg|U (R U2 R') U (R U' R')|F2L}}
{{Alg|(R U2 R' U') U' (R U' R' U)(R U R')|F2L}}
|

=== F2L 20 ===
[[Image:F2L20.png]]

{{Alg|U' F' U2 F2 (R' F' R)|F2L}}
{{Alg|y' U' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|y2 d' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|U' (R U R' U) (F' L' U2 L F)|F2L}}
{{Alg|U' (R U' R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U' R' U) (R U') (l U' R' U l')|F2L}}
{{Alg|d' L' U2 L U' L' U L|F2L}}

|-valign="top"
|

=== F2L 21 ===
[[Image:F2L21.png]]
{{Alg|(R U' R') U2 (R U R')|F2L}}
{{Alg|U2 (R U R' U)(R U' R')|F2L}}
{{Alg|R B U2 B' R'|F2L}}
{{Alg|U2 R x' U' R U x R2'|F2L}}
{{Alg|U F R U R' U' R' F' R|F2L}}
|

=== F2L 22 ===
[[Image:F2L22.png]]
{{Alg|y' (R' U R) U2 (R' U' R)|F2L}}
{{Alg|F' L' U2 L F|F2L}}
{{Alg|y' U2 (R' U' R U') (R' U R)|F2L}}
{{Alg|y2 U' d' (R' U' R U') (R' U R)|F2L}}
{{Alg| r U' r' U2 r U r'|F2L}}
{{Alg|U F R U R' U' F' R U R' U2'|F2L}}
{{Alg|d2 y' R' U' R U' R' U R|F2L}}

|-valign="top"
|}

==Weird==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 23 ===
[[Image:F2L23.png]]

{{Alg|U2 R2 U2 (R' U' R U') R2|F2L}}
{{Alg|U (F R' F' R) U (R U R')|F2L}}
{{Alg|U R U' R' U' R U' R' U R U' R'|F2L}}
{{Alg|(R U R' U') U' (R U R' U')(R U R')|F2L}}
{{Alg|(R U2 R') (F' U F) U' (R U R')|F2L}}

|

=== F2L 24 ===
[[Image:F2L24.png]]

{{Alg|U F' L' U L F R U R'|F2L}}
{{Alg|(R U R') d (R' U R U') (R' U R)|F2L}}
{{Alg|y' (R' U' R U) U (R' U' R U)(R' U' R)|F2L}}
{{Alg|y' U2 R2 U2 (R U R' U) R2|F2L}}
{{Alg|U' (R U) (R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U R' U) (R U') (l U' R' U l') |F2L}}
{{Alg|U2 F2 U2 (F U F' U) F2|F2L}}
{{Alg|F U (R U' R' F')(R U' R')|F2L}}
{{Alg|d' (F' L F L') U' (L' U' L)|F2L}}
{{Alg|y (L' U' L U) U (L' U' L U)(L' U' L )|F2L}}

|-valign="top"
|}

==Corner in Place, Edge in U Face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 25 ===
[[Image:F2L25.png]]

{{Alg|d' (L' U L) d (R U' R')|F2L}}
{{Alg|d' (L' U L) (F' L F L')|F2L}}
{{Alg|y U' (L' U' L) U (F U F')|F2L}}
{{Alg|U' (F' U F) U (R U' R')|F2L}}
{{Alg|U' M' U R U' r' (R U R')|F2L}}
{{Alg|R U2 R' U R U2 R' U2 R U' R'|F2L}}
{{Alg|R U R' U2 R U R' U2 R U' R'|F2L}}
{{Alg|R' F' R U R U' R' F|F2L}}
{{Alg|(U') F' R U R' U' R' F R|F2L}}
{{Alg|(R U' R' U') (R U' R' U) (R U R')|F2L}}
{{Alg|y' (l' U' l U) (l F' l' F)|F2L}}
{{Alg|(U) (R' U' R' U') R2 (U R U R)|F2L}}
{{Alg|y U R' u' R U' R' U u R|F2L}}
If the back right slot is open:
{{Alg|R2 U' R' U R2|F2L}}
{{Alg|U D' R U' R' D|F2L}}

|

=== F2L 26 ===
[[Image:F2L26.png]]

{{Alg|U (R U' R') d' (L' U L)|F2L}}
{{Alg|U (R U' R') U' (F' U F)|F2L}}
{{Alg|U (R U' R') (F R' F' R)|F2L}}
{{Alg|U R U (r' R U' R' U M')|F2L}}
{{Alg|U R U' M' U R' U' M|F2L}}
{{Alg|r U r' U2 r U r' U2 r U' r'|F2L}}
{{Alg|y (r U r' U') (r' F r F')|F2L}}

|-valign="top"
|

=== F2L 27 ===
[[Image:F2L27.png]]

{{Alg|(R U' R' U)(R U' R')|F2L}}
{{Alg|(R U' R2)(F R F')|F2L}}
{{Alg|F' U' F U2 (R U' R')|F2L}}

|

=== F2L 28 ===
[[Image:F2L28.png]]

{{Alg|(R U R' U') F R' F' R |F2L}}
{{Alg|(R U R') d (R' U2 R) |F2L}}
{{Alg|y' (R' U R U')(R' U R)|F2L}}
{{Alg|(R U R') U (F' U2 F)|F2L}}
{{Alg|R U2 l U' R' U l'|F2L}}
{{Alg|(R U R') U l2 F' l' U l'|F2L}}
{{Alg|(F' U F2)(R' F' R)|F2L}}
{{Alg|(U2) R' F R F2 L' U2 L F|F2L}}

|-valign="top"
|

=== F2L 29 ===
[[Image:F2L29.png]]

{{Alg|y' (R' U' R U)(R' U' R)|F2L}}
{{Alg|U2 (R U' R') y' (R' U' R)|F2L}}
{{Alg|(R' F R F')(R' F R F')|F2L}}
{{Alg|M' U R U' r' U (R U' R')|F2L}}

|

=== F2L 30 ===
[[Image:F2L30.png]]

{{Alg|(R U R' U')(R U R')|F2L}}
{{Alg|U2 (F' U F)(R U R')|F2L}}
{{Alg|U' (R U2 R')U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge in Place, Corner in U face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 31 ===
[[Image:F2L31.png]]

{{Alg|(R U' R') d (R' U R)|F2L}}
{{Alg|(R U' R' U)(F' U F)|F2L}}
{{Alg|U' R' F R F' R U' R'|F2L}}
{{Alg|R U' l U' R' U l'|F2L}}
{{Alg|F2 r U r' F R U' R'|F2L}}
{{Alg|R U2 R' U' F R' F' R|F2L}}
{{Alg|R U' R B' R' B R'|F2L}}
|

=== F2L 32 ===
[[Image:F2L32.png]]

{{Alg|(R U R' U')(R U R' U')(R U R')|F2L}}
{{Alg|(U R U' R')(U R U' R')(U R U' R')|F2L}}
{{Alg|U2 R d' R U R' d R'|F2L}}
{{Alg|U R d' R U2 R' d R'|F2L}}
{{Alg|R2 U R2 U R2 U2 R2|F2L}}
{{Alg|U2 R2 U2 R2 U' R2 U' R2|F2L}}
{{Alg|(R U2 R') (F' U2 F) U' (R U R')|F2L}}

|-valign="top"
|

=== F2L 33 ===
[[Image:F2L33.png]]

{{Alg|U' (R U' R') U'2 (R U' R')|F2L}}
{{Alg|y U' L' U' R' U L U' R|F2L}}
{{Alg|(U' R U' R') U2 (R U' R')|F2L}}
{{Alg|y U' (L' U' L) U2 (L' U' L)|F2L}}
{{Alg|U y F U R U R' U' R U' R' F'|F2L}}
{{Alg|(U' F' U' F) U2 (F' U' F)|F2L}}
{{Alg|y' U' R D R' U R D' R'|F2L}}

|

=== F2L 34 ===
[[Image:F2L34.png]]

{{Alg|U (F' U F) U2 (F' U F)|F2L}}
{{Alg|U' (R U2' R') U (R U R')|F2L}}
{{Alg|U (R U R') U2 (R U R')|F2L}}
{{Alg|d (R' U R) U2 (R' U R)|F2L}}
{{Alg|y (U L' U L) U2 (L' U L)|F2L}}
{{Alg|U y F U2 R U2 R' F'|F2L}}
Back right slot open:
{{Alg|E' R U R' E|F2L}}
{{Alg|E' U' F' U F E|F2L}}

|-valign="top"
|

=== F2L 35 ===
[[Image:F2L35.png]]

{{Alg|(U' R U R') d (R' U' R)|F2L}}
{{Alg|U2 (R U' R') U' (F' U' F)|F2L}}
{{Alg|U M' U R U' r' R U' R'|F2L}}
{{Alg|U' l U' R U l' U R'|F2L}}

|

=== F2L 36 ===
[[Image:F2L36.png]]

{{Alg|d (R' U' R) d' (R U R')|F2L}}
{{Alg|y U2 (L' U L) U (F U F')|F2L}}
{{Alg|U F' U' F U' (R U R')|F2L}}
{{Alg|U2 (R' F R F') U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge and Corner in Place==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 37 ===
[[Image:F2L37.png]]

Solved

|

=== F2L 38 ===
[[Image:F2L38.png]]

{{Alg|(R' F R F') (R U' R' U) (R U' R' U2) (R U' R')|F2L}}
{{Alg|(R U' R') d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|(R U R') U2 (R U2 R') d (R' U' R)|F2L}}
{{Alg|(R2 U2) (F R2 F') (U2 R' U R')|F2L}}

Back right corner free- D' R U R' F R' F' R
|-valign="top"
|

=== F2L 39 ===
[[Image:F2L39.png]]

{{Alg|(R U' R') U' (R U R') U2 (R U' R')|F2L}}
{{Alg|y' (R' U' R) U2 (R' U R U') (R' U' R)|F2L}}
{{Alg|y (L' U' L) U2 (L' U L U')(L' U' L)|F2L}}
{{Alg|(R U R' U') (R U2 R') U' (R U R')|F2L}}
{{Alg|(R U2 R' U2) (R U2 R' U') R U R'|F2L}}
{{Alg|R U' R' F2 L' U' L U F2|F2L}}
{{Alg|(R2 U2) (R' U' R U') (R' U2 R')|F2L}}

=== F2L 40 ===
[[Image:F2L40.png]]

{{Alg|(R U' R' U)(R U2' R') U (R U' R')|F2L}}
{{Alg|(R U R') U2 (R U' R' U)(R U R')|F2L}}
{{Alg|(R U2) (R U R' U) (R U2 R2')|F2L}}

|-valign="top"
|

=== F2L 41 ===
[[Image:F2L41.png]]

{{Alg|(R U' R') d (R' U' R U') (R' U' R)|F2L}}
{{Alg|R U' R' U' R U' R' d R' U' R|F2L}}
{{Alg|y (L' U' L U)(L' U L) U2 (F U F')|F2L}}
{{Alg|(R U' R) y (U R U' R') y' R2|F2L}}
{{Alg|F2 (L' U' L U) y (L U' L)|F2L}}
{{Alg|R F (U R U' R' F') U' R'|F2L}}
|

=== F2L 42 ===
[[Image:F2L42.png]]

{{Alg|(R U' R' U) d (R' U' R U') (R' U R)|F2L}}
{{Alg|(R U' R' U2) y' (R' U' R U' R' U R)|F2L}}
{{Alg|(R U R' U') (R U' R') U2 (F' U' F)|F2L}}
{{Alg|y (L' U L) d' (L U L' U) (L U L')|F2L}}
{{Alg|R2 y (R U R' U') y' (R' U R')|F2L}}
{{Alg|(R U' R')(F' L' U2 L F)|F2L}}
{{Alg| R U (F R U R' U' F') R'|F2L}}
|-valign="top"
|}

== See also ==
* [[Keyhole First Two Layers]]
* [[Intuitive solving]]
* [[Advanced F2L]]
* [[ZBLS]]
* [[Fridrich Method]]
* [[Petrus Method]]

== External Resources ==
=== Beginner ===
* [http://rishidoshi.blogspot.com/ RiDo's Hunting Story] - Simple analogy method for F2L

=== Standard ===
* [http://erikku.er.funpic.org/rubik/F2L.html Erik Akkersdijk's F2L Cases (from his old site)]
* [http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l Dan Harris's F2L Cases]
* [http://www.opticubes.com/cubing/f2l/ Opticubes.com Optimal F2L Cases]
* [http://jmbaum.110mb.com/f2l.htm Jason Baum's F2L Cases]
* [http://www.kungfoomanchu.com/#333speedcubing Andy Klise's Printable F2L PDF]
* [http://www.cubeloop.com/php/cube/advanced.php?chapter=f2l CubeLoop F2L Algs]
* [http://www.cubewhiz.com/pll.php Bob Burton's F2L Cases]
* [http://cubefreak.net/speed/advancedf2l/standard.php F2L algs for every case from all angles by Shotaro Makisumi]
* Youtube: [http://www.youtube.com/watch?v=J8Yl3lioY8c How to get faster at the 3x3 Rubik's cube - F2L] - by Feliks Zemdegs
* Youtube: [http://www.youtube.com/watch?v=k-xbcAMfWwM Rubik's Cube: Fridrich F2L explained] - by Badmephisto

=== Advanced ===
* Youtube: [https://www.youtube.com/playlist?list=PL83bqDZwr97mik_tbQrCJQQcXsb-wzC53 Expert F2L (Russian language)] - by Viktor Danilov
* [http://www.speedsolving.com/forum/showthread.php?t=15050 Erik Expert F2L tutorial]
* [http://cubefreak.net/advancedf2l/ Cubefreak Advanced F2L]
* [http://pagesperso-orange.fr/absolutemind/ms-angl.html Multislotting Tutorial]

== F2L Trainers ==
[http://expertcuber.by/ ExpertCuber.by]

[[Category:3x3x3 other substeps]]

__NOTOC__

First Two Layers

2016-02-18T03:13:40Z

Addons zz: /* F2L 34 */

{{Substep Infobox
|name=F2L
|image=F2Linfo.png
|proposers=[[René Schoof]]
|year=1981
|anames=First Two Layers
|variants=[[ZBLS]], [[VHF2L]], [[WV]], [[MGLS]], possibly others
|subgroup=<nowiki><U,R,L,F,B></nowiki>
|algs=42
|moves=6.7 [[HTM]] a slot
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[Cross cube state]]
|next=[[F2L cube state]]
|previousimage=[[Image:VisualCube_3_Egell.png|120px|left|link=Cross cube state]]
|nextimage=[[Image:F2L_higlight.jpg|120px|right|link=F2L cube state]]

}}
'''First Two Layers''', or '''F2L''' are normally the first two bottom layers of the [[3x3x3 cube]], or essentially all layers up until the last layer on larger cubes.

The definition is a little different depending on the subject or who you are talking to. Normally it is as above but it may also refer to the part of the [[Fridrich method]] that solves the [[pair]]s without counting the [[cross]] part.

[[2-gen]] F2L, most pairs (30:42) have the edge sitting in the U-layer having two orientations, it shows R or F colour at the side. If it is the R colour you can solve the pair using only RU and if it is the F colour you can turn the cube (y') and sovle the pair to the back slot using only RU. The only pairs that needs both R and F turns are the six ones with the edge unoriented in the slot, if the edge is oriented in the slot both ways works.

 
== Approaches ==

=== Petrus F2L ===

Another way to solve the 'F2L' is by building blocks, common during the first two layers of the [[Petrus]] method.

=== Fridrich F2L ===
There are many ways to solve the 'F2L' on a cube. A common system is using the [[Fridrich]] method first two layer approach. After solving the cross, a corner-edge pair is paired up, and then inserted into the correct slot. A total of four corner edge (or 'CE') pairs are made and inserted to solve the first two layers.

The concept of pairing up four corner/edge pairs was first proposed by [[René Schoof]] in 1981.

{{F2L}}

==Easy Cases==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 1 ===
[[Image:F2L01.png]]

{{Alg|U (R U' R')|F2L}}
{{Alg|R' F R F'|F2L}}
{{Alg|U2 (R U2 R')|F2L}}

|

=== F2L 2 ===
[[Image:F2L02.png]]

{{Alg|y' U' (R' U R)|F2L}}
{{Alg|U' (F' U F)|F2L}}
{{Alg|F R' F' R|F2L}}
{{Alg|d' L' U L|F2L}}
{{Alg|r U R' U' M|F2L}}
{{Alg|(U2) l R U' R' U l'|F2L}}
{{Alg|(U2) l2 F' l' U l'|F2L}}
{{Alg|(U') F R' F' R2 U' R'|F2L}}

|-valign="top"
|

=== F2L 3 ===
[[Image:F2L03.png]]

{{Alg|y' (R' U' R)|F2L}}
{{Alg|y (L' U' L)|F2L}}
{{alg|F' U' F|F2L}}
{{Alg|U M R U' R' U M'|F2L}}
{{Alg|U r' R2 U' R' U M'|F2L}}

|

=== F2L 4 ===
[[Image:F2L04.png]]

{{Alg|(R U R')|F2L}}
{{Alg|(U2) L (R U' R') U L'|F2L}}

|-valign="top"
|}

==Reposition Edge==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 5 ===
[[Image:F2L05.png]]

{{Alg|(U' R U R') U2 (R U' R')|F2L}}
{{Alg|(U' R U R') U (R' F R F')|F2L}}
{{Alg|F2 (L' U' L U) F2|F2L}}
{{Alg|L U' R U L' R' U2 R U' R'|F2L}}
{{Alg|U' (R U R') U' R U2 R'|F2L}}

|

=== F2L 6 ===
[[Image:F2L06.png]]

{{Alg|d (R' U' R) U2' (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U2 (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U' y (F R' F' R)|F2L}}
{{Alg|U' (r U' R' U) (R U r')|F2L}}
{{Alg|R2 (B U B' U') R2|F2L}}
{{Alg|y F2 (R U R' U') F2|F2L}}

|-valign="top"
|

=== F2L 7 ===
[[Image:F2L07.png]]

{{Alg|U' (R U2' R') U2 (R U' R')|F2L}}
{{Alg|U' R U2 R' U' R U2 R'|F2L}}
{{Alg|M' U' M U2 r U' r'|F2L}}
{{Alg|R U B U2 B' U R'|F2L}}

|

=== F2L 8 ===
[[Image:F2L08.png]]

{{Alg|d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|y' U (R' U2 R) U2 (R' U R)|F2L}}
{{Alg|(r' U2) (R2 U R2 U r)|F2L}}
{{Alg|y' R' U' F' U2 F U' R|F2L}}

|-valign="top"
|}

==Reposition Edge and Flip Corner==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 9 ===
[[Image:F2L09.png]]

{{Alg|U' R U' R' d R' U' R |F2L}}
{{Alg|d (R' U' R U') (R' U' R)|F2L}}
{{Alg|y2 U' (L U' L') d (L' U' L)|F2L}}
{{Alg|U r U R' U' R2 r' U' R'|F2L}}
{{Alg|U' R U' R' U2 M R U' R' U M'|F2L}}
{{Alg|F (R U R' U') F' R U' R'|F2L}}
{{Alg|(U F' U' F) U' (F' U' F)|F2L}}
{{Alg|y F2 (U R U' R') F2|F2L}}

|

=== F2L 10 ===
[[Image:F2L10.png]]

{{Alg|U' (R U R' U)(R U R')|F2L}}
{{Alg|R d' R U R' U2 F'|F2L}}
{{Alg|U F' U F U' R U R'|F2L}}
{{Alg|d R' U R d' R U R'|F2L}}
{{Alg|y2 B2 (U' R' U R) B2|F2L}}

Back Right Slot Open: R' U R2 U R'

|-valign="top"
|

=== F2L 11 ===
[[Image:F2L11.png]]

{{Alg|U' (R U2' R') d (R' U' R)|F2L}}
{{Alg|(y) L' d L' U2 L U2 F|F2L}}
{{Alg|U' R U2 R' U2 M R U' R' U M'|F2L}}
{{Alg|U (F R' F' R)2 U' R U R'|F2L}}
{{Alg|(y') R U2 R2 U' R2 U' R'|F2L}}
{{Alg|U' l F U' R U l' U R'|F2L}}
|

=== F2L 12 ===
[[Image:F2L12.png]]

{{Alg|R U' R' U R U' R' U2 R U' R'|F2L}}
{{Alg|d (R' U2 R) d' (R U R')|F2L}}
{{Alg|R U2 R' U2' R U2' R' U2' R U' R'|F2L}}
{{Alg|R' U2 R2 U R2 U R|F2L}}
{{Alg|y (F U') (R U2 R' U2') F'|F2L}}
{{Alg|(U R U' R') U' (R U R' U') (R U R')|F2L}}
Back right slot open: R' U2 R2 U R'

|-valign="top"
|

=== F2L 13 ===
[[Image:F2L13.png]]

{{Alg|d (R' U R U') (R' U' R)|F2L}}
{{Alg|y' U (R' U R U') (R' U' R)|F2L}}
{{Alg|(U F' U F) U' (F' U' F)|F2L}}
{{Alg|M' U' (R U R') U' (R U2 r')|F2L}}
{{Alg|(R U' R') U (R' F R F') (R U' R')|F2L}}
{{Alg|(R U R') d' (L' U' L U) (L' U' L)|F2L}}
{{Alg|(R U' R' U2) (R U' l U' R' U l')|F2L}}
Back right slot open : R' U R F' U' F

|

=== F2L 14 ===
[[Image:F2L14.png]]

{{Alg|U' (R U' R' U) (R U R')|F2L}}
{{Alg|d' F U' F' d R U R'|F2L}}

|-valign="top"
|}

==Split Pair by Going Over==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 15 ===
[[Image:F2L15.png]]

{{Alg|M U L F' L' U' M'|F2L}}
{{Alg|U (R' F R F') U (R U R')|F2L}}
{{Alg|y' (R' U R U') d' (R U R')|F2L}}
{{Alg|y (L' U L) U2 y' (R U R')|F2L}}
{{Alg|R U2 R' U R U R' U R U' R'|F2L}}
{{Alg|R U R' U2 R U' R' U R U' R'|F2L}}
{{Alg|R U' R U2' R2' U' R2 U' R2'|F2L}}
{{Alg|U' R2 U2 R U' R' U R' U2 R2|F2L}}
{{Alg|U2 (R U R' U') R U2 R' U R U R'|F2L}}
Front left slot open: U (R U' R') D (R U' R') D'

Back right slot open: U' (R' U R U') (R U R')

=== F2L 16 ===
[[Image:F2L16.png]]

{{Alg|(R U' R' U) d (R' U' R)|F2L}}
{{Alg|(R U' R') U2 (F' U' F)|F2L}}
{{Alg|(U') (R U2 M' U' R' U) (R U r')|F2L}}
{{Alg|(U) R (F R U R' U' F') R'|F2L}}
{{Alg|(U) M' (U R U' r') (U' R U R')|F2L}}
{{Alg|y' U R U2 R U' R U R' U2 R'|F2L}}
{{Alg|y M U' R' F R U M' y'|F2L}}

|-valign="top"
|

=== F2L 17 ===
[[Image:F2L17.png]]

{{Alg|(R U2 R') U' (R U R')|F2L}}

|

=== F2L 18 ===
[[Image:F2L18.png]]

{{Alg|y' (R' U2 R) U (R' U' R)|F2L}}
{{Alg|y (L' U2 L) U (L' U' L)|F2L}}
{{Alg|(R U R' U') R U2 R' U y (L' U L)|F2L}}
{{Alg|(R U R' U') (R U R' U') F R' F' R |F2L}}
{{Alg|F' U2 F U F' U' F|F2L}}
{{Alg|(R' F R F') (R U' R' U) (R U' R')|F2L}}

|-valign="top"
|}

==Pair Made on Side==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 19 ===
[[Image:F2L19.png]]

{{Alg|U R U2 R2 (F R F')|F2L}}
{{Alg|U (R U2 R') U (R U' R')|F2L}}
{{Alg|(R U2 R' U') U' (R U' R' U)(R U R')|F2L}}
|

=== F2L 20 ===
[[Image:F2L20.png]]

{{Alg|U' F' U2 F2 (R' F' R)|F2L}}
{{Alg|y' U' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|y2 d' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|U' (R U R' U) (F' L' U2 L F)|F2L}}
{{Alg|U' (R U' R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U' R' U) (R U') (l U' R' U l')|F2L}}
{{Alg|d' L' U2 L U' L' U L|F2L}}

|-valign="top"
|

=== F2L 21 ===
[[Image:F2L21.png]]
{{Alg|(R U' R') U2 (R U R')|F2L}}
{{Alg|U2 (R U R' U)(R U' R')|F2L}}
{{Alg|R B U2 B' R'|F2L}}
{{Alg|U2 R x' U' R U x R2'|F2L}}
{{Alg|U F R U R' U' R' F' R|F2L}}
|

=== F2L 22 ===
[[Image:F2L22.png]]
{{Alg|y' (R' U R) U2 (R' U' R)|F2L}}
{{Alg|F' L' U2 L F|F2L}}
{{Alg|y' U2 (R' U' R U') (R' U R)|F2L}}
{{Alg|y2 U' d' (R' U' R U') (R' U R)|F2L}}
{{Alg| r U' r' U2 r U r'|F2L}}
{{Alg|U F R U R' U' F' R U R' U2'|F2L}}
{{Alg|d2 y' R' U' R U' R' U R|F2L}}

|-valign="top"
|}

==Weird==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 23 ===
[[Image:F2L23.png]]

{{Alg|U2 R2 U2 (R' U' R U') R2|F2L}}
{{Alg|U (F R' F' R) U (R U R')|F2L}}
{{Alg|U R U' R' U' R U' R' U R U' R'|F2L}}
{{Alg|(R U R' U') U' (R U R' U')(R U R')|F2L}}
{{Alg|(R U2 R') (F' U F) U' (R U R')|F2L}}

|

=== F2L 24 ===
[[Image:F2L24.png]]

{{Alg|U F' L' U L F R U R'|F2L}}
{{Alg|(R U R') d (R' U R U') (R' U R)|F2L}}
{{Alg|y' (R' U' R U) U (R' U' R U)(R' U' R)|F2L}}
{{Alg|y' U2 R2 U2 (R U R' U) R2|F2L}}
{{Alg|U' (R U) (R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U R' U) (R U') (l U' R' U l') |F2L}}
{{Alg|U2 F2 U2 (F U F' U) F2|F2L}}
{{Alg|F U (R U' R' F')(R U' R')|F2L}}
{{Alg|d' (F' L F L') U' (L' U' L)|F2L}}
{{Alg|y (L' U' L U) U (L' U' L U)(L' U' L )|F2L}}

|-valign="top"
|}

==Corner in Place, Edge in U Face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 25 ===
[[Image:F2L25.png]]

{{Alg|d' (L' U L) d (R U' R')|F2L}}
{{Alg|d' (L' U L) (F' L F L')|F2L}}
{{Alg|y U' (L' U' L) U (F U F')|F2L}}
{{Alg|U' (F' U F) U (R U' R')|F2L}}
{{Alg|U' M' U R U' r' (R U R')|F2L}}
{{Alg|R U2 R' U R U2 R' U2 R U' R'|F2L}}
{{Alg|R U R' U2 R U R' U2 R U' R'|F2L}}
{{Alg|R' F' R U R U' R' F|F2L}}
{{Alg|(U') F' R U R' U' R' F R|F2L}}
{{Alg|(R U' R' U') (R U' R' U) (R U R')|F2L}}
{{Alg|y' (l' U' l U) (l F' l' F)|F2L}}
{{Alg|(U) (R' U' R' U') R2 (U R U R)|F2L}}
{{Alg|y U R' u' R U' R' U u R|F2L}}
If the back right slot is open:
{{Alg|R2 U' R' U R2|F2L}}
{{Alg|U D' R U' R' D|F2L}}

|

=== F2L 26 ===
[[Image:F2L26.png]]

{{Alg|U (R U' R') d' (L' U L)|F2L}}
{{Alg|U (R U' R') U' (F' U F)|F2L}}
{{Alg|U (R U' R') (F R' F' R)|F2L}}
{{Alg|U R U (r' R U' R' U M')|F2L}}
{{Alg|U R U' M' U R' U' M|F2L}}
{{Alg|r U r' U2 r U r' U2 r U' r'|F2L}}
{{Alg|y (r U r' U') (r' F r F')|F2L}}

|-valign="top"
|

=== F2L 27 ===
[[Image:F2L27.png]]

{{Alg|(R U' R' U)(R U' R')|F2L}}
{{Alg|(R U' R2)(F R F')|F2L}}
{{Alg|F' U' F U2 (R U' R')|F2L}}

|

=== F2L 28 ===
[[Image:F2L28.png]]

{{Alg|(R U R' U') F R' F' R |F2L}}
{{Alg|(R U R') d (R' U2 R) |F2L}}
{{Alg|y' (R' U R U')(R' U R)|F2L}}
{{Alg|(R U R') U (F' U2 F)|F2L}}
{{Alg|R U2 l U' R' U l'|F2L}}
{{Alg|(R U R') U l2 F' l' U l'|F2L}}
{{Alg|(F' U F2)(R' F' R)|F2L}}
{{Alg|(U2) R' F R F2 L' U2 L F|F2L}}

|-valign="top"
|

=== F2L 29 ===
[[Image:F2L29.png]]

{{Alg|y' (R' U' R U)(R' U' R)|F2L}}
{{Alg|U2 (R U' R') y' (R' U' R)|F2L}}
{{Alg|(R' F R F')(R' F R F')|F2L}}
{{Alg|M' U R U' r' U (R U' R')|F2L}}

|

=== F2L 30 ===
[[Image:F2L30.png]]

{{Alg|(R U R' U')(R U R')|F2L}}
{{Alg|U2 (F' U F)(R U R')|F2L}}
{{Alg|U' (R U2 R')U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge in Place, Corner in U face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 31 ===
[[Image:F2L31.png]]

{{Alg|(R U' R') d (R' U R)|F2L}}
{{Alg|(R U' R' U)(F' U F)|F2L}}
{{Alg|U' R' F R F' R U' R'|F2L}}
{{Alg|R U' l U' R' U l'|F2L}}
{{Alg|F2 r U r' F R U' R'|F2L}}
{{Alg|R U2 R' U' F R' F' R|F2L}}
{{Alg|R U' R B' R' B R'|F2L}}
|

=== F2L 32 ===
[[Image:F2L32.png]]

{{Alg|(R U R' U')(R U R' U')(R U R')|F2L}}
{{Alg|(U R U' R')(U R U' R')(U R U' R')|F2L}}
{{Alg|U2 R d' R U R' d R'|F2L}}
{{Alg|U R d' R U2 R' d R'|F2L}}
{{Alg|R2 U R2 U R2 U2 R2|F2L}}
{{Alg|U2 R2 U2 R2 U' R2 U' R2|F2L}}
{{Alg|(R U2 R') (F' U2 F) U' (R U R')|F2L}}

|-valign="top"
|

=== F2L 33 ===
[[Image:F2L33.png]]

{{Alg|y U' L' U' R' U L U' R|F2L}}
{{Alg|(U' R U' R') U2 (R U' R')|F2L}}
{{Alg|y U' (L' U' L) U2 (L' U' L)|F2L}}
{{Alg|U y F U R U R' U' R U' R' F'|F2L}}
{{Alg|(U' F' U' F) U2 (F' U' F)|F2L}}
{{Alg|y' U' R D R' U R D' R'|F2L}}

|

=== F2L 34 ===
[[Image:F2L34.png]]

{{Alg|U (F' U F) U2 (F' U F)|F2L}}
{{Alg|U' (R U2' R') U (R U R')|F2L}}
{{Alg|U (R U R') U2 (R U R')|F2L}}
{{Alg|d (R' U R) U2 (R' U R)|F2L}}
{{Alg|y (U L' U L) U2 (L' U L)|F2L}}
{{Alg|U y F U2 R U2 R' F'|F2L}}
Back right slot open:
{{Alg|E' R U R' E|F2L}}
{{Alg|E' U' F' U F E|F2L}}

|-valign="top"
|

=== F2L 35 ===
[[Image:F2L35.png]]

{{Alg|(U' R U R') d (R' U' R)|F2L}}
{{Alg|U2 (R U' R') U' (F' U' F)|F2L}}
{{Alg|U M' U R U' r' R U' R'|F2L}}
{{Alg|U' l U' R U l' U R'|F2L}}

|

=== F2L 36 ===
[[Image:F2L36.png]]

{{Alg|d (R' U' R) d' (R U R')|F2L}}
{{Alg|y U2 (L' U L) U (F U F')|F2L}}
{{Alg|U F' U' F U' (R U R')|F2L}}
{{Alg|U2 (R' F R F') U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge and Corner in Place==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 37 ===
[[Image:F2L37.png]]

Solved

|

=== F2L 38 ===
[[Image:F2L38.png]]

{{Alg|(R' F R F') (R U' R' U) (R U' R' U2) (R U' R')|F2L}}
{{Alg|(R U' R') d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|(R U R') U2 (R U2 R') d (R' U' R)|F2L}}
{{Alg|(R2 U2) (F R2 F') (U2 R' U R')|F2L}}

Back right corner free- D' R U R' F R' F' R
|-valign="top"
|

=== F2L 39 ===
[[Image:F2L39.png]]

{{Alg|(R U' R') U' (R U R') U2 (R U' R')|F2L}}
{{Alg|y' (R' U' R) U2 (R' U R U') (R' U' R)|F2L}}
{{Alg|y (L' U' L) U2 (L' U L U')(L' U' L)|F2L}}
{{Alg|(R U R' U') (R U2 R') U' (R U R')|F2L}}
{{Alg|(R U2 R' U2) (R U2 R' U') R U R'|F2L}}
{{Alg|R U' R' F2 L' U' L U F2|F2L}}
{{Alg|(R2 U2) (R' U' R U') (R' U2 R')|F2L}}

=== F2L 40 ===
[[Image:F2L40.png]]

{{Alg|(R U' R' U)(R U2' R') U (R U' R')|F2L}}
{{Alg|(R U R') U2 (R U' R' U)(R U R')|F2L}}
{{Alg|(R U2) (R U R' U) (R U2 R2')|F2L}}

|-valign="top"
|

=== F2L 41 ===
[[Image:F2L41.png]]

{{Alg|(R U' R') d (R' U' R U') (R' U' R)|F2L}}
{{Alg|R U' R' U' R U' R' d R' U' R|F2L}}
{{Alg|y (L' U' L U)(L' U L) U2 (F U F')|F2L}}
{{Alg|(R U' R) y (U R U' R') y' R2|F2L}}
{{Alg|F2 (L' U' L U) y (L U' L)|F2L}}
{{Alg|R F (U R U' R' F') U' R'|F2L}}
|

=== F2L 42 ===
[[Image:F2L42.png]]

{{Alg|(R U' R' U) d (R' U' R U') (R' U R)|F2L}}
{{Alg|(R U' R' U2) y' (R' U' R U' R' U R)|F2L}}
{{Alg|(R U R' U') (R U' R') U2 (F' U' F)|F2L}}
{{Alg|y (L' U L) d' (L U L' U) (L U L')|F2L}}
{{Alg|R2 y (R U R' U') y' (R' U R')|F2L}}
{{Alg|(R U' R')(F' L' U2 L F)|F2L}}
{{Alg| R U (F R U R' U' F') R'|F2L}}
|-valign="top"
|}

== See also ==
* [[Keyhole First Two Layers]]
* [[Intuitive solving]]
* [[Advanced F2L]]
* [[ZBLS]]
* [[Fridrich Method]]
* [[Petrus Method]]

== External Resources ==
=== Beginner ===
* [http://rishidoshi.blogspot.com/ RiDo's Hunting Story] - Simple analogy method for F2L

=== Standard ===
* [http://erikku.er.funpic.org/rubik/F2L.html Erik Akkersdijk's F2L Cases (from his old site)]
* [http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l Dan Harris's F2L Cases]
* [http://www.opticubes.com/cubing/f2l/ Opticubes.com Optimal F2L Cases]
* [http://jmbaum.110mb.com/f2l.htm Jason Baum's F2L Cases]
* [http://www.kungfoomanchu.com/#333speedcubing Andy Klise's Printable F2L PDF]
* [http://www.cubeloop.com/php/cube/advanced.php?chapter=f2l CubeLoop F2L Algs]
* [http://www.cubewhiz.com/pll.php Bob Burton's F2L Cases]
* [http://cubefreak.net/speed/advancedf2l/standard.php F2L algs for every case from all angles by Shotaro Makisumi]
* Youtube: [http://www.youtube.com/watch?v=J8Yl3lioY8c How to get faster at the 3x3 Rubik's cube - F2L] - by Feliks Zemdegs
* Youtube: [http://www.youtube.com/watch?v=k-xbcAMfWwM Rubik's Cube: Fridrich F2L explained] - by Badmephisto

=== Advanced ===
* Youtube: [https://www.youtube.com/playlist?list=PL83bqDZwr97mik_tbQrCJQQcXsb-wzC53 Expert F2L (Russian language)] - by Viktor Danilov
* [http://www.speedsolving.com/forum/showthread.php?t=15050 Erik Expert F2L tutorial]
* [http://cubefreak.net/advancedf2l/ Cubefreak Advanced F2L]
* [http://pagesperso-orange.fr/absolutemind/ms-angl.html Multislotting Tutorial]

== F2L Trainers ==
[http://expertcuber.by/ ExpertCuber.by]

[[Category:3x3x3 other substeps]]

__NOTOC__

First Two Layers

2016-02-18T01:46:38Z

Addons zz: /* F2L 41 */

{{Substep Infobox
|name=F2L
|image=F2Linfo.png
|proposers=[[René Schoof]]
|year=1981
|anames=First Two Layers
|variants=[[ZBLS]], [[VHF2L]], [[WV]], [[MGLS]], possibly others
|subgroup=<nowiki><U,R,L,F,B></nowiki>
|algs=42
|moves=6.7 [[HTM]] a slot
|purpose=
* [[Speedsolving]], [[FMC]]
|previous=[[Cross cube state]]
|next=[[F2L cube state]]
|previousimage=[[Image:VisualCube_3_Egell.png|120px|left|link=Cross cube state]]
|nextimage=[[Image:F2L_higlight.jpg|120px|right|link=F2L cube state]]

}}
'''First Two Layers''', or '''F2L''' are normally the first two bottom layers of the [[3x3x3 cube]], or essentially all layers up until the last layer on larger cubes.

The definition is a little different depending on the subject or who you are talking to. Normally it is as above but it may also refer to the part of the [[Fridrich method]] that solves the [[pair]]s without counting the [[cross]] part.

[[2-gen]] F2L, most pairs (30:42) have the edge sitting in the U-layer having two orientations, it shows R or F colour at the side. If it is the R colour you can solve the pair using only RU and if it is the F colour you can turn the cube (y') and sovle the pair to the back slot using only RU. The only pairs that needs both R and F turns are the six ones with the edge unoriented in the slot, if the edge is oriented in the slot both ways works.

 
== Approaches ==

=== Petrus F2L ===

Another way to solve the 'F2L' is by building blocks, common during the first two layers of the [[Petrus]] method.

=== Fridrich F2L ===
There are many ways to solve the 'F2L' on a cube. A common system is using the [[Fridrich]] method first two layer approach. After solving the cross, a corner-edge pair is paired up, and then inserted into the correct slot. A total of four corner edge (or 'CE') pairs are made and inserted to solve the first two layers.

The concept of pairing up four corner/edge pairs was first proposed by [[René Schoof]] in 1981.

{{F2L}}

==Easy Cases==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 1 ===
[[Image:F2L01.png]]

{{Alg|U (R U' R')|F2L}}
{{Alg|R' F R F'|F2L}}
{{Alg|U2 (R U2 R')|F2L}}

|

=== F2L 2 ===
[[Image:F2L02.png]]

{{Alg|y' U' (R' U R)|F2L}}
{{Alg|U' (F' U F)|F2L}}
{{Alg|F R' F' R|F2L}}
{{Alg|d' L' U L|F2L}}
{{Alg|r U R' U' M|F2L}}
{{Alg|(U2) l R U' R' U l'|F2L}}
{{Alg|(U2) l2 F' l' U l'|F2L}}
{{Alg|(U') F R' F' R2 U' R'|F2L}}

|-valign="top"
|

=== F2L 3 ===
[[Image:F2L03.png]]

{{Alg|y' (R' U' R)|F2L}}
{{Alg|y (L' U' L)|F2L}}
{{alg|F' U' F|F2L}}
{{Alg|U M R U' R' U M'|F2L}}
{{Alg|U r' R2 U' R' U M'|F2L}}

|

=== F2L 4 ===
[[Image:F2L04.png]]

{{Alg|(R U R')|F2L}}
{{Alg|(U2) L (R U' R') U L'|F2L}}

|-valign="top"
|}

==Reposition Edge==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 5 ===
[[Image:F2L05.png]]

{{Alg|(U' R U R') U2 (R U' R')|F2L}}
{{Alg|(U' R U R') U (R' F R F')|F2L}}
{{Alg|F2 (L' U' L U) F2|F2L}}
{{Alg|L U' R U L' R' U2 R U' R'|F2L}}
{{Alg|U' (R U R') U' R U2 R'|F2L}}

|

=== F2L 6 ===
[[Image:F2L06.png]]

{{Alg|d (R' U' R) U2' (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U2 (R' U R)|F2L}}
{{Alg|y' (U R' U' R) U' y (F R' F' R)|F2L}}
{{Alg|U' (r U' R' U) (R U r')|F2L}}
{{Alg|R2 (B U B' U') R2|F2L}}
{{Alg|y F2 (R U R' U') F2|F2L}}

|-valign="top"
|

=== F2L 7 ===
[[Image:F2L07.png]]

{{Alg|U' (R U2' R') U2 (R U' R')|F2L}}
{{Alg|U' R U2 R' U' R U2 R'|F2L}}
{{Alg|M' U' M U2 r U' r'|F2L}}
{{Alg|R U B U2 B' U R'|F2L}}

|

=== F2L 8 ===
[[Image:F2L08.png]]

{{Alg|d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|y' U (R' U2 R) U2 (R' U R)|F2L}}
{{Alg|(r' U2) (R2 U R2 U r)|F2L}}
{{Alg|y' R' U' F' U2 F U' R|F2L}}

|-valign="top"
|}

==Reposition Edge and Flip Corner==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 9 ===
[[Image:F2L09.png]]

{{Alg|U' R U' R' d R' U' R |F2L}}
{{Alg|d (R' U' R U') (R' U' R)|F2L}}
{{Alg|y2 U' (L U' L') d (L' U' L)|F2L}}
{{Alg|U r U R' U' R2 r' U' R'|F2L}}
{{Alg|U' R U' R' U2 M R U' R' U M'|F2L}}
{{Alg|F (R U R' U') F' R U' R'|F2L}}
{{Alg|(U F' U' F) U' (F' U' F)|F2L}}
{{Alg|y F2 (U R U' R') F2|F2L}}

|

=== F2L 10 ===
[[Image:F2L10.png]]

{{Alg|U' (R U R' U)(R U R')|F2L}}
{{Alg|R d' R U R' U2 F'|F2L}}
{{Alg|U F' U F U' R U R'|F2L}}
{{Alg|d R' U R d' R U R'|F2L}}
{{Alg|y2 B2 (U' R' U R) B2|F2L}}

Back Right Slot Open: R' U R2 U R'

|-valign="top"
|

=== F2L 11 ===
[[Image:F2L11.png]]

{{Alg|U' (R U2' R') d (R' U' R)|F2L}}
{{Alg|(y) L' d L' U2 L U2 F|F2L}}
{{Alg|U' R U2 R' U2 M R U' R' U M'|F2L}}
{{Alg|U (F R' F' R)2 U' R U R'|F2L}}
{{Alg|(y') R U2 R2 U' R2 U' R'|F2L}}
{{Alg|U' l F U' R U l' U R'|F2L}}
|

=== F2L 12 ===
[[Image:F2L12.png]]

{{Alg|R U' R' U R U' R' U2 R U' R'|F2L}}
{{Alg|d (R' U2 R) d' (R U R')|F2L}}
{{Alg|R U2 R' U2' R U2' R' U2' R U' R'|F2L}}
{{Alg|R' U2 R2 U R2 U R|F2L}}
{{Alg|y (F U') (R U2 R' U2') F'|F2L}}
{{Alg|(U R U' R') U' (R U R' U') (R U R')|F2L}}
Back right slot open: R' U2 R2 U R'

|-valign="top"
|

=== F2L 13 ===
[[Image:F2L13.png]]

{{Alg|d (R' U R U') (R' U' R)|F2L}}
{{Alg|y' U (R' U R U') (R' U' R)|F2L}}
{{Alg|(U F' U F) U' (F' U' F)|F2L}}
{{Alg|M' U' (R U R') U' (R U2 r')|F2L}}
{{Alg|(R U' R') U (R' F R F') (R U' R')|F2L}}
{{Alg|(R U R') d' (L' U' L U) (L' U' L)|F2L}}
{{Alg|(R U' R' U2) (R U' l U' R' U l')|F2L}}
Back right slot open : R' U R F' U' F

|

=== F2L 14 ===
[[Image:F2L14.png]]

{{Alg|U' (R U' R' U) (R U R')|F2L}}
{{Alg|d' F U' F' d R U R'|F2L}}

|-valign="top"
|}

==Split Pair by Going Over==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 15 ===
[[Image:F2L15.png]]

{{Alg|M U L F' L' U' M'|F2L}}
{{Alg|U (R' F R F') U (R U R')|F2L}}
{{Alg|y' (R' U R U') d' (R U R')|F2L}}
{{Alg|y (L' U L) U2 y' (R U R')|F2L}}
{{Alg|R U2 R' U R U R' U R U' R'|F2L}}
{{Alg|R U R' U2 R U' R' U R U' R'|F2L}}
{{Alg|R U' R U2' R2' U' R2 U' R2'|F2L}}
{{Alg|U' R2 U2 R U' R' U R' U2 R2|F2L}}
{{Alg|U2 (R U R' U') R U2 R' U R U R'|F2L}}
Front left slot open: U (R U' R') D (R U' R') D'

Back right slot open: U' (R' U R U') (R U R')

=== F2L 16 ===
[[Image:F2L16.png]]

{{Alg|(R U' R' U) d (R' U' R)|F2L}}
{{Alg|(R U' R') U2 (F' U' F)|F2L}}
{{Alg|(U') (R U2 M' U' R' U) (R U r')|F2L}}
{{Alg|(U) R (F R U R' U' F') R'|F2L}}
{{Alg|(U) M' (U R U' r') (U' R U R')|F2L}}
{{Alg|y' U R U2 R U' R U R' U2 R'|F2L}}
{{Alg|y M U' R' F R U M' y'|F2L}}

|-valign="top"
|

=== F2L 17 ===
[[Image:F2L17.png]]

{{Alg|(R U2 R') U' (R U R')|F2L}}

|

=== F2L 18 ===
[[Image:F2L18.png]]

{{Alg|y' (R' U2 R) U (R' U' R)|F2L}}
{{Alg|y (L' U2 L) U (L' U' L)|F2L}}
{{Alg|(R U R' U') R U2 R' U y (L' U L)|F2L}}
{{Alg|(R U R' U') (R U R' U') F R' F' R |F2L}}
{{Alg|F' U2 F U F' U' F|F2L}}
{{Alg|(R' F R F') (R U' R' U) (R U' R')|F2L}}

|-valign="top"
|}

==Pair Made on Side==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 19 ===
[[Image:F2L19.png]]

{{Alg|U R U2 R2 (F R F')|F2L}}
{{Alg|U (R U2 R') U (R U' R')|F2L}}
{{Alg|(R U2 R' U') U' (R U' R' U)(R U R')|F2L}}
|

=== F2L 20 ===
[[Image:F2L20.png]]

{{Alg|U' F' U2 F2 (R' F' R)|F2L}}
{{Alg|y' U' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|y2 d' (R' U2 R) U' (R' U R)|F2L}}
{{Alg|U' (R U R' U) (F' L' U2 L F)|F2L}}
{{Alg|U' (R U' R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U' R' U) (R U') (l U' R' U l')|F2L}}
{{Alg|d' L' U2 L U' L' U L|F2L}}

|-valign="top"
|

=== F2L 21 ===
[[Image:F2L21.png]]
{{Alg|(R U' R') U2 (R U R')|F2L}}
{{Alg|U2 (R U R' U)(R U' R')|F2L}}
{{Alg|R B U2 B' R'|F2L}}
{{Alg|U2 R x' U' R U x R2'|F2L}}
{{Alg|U F R U R' U' R' F' R|F2L}}
|

=== F2L 22 ===
[[Image:F2L22.png]]
{{Alg|y' (R' U R) U2 (R' U' R)|F2L}}
{{Alg|F' L' U2 L F|F2L}}
{{Alg|y' U2 (R' U' R U') (R' U R)|F2L}}
{{Alg|y2 U' d' (R' U' R U') (R' U R)|F2L}}
{{Alg| r U' r' U2 r U r'|F2L}}
{{Alg|U F R U R' U' F' R U R' U2'|F2L}}
{{Alg|d2 y' R' U' R U' R' U R|F2L}}

|-valign="top"
|}

==Weird==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 23 ===
[[Image:F2L23.png]]

{{Alg|U2 R2 U2 (R' U' R U') R2|F2L}}
{{Alg|U (F R' F' R) U (R U R')|F2L}}
{{Alg|U R U' R' U' R U' R' U R U' R'|F2L}}
{{Alg|(R U R' U') U' (R U R' U')(R U R')|F2L}}
{{Alg|(R U2 R') (F' U F) U' (R U R')|F2L}}

|

=== F2L 24 ===
[[Image:F2L24.png]]

{{Alg|U F' L' U L F R U R'|F2L}}
{{Alg|(R U R') d (R' U R U') (R' U R)|F2L}}
{{Alg|y' (R' U' R U) U (R' U' R U)(R' U' R)|F2L}}
{{Alg|y' U2 R2 U2 (R U R' U) R2|F2L}}
{{Alg|U' (R U) (R2' F R F') (R U' R')|F2L}}
{{Alg|U' (R U R' U) (R U') (l U' R' U l') |F2L}}
{{Alg|U2 F2 U2 (F U F' U) F2|F2L}}
{{Alg|F U (R U' R' F')(R U' R')|F2L}}
{{Alg|d' (F' L F L') U' (L' U' L)|F2L}}
{{Alg|y (L' U' L U) U (L' U' L U)(L' U' L )|F2L}}

|-valign="top"
|}

==Corner in Place, Edge in U Face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 25 ===
[[Image:F2L25.png]]

{{Alg|d' (L' U L) d (R U' R')|F2L}}
{{Alg|d' (L' U L) (F' L F L')|F2L}}
{{Alg|y U' (L' U' L) U (F U F')|F2L}}
{{Alg|U' (F' U F) U (R U' R')|F2L}}
{{Alg|U' M' U R U' r' (R U R')|F2L}}
{{Alg|R U2 R' U R U2 R' U2 R U' R'|F2L}}
{{Alg|R U R' U2 R U R' U2 R U' R'|F2L}}
{{Alg|R' F' R U R U' R' F|F2L}}
{{Alg|(U') F' R U R' U' R' F R|F2L}}
{{Alg|(R U' R' U') (R U' R' U) (R U R')|F2L}}
{{Alg|y' (l' U' l U) (l F' l' F)|F2L}}
{{Alg|(U) (R' U' R' U') R2 (U R U R)|F2L}}
{{Alg|y U R' u' R U' R' U u R|F2L}}
If the back right slot is open:
{{Alg|R2 U' R' U R2|F2L}}
{{Alg|U D' R U' R' D|F2L}}

|

=== F2L 26 ===
[[Image:F2L26.png]]

{{Alg|U (R U' R') d' (L' U L)|F2L}}
{{Alg|U (R U' R') U' (F' U F)|F2L}}
{{Alg|U (R U' R') (F R' F' R)|F2L}}
{{Alg|U R U (r' R U' R' U M')|F2L}}
{{Alg|U R U' M' U R' U' M|F2L}}
{{Alg|r U r' U2 r U r' U2 r U' r'|F2L}}
{{Alg|y (r U r' U') (r' F r F')|F2L}}

|-valign="top"
|

=== F2L 27 ===
[[Image:F2L27.png]]

{{Alg|(R U' R' U)(R U' R')|F2L}}
{{Alg|(R U' R2)(F R F')|F2L}}
{{Alg|F' U' F U2 (R U' R')|F2L}}

|

=== F2L 28 ===
[[Image:F2L28.png]]

{{Alg|(R U R' U') F R' F' R |F2L}}
{{Alg|(R U R') d (R' U2 R) |F2L}}
{{Alg|y' (R' U R U')(R' U R)|F2L}}
{{Alg|(R U R') U (F' U2 F)|F2L}}
{{Alg|R U2 l U' R' U l'|F2L}}
{{Alg|(R U R') U l2 F' l' U l'|F2L}}
{{Alg|(F' U F2)(R' F' R)|F2L}}
{{Alg|(U2) R' F R F2 L' U2 L F|F2L}}

|-valign="top"
|

=== F2L 29 ===
[[Image:F2L29.png]]

{{Alg|y' (R' U' R U)(R' U' R)|F2L}}
{{Alg|U2 (R U' R') y' (R' U' R)|F2L}}
{{Alg|(R' F R F')(R' F R F')|F2L}}
{{Alg|M' U R U' r' U (R U' R')|F2L}}

|

=== F2L 30 ===
[[Image:F2L30.png]]

{{Alg|(R U R' U')(R U R')|F2L}}
{{Alg|U2 (F' U F)(R U R')|F2L}}
{{Alg|U' (R U2 R')U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge in Place, Corner in U face==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 31 ===
[[Image:F2L31.png]]

{{Alg|(R U' R') d (R' U R)|F2L}}
{{Alg|(R U' R' U)(F' U F)|F2L}}
{{Alg|U' R' F R F' R U' R'|F2L}}
{{Alg|R U' l U' R' U l'|F2L}}
{{Alg|F2 r U r' F R U' R'|F2L}}
{{Alg|R U2 R' U' F R' F' R|F2L}}
{{Alg|R U' R B' R' B R'|F2L}}
|

=== F2L 32 ===
[[Image:F2L32.png]]

{{Alg|(R U R' U')(R U R' U')(R U R')|F2L}}
{{Alg|(U R U' R')(U R U' R')(U R U' R')|F2L}}
{{Alg|U2 R d' R U R' d R'|F2L}}
{{Alg|U R d' R U2 R' d R'|F2L}}
{{Alg|R2 U R2 U R2 U2 R2|F2L}}
{{Alg|U2 R2 U2 R2 U' R2 U' R2|F2L}}
{{Alg|(R U2 R') (F' U2 F) U' (R U R')|F2L}}

|-valign="top"
|

=== F2L 33 ===
[[Image:F2L33.png]]

{{Alg|y U' L' U' R' U L U' R|F2L}}
{{Alg|(U' R U' R') U2 (R U' R')|F2L}}
{{Alg|y U' (L' U' L) U2 (L' U' L)|F2L}}
{{Alg|U y F U R U R' U' R U' R' F'|F2L}}
{{Alg|(U' F' U' F) U2 (F' U' F)|F2L}}
{{Alg|y' U' R D R' U R D' R'|F2L}}

|

=== F2L 34 ===
[[Image:F2L34.png]]

{{Alg|U' (R U2' R') U (R U R')|F2L}}
{{Alg|U (R U R') U2 (R U R')|F2L}}
{{Alg|d (R' U R) U2 (R' U R)|F2L}}
{{Alg|y (U L' U L) U2 (L' U L)|F2L}}
{{Alg|U y F U2 R U2 R' F'|F2L}}
Back right slot open:
{{Alg|E' R U R' E|F2L}}
{{Alg|E' U' F' U F E|F2L}}

|-valign="top"
|

=== F2L 35 ===
[[Image:F2L35.png]]

{{Alg|(U' R U R') d (R' U' R)|F2L}}
{{Alg|U2 (R U' R') U' (F' U' F)|F2L}}
{{Alg|U M' U R U' r' R U' R'|F2L}}
{{Alg|U' l U' R U l' U R'|F2L}}

|

=== F2L 36 ===
[[Image:F2L36.png]]

{{Alg|d (R' U' R) d' (R U R')|F2L}}
{{Alg|y U2 (L' U L) U (F U F')|F2L}}
{{Alg|U F' U' F U' (R U R')|F2L}}
{{Alg|U2 (R' F R F') U2 (R U R')|F2L}}

|-valign="top"
|}

==Edge and Corner in Place==

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== F2L 37 ===
[[Image:F2L37.png]]

Solved

|

=== F2L 38 ===
[[Image:F2L38.png]]

{{Alg|(R' F R F') (R U' R' U) (R U' R' U2) (R U' R')|F2L}}
{{Alg|(R U' R') d (R' U2 R) U2' (R' U R)|F2L}}
{{Alg|(R U R') U2 (R U2 R') d (R' U' R)|F2L}}
{{Alg|(R2 U2) (F R2 F') (U2 R' U R')|F2L}}

Back right corner free- D' R U R' F R' F' R
|-valign="top"
|

=== F2L 39 ===
[[Image:F2L39.png]]

{{Alg|(R U' R') U' (R U R') U2 (R U' R')|F2L}}
{{Alg|y' (R' U' R) U2 (R' U R U') (R' U' R)|F2L}}
{{Alg|y (L' U' L) U2 (L' U L U')(L' U' L)|F2L}}
{{Alg|(R U R' U') (R U2 R') U' (R U R')|F2L}}
{{Alg|(R U2 R' U2) (R U2 R' U') R U R'|F2L}}
{{Alg|R U' R' F2 L' U' L U F2|F2L}}
{{Alg|(R2 U2) (R' U' R U') (R' U2 R')|F2L}}

=== F2L 40 ===
[[Image:F2L40.png]]

{{Alg|(R U' R' U)(R U2' R') U (R U' R')|F2L}}
{{Alg|(R U R') U2 (R U' R' U)(R U R')|F2L}}
{{Alg|(R U2) (R U R' U) (R U2 R2')|F2L}}

|-valign="top"
|

=== F2L 41 ===
[[Image:F2L41.png]]

{{Alg|(R U' R') d (R' U' R U') (R' U' R)|F2L}}
{{Alg|R U' R' U' R U' R' d R' U' R|F2L}}
{{Alg|y (L' U' L U)(L' U L) U2 (F U F')|F2L}}
{{Alg|(R U' R) y (U R U' R') y' R2|F2L}}
{{Alg|F2 (L' U' L U) y (L U' L)|F2L}}
{{Alg|R F (U R U' R' F') U' R'|F2L}}
|

=== F2L 42 ===
[[Image:F2L42.png]]

{{Alg|(R U' R' U) d (R' U' R U') (R' U R)|F2L}}
{{Alg|(R U' R' U2) y' (R' U' R U' R' U R)|F2L}}
{{Alg|(R U R' U') (R U' R') U2 (F' U' F)|F2L}}
{{Alg|y (L' U L) d' (L U L' U) (L U L')|F2L}}
{{Alg|R2 y (R U R' U') y' (R' U R')|F2L}}
{{Alg|(R U' R')(F' L' U2 L F)|F2L}}
{{Alg| R U (F R U R' U' F') R'|F2L}}
|-valign="top"
|}

== See also ==
* [[Keyhole First Two Layers]]
* [[Intuitive solving]]
* [[Advanced F2L]]
* [[ZBLS]]
* [[Fridrich Method]]
* [[Petrus Method]]

== External Resources ==
=== Beginner ===
* [http://rishidoshi.blogspot.com/ RiDo's Hunting Story] - Simple analogy method for F2L

=== Standard ===
* [http://erikku.er.funpic.org/rubik/F2L.html Erik Akkersdijk's F2L Cases (from his old site)]
* [http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l Dan Harris's F2L Cases]
* [http://www.opticubes.com/cubing/f2l/ Opticubes.com Optimal F2L Cases]
* [http://jmbaum.110mb.com/f2l.htm Jason Baum's F2L Cases]
* [http://www.kungfoomanchu.com/#333speedcubing Andy Klise's Printable F2L PDF]
* [http://www.cubeloop.com/php/cube/advanced.php?chapter=f2l CubeLoop F2L Algs]
* [http://www.cubewhiz.com/pll.php Bob Burton's F2L Cases]
* [http://cubefreak.net/speed/advancedf2l/standard.php F2L algs for every case from all angles by Shotaro Makisumi]
* Youtube: [http://www.youtube.com/watch?v=J8Yl3lioY8c How to get faster at the 3x3 Rubik's cube - F2L] - by Feliks Zemdegs
* Youtube: [http://www.youtube.com/watch?v=k-xbcAMfWwM Rubik's Cube: Fridrich F2L explained] - by Badmephisto

=== Advanced ===
* Youtube: [https://www.youtube.com/playlist?list=PL83bqDZwr97mik_tbQrCJQQcXsb-wzC53 Expert F2L (Russian language)] - by Viktor Danilov
* [http://www.speedsolving.com/forum/showthread.php?t=15050 Erik Expert F2L tutorial]
* [http://cubefreak.net/advancedf2l/ Cubefreak Advanced F2L]
* [http://pagesperso-orange.fr/absolutemind/ms-angl.html Multislotting Tutorial]

== F2L Trainers ==
[http://expertcuber.by/ ExpertCuber.by]

[[Category:3x3x3 other substeps]]

__NOTOC__

Template:OCLL

2016-02-17T02:08:35Z

Addons zz: /* OLL 26 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|(U L U' R') (U L' U' R)|OLL}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|(R' U L U') (R U L')|OLL}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') U2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:OCLL

2016-02-17T02:07:33Z

Addons zz: /* OLL 27 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|(U L U' R') (U L' U' R)|OLL}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R' U L U' R U L'|OLL}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') U2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

PLL

2016-02-17T01:21:34Z

Addons zz: /* F Permutation */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y) R2' u R' U R' U' R u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u R' U R U' R u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

PLL

2016-02-17T01:17:57Z

Addons zz: /* F Permutation */

{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=
* [[Speedsolving]]
|previous=[[OLL cube state]]
|next=[[Solved cube state]]
|previousimage=[[Image:OLLinfo.png|120px|left|link=OLL cube state]]
|nextimage=[[Image:Mini maru.jpg|120px|left|link=Solved_cube_state]]

}}
'''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 [[algorithm]]s for each one. The diagrams below are top views of where you want the pieces to go. For example, the [[PLL#T_Permutation|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]].

{{PLL}}
== See also ==
* [[2-Look PLL]]
* [http://www.speedsolving.com/wiki/index.php/Special:MediaWikiAlgDB?mode=view&view=default&puzzle=3&group=PLL PLL Algorithm Database]
* [[2-Sided PLL Recognition]]

== External links ==

* [https://paritycasecubing.wordpress.com/2014/05/29/updated-pll-2sr-a-guide-to-recognising-plls-by-looking-at-only-two-sides-v2-0 "PLL 2SR: A guide to recognising PLLs by looking at only two sides (V2.0)"] (Comparative pattern analysis of PLLs from all angles, by Parity Case)
* [http://rishidoshi.blogspot.com/2010/12/pllpatterns.html Recognize PLLs by patterns] (PLL patterns and Algs by RiDo)
* [http://mordred.awardspace.us/PLLCheatSheet.pdf PLL Cheat Sheet] (Printable PDF of all PLL algorithms on a single page)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19867 Recognizing PLLs from only 2 sides]
* [http://rishidoshi.blogspot.in/2010/11/2-sided-pll-recognition-play-tool-excel.html Recognizing PLLs from only 2 sides] - Improved version
*[http://www.youtube.com/watch?v=pnnb2rgLRuU&list=PLR6AczKIDIf2YOjujNNPvif3EPrNS2Jhz|PLL YouTube series]

=PLL algorithms=
{{Algnote}}
==Permutations of Edges Only==
This subgroup, [[EPLL]] is used as a [[substep]] for many speedsolving methods, for example in the [[VH method]] ([[COLL]]).

{{H-PLL}}
{{U-PLL(a)}}
{{U-PLL(b)}}
{{Z-PLL}}

==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]].

{{A-PLL(a)}}
{{A-PLL(b)}}
{{E-PLL}}

==Permutations of Edges and Corners==

===F Permutation===
{{case
|image=f.gif
|name=F-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U R U' R2) (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 (y') R' U' R U (y x) R U R' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.1(v3)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=QA5DZnPYVzE}}
{{Alg|(y’) L U F L' U' L U L F' L2 U L U L' U' L U' L'|Alg.1(v4)|cube=3x3x3$stage=PLL}}
Decomposition(Alg.1) = [R', U] [R2: [F', U'] [R, F] ] (U')
{{Alg|L' U2 L' U' F' L' F2 U' F' U F' L F U' L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R' d' R' F' R2 U' R' U R' F R U' F|Alg.2(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=yangrM_N1Pc#t=00m30s}}
Decomposition(Alg.2) = [L' U: [U: (L')] [F' L' F: [F, U'] ] ]
{{Alg|L B2 F' D2 B R' B' D2 F2 L' F' L B2 L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') F r2 R' U2 r U' r' U2 (x') R2 U' R' U r2 u' (z')|Alg.3(v2)|cube=3x3x3&stage=PLL|}}
Decomposition(Alg.3) = [L B2: [F' D2 B: (R')] [F, L'] ]
{{Alg|B' U' R' B U B' U' B' R B2 U' B' U' B U B' U B|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [B' U': [R': [B, U] [B', R] ] [B U' B': (U')] ]
{{Alg|L U' L' U L2 F U F' U' L' F' L F L2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' R' U R2 (y) R U R' U' (x) U' R' U R U2 (x')|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z) R U R' U' R U2 (z' y') R U R' U' (y' x') R' U' R U R2 (x)|Alg.5(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L, U'] [L2: [F, U] [L', F'] ] (U)
{{Alg|R' U2 R' U2 L U' R' U' R' U R U2 L' U2 R U R|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R' U': [R' U2 L U': [U, L' U2 R] [U' R' U': (R')] ] ]
{{Alg|L U2 L U2 R' U L U L U' L' U2 R U2 L' U' L'|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L2: [L', U2] [R': [U L U: (L)] [U', R] ] [U, L'] ]
{{Alg|L R' F2 R' D L' F2 R U' L2 R B2 L2 U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) M U2 r' U l' U2 r U' R2 r U2 R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L R': [F2 R': (D)] [F2, L' R'] ] [R', U'] [U' L2: B2]
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(r U R' U') (z) U' (l' U2 r' U') (r U2 l' U R2) (x)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [F2 R': [R, F2 L F] [F D2 B': (L')] ]
{{Alg|R B2 D B2 R' B' R B' D2 F L' F' D B2 R'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y x) U R2 F R2 U' R' U l' U2 L F' L' U (x') R2 U' (x')|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R B2 D: [B2: [R', B'] ] [D2 F: (L')] ]
{{Alg|B U B' U B U2 B2 U' B U' B' U2 B U F R B' R' F' R B R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U R' U R U2 R2) (U' R U' R' U2 R) U (r U R' U' r' F R F')|Alg.11(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [B: (U)] [U': [U2, B] [B', U'] [U2, B'] ] [F, R B' R']
{{Alg|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|cube=3x3x3&stage=PLL}}
{{Alg|(y) M2 U M2 (y') (R U R' U' R' F R2 U' R' U' R U R' F') (y) M2 U' M2|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F2 B2 D B2 F': [F': [R, U] [R', F] ] [R U' R': (U')] ]
{{Alg|R U' F R F' U F' U' F2 R' F' U' R' U2 R'|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y) F U' r U r' U r' F' r2 U' r' U' F' U2 F'|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R U': [F R F': [U, F'] ] [U': (R')] ]

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg| R2 U (R' U R' U') R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y) R2' u R' U R' U' R u' R2 (y') R' U R|PLL}}
{{Alg|(y) R2 U R' U R' U' R U' R2 D U' R' U R D'|PLL}}
{{Alg|(y2) F2' D R' U R' U' R D' F2 L' U L|PLL}}
{{Alg|R L U2 R' L' (y') R' U L' U2 R U' L|PLL}}
{{Alg|R U R' U' R' U F R U R U' R' F' U R' U2 R|PLL}}
{{Alg|(y) L F2 R F' L' F U R' U' F' L F' L'|PLL}}
{{Alg|(y) R2' S2 U l2' U' l2' u R2 U' r2' F2|PLL}}

===G Permutation : b===
{{case
|image=g2.gif
|name=G-PLL b
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|R' U' R (y) R2 u R' U R U' R u' R2|PLL}}
{{Alg|(y) F' U' F R2 u R' U R U' R u' R2'|PLL}}
{{Alg|R' U' R B2 D L' U L U' L D' B2|PLL}}
{{Alg|(y2) L' U' L (y') R2' u R' U R U' R u' R2|PLL}}
{{Alg|(y') R' U L' U2 R U' L (y) R L U2 L' R'|PLL}}
{{Alg|R2 D L2 D F2 L D R' D2 L D' R' U2 |PLL}}

===G Permutation : c===
{{case
|image=g1.gif
|name=G-PLL c
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) R2' u' R U' R U R' u R2 (y) R U' R'|PLL}}
{{Alg|(y) R2' u' R U' R U R' u R2 B U' B'|PLL}}
{{Alg|(y) R2' U' R U' R U R' U R2 D' U R U' R' D|PLL}}
{{Alg|(y) R2' D' F U' F U F' D R2 B U' B'|PLL}}
{{Alg|(y2) F2' D' L U' L U L' D F2 R U' R'|PLL}}
{{Alg|L' U' L U L U' F' L' U' L' U L F U' L U2 L'|PLL}}
{{Alg|L' R' U2 L R (y) L U' R U2 L' U R'|PLL}}
{{Alg|(y') R2' F2 R U2 R U2 R' F R U R' U' R' F R2|PLL}}
{{Alg|(y') l' U2' L' U l F' U' L U F R' F R|PLL}}
{{Alg|(y) U F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 U'|PLL}}

===G Permutation : d===
{{case
|image=g.gif
|name=G-PLL d
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y2) R U R' (y') R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y2) R U R' F2 D' L U' L' U L' D F2|PLL}}
{{Alg|(y2) L U2 L' U F' L' U' L U L F U L' U' L' U L|PLL}}
{{Alg|(y2) l2 U' L2 U' F2 L' U' R U2 L' U l (x')|PLL}}
{{Alg|(y) L U' R U2 L' U R' (y) R' L' U2 R L|PLL}}
{{Alg|(y) f R f' R2 u' R U' R' U R' u R2|PLL}}
{{Alg|(y') R' F' R F' U' L' U F R' F' L F2 R|PLL}}
{{Alg|(y') R2' F' (R U R U') (R' F' R) (U2' R' U2' R') F2 R2|PLL}}
{{Alg|(y2) (R U R') F2 D' L U' L' U L' D F2 U2|PLL}}

===J Permutation : a===
{{case
|image=j1.gif
|name=J-PLL a, L-perm
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B' U F' U2 B U' B' U2 F B U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U L' U2 R U' R' U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 R L|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B' U: [F' U2 B: (U')] [B, U'] ]
{{Alg|B2 R' U' R B2 L' D L' D' L2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L F2 R' D R' D' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 L' U' L b2 L' U L' U' r2|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R2 u' R' u R2 (x' y') R' U R' U' l2'|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 r' U' r U2 l' U R' U' l2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) l2 U R U' l U2 r' U r U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 R': (U')] [L': [D, L'] ]
{{Alg|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' R': [R, U] [U' L U', R] (U) [U, L] ]
{{Alg|L' U' L F L' U' L U L F' L2 U L U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L' U' L F: [L', U'] [L, F'] ] (U)
{{Alg|B2 R2 U' R2 D B2 D' B2 U B2 U'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2' R2 U' R2' u R2 D' R2' U R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [R2: (U')] [D, B2] [U, B2] ]
{{Alg|B2 U' D B2 U' B2 U B2 D' B2 U B2 U'|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 (U' D) R2' U' R2 U R2' D' R2 U R2'|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D B2: [B2, D'] (U') [B2, U'] ] [B2, U]
{{Alg|L' U2 L U L' U2 R U' L U R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 R U R' U2' L U' R U L'|Alg.7(v2)|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/}}
{{Alg|(y2) R' U2 R U R' (z) R2' U R' D R U' (z')|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2' R U R' (z) R2 U R' D R U' (z')|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) D R' U' R D' R (R U R' U') R2 U (z')|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L' U R' U2 L U' L' U2' L|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
Decomposition(Alg.7) = [L': [U2 L: (U)] [R: [U', L]] ]
{{Alg|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' R' U2 R U R' U2 L U' R|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' L' d2 R U R' d2 R U' L|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' D' R2 U R U' R2 (z') R U' L|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' U2 L U' L' U2 L R|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') L' U R' (z) R2 U R' U' R2 U D (z')|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L': [R' U2 L: (U)] [U', L] ]
{{Alg|B U' L' B L2 U' L' U' L U L' B' L U L' B'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R' F R2 U' R' U' R U R' F' R U R' F'|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B L U' L' B: [B' L U, L'] [L, U'] (U') [U', L] ]
{{Alg|B' U B' R2 F D' F D F2 R2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U l' U2 r U' L U r2 F2 R2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B: (U)] [R2 F: [D', F] ] ]
{{Alg|R U' L' U R' U2 L U' L' U2 L|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 u' R U' R U R' u r2 (y) U' R' U' (R' U R) U2|Alg.12|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B U' F U2 B' U B U2 F' B' U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' R U2 L' U L U2 R' L'|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 D' U' (z)|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.2|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [B U': [F U2 B': (U)] [B', U] ]
{{Alg|B2 L U L' B2 R D' R D R2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' F2 L D' L D L2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F2 R U R' b2 R U' R U l2'|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') L2 u L u' L2 (x' y) L U' L U r2|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 x) U2 l U l' U2 r U' L U r2|Alg.2(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) r2 U' L' U r' U2 l U' l' U2 (x')|Alg.2(v6):Inv(Alg.2(v5))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [B2 L: (U)] [R: [D', R] ]
{{Alg|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L R: [L', U'] [U R' U, L'] (U') [U', R'] ]
{{Alg|R U R' F' R U R' U' R' F R2 U' R' U'|Alg.4|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=RnfFAp3zBYw}}
Decomposition(Alg.4) = [R U R' F': [R, U] [R', F]] (U')
{{Alg|B2 L2 U L2 D' B2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|B2 L2 U L2 u' L2 D L2 U' L2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [B2: [L2: (U)] [D', B2] [U', B2] ]
{{Alg|B2 U D' B2 U B2 U' B2 D B2 U' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y') L2 (U D') L2 U L2 U' L2 D L2 U' L2|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [D' B2: [B2, D] (U) [B2, U] ] [B2, U']
{{Alg|R U2 R' U' R U2 L' U R' U' L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L U2' R' U L' U' R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2' L' U' L (z') L2' U' L D' L' U (z)|Alg.7(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z') D' L U L' D L' (L' U' L U) L2' U' (z)|Alg.7(v5)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2' R'|Alg.7(v6):Inv(Alg.7)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U L U' R U2 L' U L U2 L'|Alg.7(v7):Inv(Alg.7(v2))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R: [U2 R': (U')] [L': [U, R'] ] ]
{{Alg|L R U2 R' U' R U2 L' U R' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R L U2 L' U' L U2 R' U L'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
{{Alg|L R d2 L' U' L d2 L' U R'|Alg.8(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U D L2 U' L' U L2 (z) L' U R'|Alg.8(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L U2 R' U R U2 R' L'|Alg.8(v5):Inv(Alg.8)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R U' L (z') L2 U' L U L2 U' D' (z)|Alg.8(v6):Inv(Alg.8(v4))|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R: [L U2 R': (U')] [U, R'] ]
{{Alg|B' U R B' R2 U R U R' U' R B R' U' R B|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F' U L F' L2 U L U L' U' L F L' U' L F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [B' R' U R B': [B R' U', R] [R', U] (U) [U, R'] ]
{{Alg|B U' B L2 F' D F' D' F2 L2 B2|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y') L U' r U2 l' U R' U' l2 F2 L2|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [B2: [B': (U')] [L2 F': [D, F'] ] ]
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|r2 u R' U R' U' R u' r2 (y) U (L U L U' L') U2|Alg.12|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(L U' R U2 L' U R')2 U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) R' (U R' D R2 U' R D')2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(R U' L U2 R' U L')2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D R' U R2 D' R U')2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' D R2 U' R U (z') R' U' R (z) R2 U' R (z') R'|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|R U' L d2 L' U L R' U' R U2 r' F l'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L R: [R', U'] [U2: [U': [L', U] ] [R', U'] ] [U', L'] ] (U')
{{Alg|L U' L' U L F U F' L' U' L F' L F L' U L'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z) U R' U' R U F R F' U' R' U F' U F U' R U' (z')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(L U' L F') L' F (L' U L) F U' (F' L' U' L U) L'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [L U': [L' U L F: (U)] [F', L] ]
{{Alg|R U' R' U R B U B' R' U' R B' R B R' U R'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R U' R' U l U F U' R' F' R U' R U l' U R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R U': [R' U R B: (U)] [B', R] ]
{{Alg|R' U R2 B2 U R' B2' R U' B2 R2' U' R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R' U R2 B2 U R': B2] (U')
{{Alg|F' (R U R' U') R' F R2 F U' (R' U' R U) F' R'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' R U, R'] [R F U' R': (U')]
{{Alg|R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R'|Alg.6|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=pnnb2rgLRuU}}
Decompositon(Alg.6) = [R U R': [U2: [U', R] [F' R U, R'] [R, U'] ] (U')]
{{Alg|R U R' B U B' R' B U B' U' B' R B2 U' B' U' R U' R'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|L U L' (y') (R U R' F' R U R' U' R' F R2 U' R') (y') U' R U' R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R U R': [B U B' R': [B, U] [B', R]] (U')]
{{Alg|L2 U2 L' U2 F2 L2 F2 L F2 U2 L2 U2 L F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z) U2 R2 U' R2 (y') R2 U2 R2 U R2 (y) R2 U2 R2 d R2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [L: [L, U2] [F2, L2] ] [F2: [U2, L2] (L')]
{{Alg|R U R' U' L U2 L' U' L U2 R' U L' U' R U R U' R'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(R U R' U') L U2 L' U' L (z') L2 U' L D' L' U (L U L' U') (z)|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U R' U': [L: [U2 L': (U')] [R' U, L'] ] ]
{{Alg|L' U L2 F2 U L' F2 L U' F2 L2 U' L U'|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U L2 F2 U L': F2] (U')
{{Alg|L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [L2 U F2: [F2, U'] [U, F2] [L2, U2] [U, F2] ] (U')
{{Alg|(L U L' U) (R' U L U') R U2 (L' U L U2) L' (U' L U' L')|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [L U L' U: [L: [R': [L', U] ] [U2 L': (U)] ] ]
{{Alg|F B L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L F' B'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : b===
{{case
|image=n.gif
|name=N-PLL b
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(R' U L' U2 R U' L)2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y' z') L (U' L D' L2 U L' D)2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(L' U R' U2' L U' R)2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|(z) U' R D' R2 U R' U' (z') R U R' (z) R2 U R' (z') R|Alg.1(v6)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|Alg.1(v7)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [L' R': [L, U] [U2: [U: [R, U'] ] [L, U] ] [U, R] ] (U)
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L U L' U' F' L' F U L U' F U' F' U L' U (z)|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(R' U R' F) R F' (R U' R') F' U (F R U R' U') R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R U' R' F': (U')] [F, R'] ]
{{Alg|L' U L U' L' B' U' B L U L' B L' B' L U' L|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|L' U L U' r' U' F' U L F L' U L' U' r U' L|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [L' U: [L U' L' B': (U')] [B, L'] ]
{{Alg|L U' L2 B2 U' L B2 L' U B2 L2 U L' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [L U' L2 B2 U' L: B2] (U)

{{Alg|F L' U' L U L F' L2 F' U L U L' U' F L|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F L' U', L] [L' F' U L: (U)]
{{Alg|L' U' L U' (L' U' L F L' U' L U L F' L2 U L) U2 L' U L|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L' U' L: [U2: [U, L'] [F L' U', L] [L', U] ] (U)]
{{Alg|L' U' L B' U' B L B' U' B U B L' B2 U B U L' U L|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R (y) (L' U' L F L' U' L U L F' L2 U L) (y) U L' U L|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [L' U' L: [B' U' B L: [B', U'] [B, L']] (U)]
{{Alg|R2 U2 R U2 F2 R2 F2 R' F2 U2 R2 U2 R' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L2 U L2 (y) L2 U2 L2 U' L2 (y') L2 U2 L2 d' L2 (x')|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R': [R', U2] [F2, R2] ] [F2: [U2, R2] (R)]
{{Alg|L' U' L U R' U2 R U R' U2 L U' R U L' U' L' U L|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(L' U' L U) R' U2' R U R' (z) R2 U R' D R U' (R' U' R U) (z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [L' U' L U: [R': [U2 R: (U)] [L U', R] ] ]
{{Alg|R U' R2' F2 U' R F2' R' U F2 R2 U R' U|Alg.10|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [R U' R2 F2 U' R: F2] (U)
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R2 U' F2: [F2, U] [U', F2] [R2, U2] [U', F2] ] (U)
{{Alg|(R' U' R U') (L U' R' U) L' U2 (R U' R' U2) R (U R' U R)|Alg.12|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [R' U' R U': [R': [L: [R, U'] ] [U2 R: (U')] ] ]
{{Alg|F' B' R U R' U (R U R' F' R U R' U' R' F R2 U' R') U2 R U' R' F B|Alg.13}cube=3x3x3&stage=PLL}}
R' U' R (y) R U' L' U R' U2 L U' L' U2 L F' U F'

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U2] [R B' R', U' R U] [U' R: (U)]
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R U': [R F2 U R U: (R)] [R', U] ]
{{Alg|F U F' L' F U2 F' U2 F' L F U F U2 F' U'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U R' F' R U2 R' U2 R' F R U R U2 R' U'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [F U F' L' F U2, F'] [U2, F] (U')
{{Alg|R U2 R' U' R' F' R U2 R U2 R' F R U' R' U|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R: [U2 R' U2, U R' F' R] ] (U)
{{Alg|L' U' L U2 L U2 R' L2 U L U' L R U2 L' U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U' R U2 R U2 L' R2 U R U' R L U2 R' U2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L': (U')] [U2, L] [R': [L', U] ] [L, U2]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U' R: [R', U] [U', R D R'] [U' R': (U)] ]
{{Alg|F U' F' U' F U F D F' U' F D' F' U2 F' U'|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [U' F': (U')] [F D F', U'] [U, F'] ]
{{Alg|B' L' U' L B' L' U B' U' B' U B L B2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y x') R' U' F' U R' U' (x) U R' U' R' U R B R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [B2 L': [L B L', U'] [B' U': (B')] ]
{{Alg|R U2 R' U B L' B' R B L B' U R' U|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U (y) R B' R' F R B R' (z x) R U' (x' z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R U' R': [R, U'] [B L' B', R] ] (U)
{{Alg|L U2 L2 B L B' L U2 L' F' L' U L U L' U' L F|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U2 l' R' U R U' l U2 R' B' R' U R U R' U' R B|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L U2 L': [L', B] ] [F' L': [U L: (U)] ]
{{Alg|R U2 R D R' U R D' R' U' R' U R U R' U|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R U2: [R D R', U] [R', U] ] (U)

===R Permutation : b===
{{case
|image=r.gif
|name=R-PLL b
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U2 R U2 R' F (R U R' U') R' F' R2' U'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U)' l' U' R2 (x')|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v5):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 F R U R U' R' F' R U2 R' U2 R|Alg.1(v6):Inv(Alg.1(v4))|cube=3x3x3&stage=PLL}}
{{Alg|B2 R B U B U' B' R' B U2 B' U2 B|Alg.1(v7)|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|Alg.1(v8)|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|Alg.1(v9)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R', U2] [R' F R, U R' U'] [U R': (U')]
{{Alg|B2 L2 U' B' U' B U B U L2 B U' B U|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' B2 U' R' U' R' U R U B2 R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) R2 B2 U' R' U' R U R U B2 R U' R|Alg.2(v3):Inv(Alg.2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R' U: [R' B2 U' R' U': (R')] [R, U'] ]
{{Alg|B' U' B L B' U2 B U2 B L' B' U' B' U2 B U|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' R B R' U2 R U2 R B' R' U' R' U2 R|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [B' U' B L B' U2, B] [U2, B'] (U)
{{Alg|R' U2 R U R B R' U2 R' U2 R B' R' U R U'|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R': [U2 R U2, U' R B R'] ] (U')
{{Alg|L U L' U2 L' U2 R L2 U' L' U L' R' U2 L U2|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U R' U2 R' U2 L R2 U' R' U R' L' U2 R|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [L: (U)] [U2, L'] [R: [L, U'] ] [L', U2]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.6|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [U R': [R, U'] [U, R' D' R] [U R: (U')] ]
{{Alg|B' U B U B' U' B' D' B U B' D B U2 B U|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U R U R' U' R' D' R U R' D R U2 R|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [B': [U B: (U)] [B' D' B, U] [U', B] ]
{{Alg|F L U L' F L U' F U F U' F' L' F2|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|(y' x) R U B U' R U (x') U' R U R U' R' F' R2|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [F2 L: [L' F' L, U] [F U: (F)] ]
{{Alg|R' U2 R U' F' L F R' F' L' F U' R U'|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U' (y') R' F R B' R' F' R (z x') R' U (x z')|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' U R: [R', U] [F' L F, R'] ] (U')
{{Alg|L' U2 L2 F' L' F L' U2 L B L U' L' U' L U L' B'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R' U2 l R U' R' U l' U2' R F R U' R' U' R U R' F'|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [L' U2 L: [L, F'] ] [B L: [U' L': (U')] ]
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R U'|Alg.11|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R' U2: [R' D' R, U'] [R, U'] ] (U')
{{Alg|(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')|Alg.12|cube=3x3x3&stage=PLL}}

===T Permutation===
{{case
|image=t.gif
|name=T-PLL
|methods=PLL, [[ZBLL]], [[ZZLL]], [[BLD]]
|optimal=11 [[HTM]]
|text=
}}
{{Alg|R U R' U' R' F R2 U' R' U' R U R' F'|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|Alg.1(v2):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) B L U' L' U L U L2 B' L U L U' L'|Alg.1(v3):Inv(Alg.1)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R, U] [F: [F', R'] [R U' R': (U')] ]
{{Alg|R' U' R U R B' R2 U R U R' U' R B|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R', U'] [B': [B, R] [R' U R: (U)] ]
{{Alg|R2 U R2 U' R2' U' D R2 U' R2' U R2 D'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2' U' R2 U' D R2' U' R2 U R2' D'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2, U] [D R2: [R2, D'] [U' R2: (U')] ]
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2 U|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L2 U' L2 D F2 R2 U R2 D' F2|Alg.4(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 D B2 L2 U L2 D' B2|Alg.4(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [U': [U, R2] [B2 D: [D', B2] [L2: (U)] ] ]
{{Alg|R2 D' F2 U F2 R2 D B2 U' B2 U|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|R2' u' R2 U R2' (y) R2 u R2' U' R2|Alg.5(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [R2 D' F2: (U)] [R2, D'] [B2, U']
{{Alg|R2 D' F2 D R2 B2 D L2 D' B2 U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 r' U2 r U2 (x) U2 r U2 r' U2 (z')|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [R2 D': F2] [B2 D: L2] (U)
{{Alg|R U R' U' R2 D R' U' R' U' R U R2 D' R|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R2 D R' U' R' U' R U (z') U2 R' U (z)|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [R, U] [R' D R': [R, D'] [R' U' R': (U')] ]
{{Alg|R2 U R2 U' R2 F2 U' F2 D R2 D'|Alg.8|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R2: [U, R2] [F2: (U')] [D, R2] ]
{{Alg|F' U F' L2 B D' B' L2 F2 U' S' U2 S U2|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|y' L U' r U2 l' U l U2 x r2' (U M U2 M')|Alg.9(v1):Mirr(Alg9)|cube=3x3x3&stage=PLL}}
{{Alg|y x r' U r' d2 r U' r' d2 r2 x' U' M' U2 M|Alg.9(v2)|vidurl=https://www.youtube.com/watch?v=pe2d2ZpYNco}}
Decomposition(Alg.9) = [F', U] [U F2 L2 B: (D')] [S', U2]

===V Permutation===
{{case
|image=V.gif
|name=V-PLL
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|R' U R' U' B' R' B2 U' B' U B' R B R|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' (y) U' R' F' R2 U' R' U R' F R F|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 B' R' B R' U R U (x')|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' U' R2 (x') U' R' U R' F R F|Alg.1(v5)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' F' R2 U' R' U R' F R F|Alg.1(v6)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.1) = [R2: [R, U] [B': (R')] [B, U'] [B', R] ]
{{Alg|R' U R' U' B' D B' D' B2 R' B' R B R|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y x) R' F R' F' R2 U' R' U R U (x')|Alg.2(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x2 y') R' U R' U' l R U' R' U R U (x')|Alg.2(v3)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (x' y) U' R U' R' U2 (y') R' U' R U R (x)|Alg.2(v4)|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' (y) R' D R' D' R2 F' R' F R F|Alg.2(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [R2: [R, U] [B': [D, B'] [B: (R')] ] [B', R] ]
{{Alg|R' U2 R U2 L U' R' U L' U L U' R U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 L U' R' U r' F r U' R U L'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R', U2] [L U' R' U L': (U)]
{{Alg|R2 U' (B2 U B2) (R D') (R D) R' U R U' R|Alg.4|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [R2: [U', B2] [R D': (R)] [U, R] ]
{{Alg|F' U B U' F U F' U B' U' F U2 B U2 B'|Alg.5|cube=3x3x3&stage=PLL}}
{{Alg|(y') R' U L U' R U R' U L' U' R U2 L U2 L'|Alg.5(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y) r' F R F' r U r' F R' F' r U2 R U2 R'|Alg.5(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) L' U R U' L U L' U R' U' L U2 R U2 R'|Alg.5(v4)|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U' R D R' U R U' R D' R' U R2 D R2 D' (z')|Alg.5(v5)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F' U B U' F: (U)] [U2, B]
{{Alg|L U' R' U L' U' L U' R U L' U2 R' U2 R|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|(y2) R U' L' U R' U' R U' L U R' U2 L' U2 L|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [L U' R' U L': (U')] [U2, R']
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|Alg.7|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [U: [U': (R)] [D: [D', U R'] [R: [U', R] ] [D: [R', U']] ] ]
{{Alg|(y) R U' R U (y) L D' L D L2 (y') R F R' F' R'|Alg.8|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|F R U' R' U' R U R' F' R U R' U' R' F R F'|Alg.1|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
Decomposition(Alg.1) = [F R U' R': (U')] [R, U] [R', F]
{{Alg|R' U' R F2 R' U R U F2 U' F2 U' F2|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|Alg.2(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.2) = [F2: [F2, R' U' R] [U F2: (U')] ]
{{Alg|R2 U' R2 U' R2 U F U F' R2 F U' F'|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|Alg.3(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U2 R' U2 R' U2 R B R B' U2 B R' B' (z')|Alg.3(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.3) = [R2: [U' R2: (U')] [F U F', R2] ]
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|Alg.4|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|Alg.4(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.4) = [F2: [D R2: (U)] [R' U' R, F2] ]
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|Alg.5|cube=3x3x3&stage=PLL}}
Decomposition(Alg.5) = [F2: [F', R'] [R U' R': (U')] [F': [R, U] ] ]
{{Alg|F R' F' R U R U' R2 U' R U R B' R' B U|Alg.6|cube=3x3x3&stage=PLL}}
{{Alg|F R' F' R U R U' R2 U' R U l U' R' U (x)|Alg.6(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.6) = [F, R'] [U, R] [R', U'] [R, B'] (U)
{{Alg|F R U' R' U' R U F U F' R' F U' F2|Alg.7|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U' R d R U R' B' R U' R2|Alg.7(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.7) = [F: [R, U'] [U2, R] [R: [U', F] ] [F: (U')] ]
{{Alg|R' F R F' U' F' U F2 U F' U' F' L F L' U'|Alg.8|cube=3x3x3&stage=PLL}}
{{Alg|R' F R F' (y') U' R' U R2 U R' U' R' F R F'|Alg.8(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.8) = [R', F] [U', F'] [F, U] [F', L] (U')
{{Alg|R' F' U F U F' U' F R F' U' F U F R' F' R|Alg.9|cube=3x3x3&stage=PLL}}
{{Alg|(y) F' L' U L U L' U' L F L' U' L U L F' L' F|Alg.9(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.9) = [R' F' U F: (U)] [F', U'] [F, R']
{{Alg|F2 U F U' F' U L F R' F R F L' F'|Alg.10|cube=3x3x3&stage=PLL}}
{{Alg|(y z) U2 R U R' U' R (y) R U L' U L U R' U' (x)|Alg.10(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.10) = [F2: [U, F] (U) [L F: [R', F] ] [L, F'] ]
{{Alg|R2 U' R' U R U' B' R' F R' F' R' B R|Alg.11|cube=3x3x3&stage=PLL}}
{{Alg|(z') U2 L' U' L U L' (y') L' U' R U' R' U' L U (x)|Alg.11(v2)|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R' U R U' (z' y') L' U' R U' R' U' L U (y z)|Alg.11(v3)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.11) = [R: [R, U'] [R: (U')] ] [R2, B'] [B': [R, F] [R', B] ]
{{Alg|F R U' R' F D R' B' R' B R2 D' F2|Alg.12|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' F D R' (y x) R' U' R (z) R2 (y) L' d2 (z)|Alg.12(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.12) = [F R: (U')] [F2 D R2: [R, B'] ]
{{Alg|R' U' R2 U' L U2 R' U R U2 L' R' U R' U R|Alg.13|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U' R' U2 R' D R2 U' R U R2 U' D' R U' R U (z')|Alg.13(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.13) = [R' U' R2: [U' L U2 R': (U)] [U', R'] ]
{{Alg|F R F' U' F R' F' R B' R2 B R' U' R2 U|Alg.14|cube=3x3x3&stage=PLL}}
{{Alg|(y) r U r' U' r U' r' (y') l U' R2 U l' U' R2|Alg.14(v2)|cube=3x3x3&stage=PLL}}
Decomposition(Alg.14) = [F R F': (U')] [R: [B', R2] ] [R2, U']
{{Alg|U F' L F L' U' L' U L U2 R U R' U' R' F R F'|Alg.15|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__

Template:OCLL

2016-02-15T17:16:59Z

Addons zz: /* OLL 27 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|U L U' R' U L' U' R|OLL}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R' U L U' R U L'|OLL}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') U2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:OCLL

2016-02-15T17:11:01Z

Addons zz: /* OLL 26 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R' U L U' R U L'|OLL}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') U2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:OCLL

2016-02-15T17:07:21Z

Addons zz: /* OLL 26 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R' U L U' R U L' U'|OLL}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') U2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:OCLL

2016-02-15T17:03:39Z

Addons zz: /* OLL 22 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') U2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:OCLL

2016-02-15T16:45:59Z

Addons zz: /* OLL 22 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' U L U' R U L') y2 (R' U L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:OCLL

2016-02-15T16:45:14Z

Addons zz: /* OLL 22 */

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== OLL 27 ===
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|R U R' U R U2 R'|OLL|vidurl=http://www.youtube.com/watch?v=PPZloK1cqrE}}
{{Alg|y' R' U2 R U R' U R|OLL}}
{{Alg|y L' U2 L U L' U L|OLL}}
{{Alg|y2 L U L' U L U2 L'|OLL}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|U2 r2 U R' U' L' U R U' r' (x')|OLL}}
{{Alg|y' U R U' L' U R' U' L|OLL}}

|

=== OLL 26 ===
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[OCLL]], [[OLL]]
|optimal=7 [[HTM]]
|text=
}}
{{Alg|y2 R' U' R U' R' U2 R|OLL}}
{{Alg|y' R U2 R' U' R U' R'|OLL}}
{{Alg|y L U2 L' U' L U' L'|OLL}}
{{Alg|L' U' L U' L' U2 L|OLL|vidurl=http://www.youtube.com/watch?v=KDalwVQCLzE}}
{{Alg|L' U R U' L U R'|OLL}}
{{Alg|y' L' U R U' L U R'|OLL}}
{{Alg|y' R U2 R' U2' R' F R2 U' R' U' R U R' F'|OLL}}

|-valign="top"
|

=== OLL 21 ===
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[OCLL]], [[OLL]]
|optimal=11 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|R U R' U R U' R' U R U2 R'|OLL}}
{{Alg|y R U2 R' U' R U R' U' R U' R'|OLL}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|y F' (L' U' L U) (L' U' L U) (L' U' L U) F|OLL}}
{{Alg|R' U' R U' R' U R U' R' U2 R|OLL}}
{{Alg|L U L' U L U' L' U L U2 L'|OLL}}
{{Alg|y L' U2 L U L' U' L U L' U L|OLL}}
{{Alg|y (R' U R U) (R' U R U') (R' U R U') R' U' R U2 R' U R|OLL}}
{{Alg|L' U2 M' (y) R U2 R U2 R' U2 (y') l|OLL}}

|

=== OLL 22 ===
{{case
|image=o22.gif
|name=Pi, Bruno, Wheel, T-shirt
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R2' U' R2 U' R2' U2 R|OLL}}
{{Alg|f (R U R' U') f' F (R U R' U') F'|OLL}}
{{Alg|y2 f' (L' U' L U) f F' (L' U' L U) F|OLL}}
{{Alg|y2 L' U2 L2 U L2 U L2 U2 L'|OLL}}
{{Alg|R U2 R2 U' R' U R U' R U' R' y M' U2 M|OLL}}
{{Alg|R' U L U' R U' L' U' L U' L'|OLL}}
{{Alg|y2 L U' R' U L' U R U R' U R|OLL}}
{{Alg|y2 L' U R U' L U' R' U' R U' R'|OLL}}
{{Alg|R U' L' U R' U L U L' U L|OLL}}
{{Alg|R U R' U R U2 R' y' R U R' U R U2 R'|OLL}}
{{Alg|R U R' U' R' F R2 U R' U' R U R' U' F'|OLL}}
{{Alg|(R' R L U' R U L') y2 (R' R L U' R U L')|OLL}}
|-valign="top"
|

=== OLL 23 ===
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|R' U2 R F U' R' U' R U F'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(y') R U R' U' (R U' R' U2) (R U' R' U2) R U R'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|R' U L' U R U' L U2 R' U R|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 z' L|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(y2) R d' R' U R d R' (y) R' U2 R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}'
|

=== OLL 24 ===
{{case
|image=o24.gif
|name=T, Chameleon, Shark, Hammerhead, Little Horse, Stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D' |OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|R U R2' U' R2 U' R2' U2' R U' R U' R'|OLL}}
{{Alg|(y') R U' R' (U2 R U R') (U2 R U R') (U R U' R')|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}
{{Alg|R U' R' F R U R' U' R' F' R2 U' R' U2 R U' R'|OLL}}

|-valign="top"
|

=== OLL 25 ===
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y R' U' (R U R' F') (R U R' U') (R' F R2)|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|F R U' R' U' R U2 R' U' F'|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}
{{Alg|y' R U (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') U' R'|OLL}}
{{Alg|x U R' U' r x' U R U' r'|OLL}}

|}

Template:E-PLL

2016-02-14T00:21:46Z

Addons zz: /* E Permutation */

===E Permutation===
{{case
|image=e.gif
|name=E-PLL
|methods=[[CPLL]], [[PLL]], [[L4C]], [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(y x') (R U' R' D) (R U R' D') (R U R' D) (R U' R' D') (x)|PLL|vidurl=https://www.youtube.com/watch?v=32mxW4xKes8}}
{{Alg|R2 U R' U' (y) (R U R' U')2 R U R' (y') R U' R2'|PLL}}
{{Alg|(x) U R' U' L U R U' r2 U' R U L U' R' U (x)|PLL}}
{{Alg|(y x') R U' R' D R U R' u2 R' U R D R' U' R (x')|PLL}}
{{Alg|(y x') R U' R' D R U R' D2 L' U L D L' U' L (x)|PLL}}
{{Alg|(x) U R' U' L U R U' L' U R U' L U R' U' L' (x')|PLL}}
{{Alg|(x') U' R U L' U' R' U r2 U R' U' r' F R F'|PLL}}
{{Alg|(y) R U R' U R' U' R F' R U R' U' R' F R2 U' R2 U R|PLL}}
{{Alg|L R' U' R U L' U' R' U R r U R' U' r' F R F'|PLL}}
{{Alg|l' U' L' U R U' l U R' U' L U R U' l' U (x')|PLL}}
{{Alg|(y) r' R' U' L D' L' U L R U' R' D R U (x)|PLL}}
{{Alg|(y) l L U R' D R U' R' r' F r D' L' U'|PLL}}
{{Alg|r2 U r2 D (x') (R U' R' U)3 (x) D' r2 U' r2|PLL}}
{{Alg|L' U' L' U R U' L U L (R' l') U' L U R U' L' U (x' y)|PLL}}
{{Alg|R2 U R' (y) (R U' R' U)3 (y') R U' R2|PLL}}
{{Alg|(y' z') R' F R2 U R' B' R U' R2 F' R (z) R B R'|PLL}}
{{Alg|R' U L' D2 L U' R L' U R' D2 R U' L|PLL}}
{{Alg|R B L B' R' (y) R L (y) L B' R' B L' (y') R' L'|PLL}}
{{Alg|l' U' r' F R F' R U R' U' L U R U' R' F|PLL}}
{{Alg|F' R U R' U' L' U R U' l' U R' U' r B R (x2)|PLL}}
{{Alg|(z) U2 R2 F (R U R' U')3 F' R2 U2 (z')|PLL}}
{{Alg|R' D' R U' R' D R U R' D' R U2 R' D R U' R' D' R U R' D R|PLL}}
{{Alg|(y x') R' D R U' R' D' R U2 L D' L' U' L D L' (x)|PLL}}
{{Alg|F R' F' r U R U' r' F R F' r U R' U' r'|PLL}}
{{Alg|(x) R U' R' D R U R' D' R U R' D R U' R' D'|PLL}}
{{Alg|D R' D2 F' D L D' F D2 R D' F' L' F|PLL}}

Template:E-PLL

2016-02-14T00:13:12Z

Addons zz: /* E Permutation */

===E Permutation===
{{case
|image=e.gif
|name=E-PLL
|methods=[[CPLL]], [[PLL]], [[L4C]], [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(y x') (R U' R' D) (R U R' D') (R U R' D) (R U' R' D') (x)|PLL}}
{{Alg|(x') (R U' R' D) (R U R' D') (R U R' D) (R U' R' D') (x)|PLL|vidurl=https://www.youtube.com/watch?v=32mxW4xKes8}}
{{Alg|R2 U R' U' (y) (R U R' U')2 R U R' (y') R U' R2'|PLL}}
{{Alg|(x) U R' U' L U R U' r2 U' R U L U' R' U (x)|PLL}}
{{Alg|(y x') R U' R' D R U R' u2 R' U R D R' U' R (x')|PLL}}
{{Alg|(y x') R U' R' D R U R' D2 L' U L D L' U' L (x)|PLL}}
{{Alg|(x) U R' U' L U R U' L' U R U' L U R' U' L' (x')|PLL}}
{{Alg|(x') U' R U L' U' R' U r2 U R' U' r' F R F'|PLL}}
{{Alg|(y) R U R' U R' U' R F' R U R' U' R' F R2 U' R2 U R|PLL}}
{{Alg|L R' U' R U L' U' R' U R r U R' U' r' F R F'|PLL}}
{{Alg|l' U' L' U R U' l U R' U' L U R U' l' U (x')|PLL}}
{{Alg|(y) r' R' U' L D' L' U L R U' R' D R U (x)|PLL}}
{{Alg|(y) l L U R' D R U' R' r' F r D' L' U'|PLL}}
{{Alg|r2 U r2 D (x') (R U' R' U)3 (x) D' r2 U' r2|PLL}}
{{Alg|L' U' L' U R U' L U L (R' l') U' L U R U' L' U (x' y)|PLL}}
{{Alg|R2 U R' (y) (R U' R' U)3 (y') R U' R2|PLL}}
{{Alg|(y' z') R' F R2 U R' B' R U' R2 F' R (z) R B R'|PLL}}
{{Alg|R' U L' D2 L U' R L' U R' D2 R U' L|PLL}}
{{Alg|R B L B' R' (y) R L (y) L B' R' B L' (y') R' L'|PLL}}
{{Alg|l' U' r' F R F' R U R' U' L U R U' R' F|PLL}}
{{Alg|F' R U R' U' L' U R U' l' U R' U' r B R (x2)|PLL}}
{{Alg|(z) U2 R2 F (R U R' U')3 F' R2 U2 (z')|PLL}}
{{Alg|R' D' R U' R' D R U R' D' R U2 R' D R U' R' D' R U R' D R|PLL}}
{{Alg|(y x') R' D R U' R' D' R U2 L D' L' U' L D L' (x)|PLL}}
{{Alg|F R' F' r U R U' r' F R F' r U R' U' r'|PLL}}
{{Alg|(x) R U' R' D R U R' D' R U R' D R U' R' D'|PLL}}
{{Alg|D R' D2 F' D L D' F D2 R D' F' L' F|PLL}}

Template:E-PLL

2016-02-13T16:55:07Z

Addons zz: /* E Permutation */

===E Permutation===
{{case
|image=e.gif
|name=E-PLL
|methods=[[CPLL]], [[PLL]], [[L4C]], [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(y x') (R U' R' D) (R U R' D') (R U R' D) (R U' R' D') (x)|PLL|vidurl=http://www.youtube.com/watch?v=XVru99o6vjA}}
{{Alg|R2 U R' U' (y) (R U R' U')2 R U R' (y') R U' R2'|PLL}}
{{Alg|(x) U R' U' L U R U' r2 U' R U L U' R' U (x)|PLL}}
{{Alg|(y x') R U' R' D R U R' u2 R' U R D R' U' R (x')|PLL}}
{{Alg|(y x') R U' R' D R U R' D2 L' U L D L' U' L (x)|PLL}}
{{Alg|(x) U R' U' L U R U' L' U R U' L U R' U' L' (x')|PLL}}
{{Alg|(x') U' R U L' U' R' U r2 U R' U' r' F R F'|PLL}}
{{Alg|(y) R U R' U R' U' R F' R U R' U' R' F R2 U' R2 U R|PLL}}
{{Alg|L R' U' R U L' U' R' U R r U R' U' r' F R F'|PLL}}
{{Alg|l' U' L' U R U' l U R' U' L U R U' l' U (x')|PLL}}
{{Alg|(y) r' R' U' L D' L' U L R U' R' D R U (x)|PLL}}
{{Alg|(y) l L U R' D R U' R' r' F r D' L' U'|PLL}}
{{Alg|r2 U r2 D (x') (R U' R' U)3 (x) D' r2 U' r2|PLL}}
{{Alg|L' U' L' U R U' L U L (R' l') U' L U R U' L' U (x' y)|PLL}}
{{Alg|R2 U R' (y) (R U' R' U)3 (y') R U' R2|PLL}}
{{Alg|(y' z') R' F R2 U R' B' R U' R2 F' R (z) R B R'|PLL}}
{{Alg|R' U L' D2 L U' R L' U R' D2 R U' L|PLL}}
{{Alg|R B L B' R' (y) R L (y) L B' R' B L' (y') R' L'|PLL}}
{{Alg|l' U' r' F R F' R U R' U' L U R U' R' F|PLL}}
{{Alg|F' R U R' U' L' U R U' l' U R' U' r B R (x2)|PLL}}
{{Alg|(z) U2 R2 F (R U R' U')3 F' R2 U2 (z')|PLL}}
{{Alg|R' D' R U' R' D R U R' D' R U2 R' D R U' R' D' R U R' D R|PLL}}
{{Alg|(y x') R' D R U' R' D' R U2 L D' L' U' L D L' (x)|PLL}}
{{Alg|F R' F' r U R U' r' F R F' r U R' U' r'|PLL}}
{{Alg|(x) R U' R' D R U R' D' R U R' D R U' R' D'|PLL}}
{{Alg|D R' D2 F' D L D' F D2 R D' F' L' F|PLL}}

Template:H-PLL

2016-02-13T16:00:13Z

Addons zz: /* H Permutation */

===H Permutation===
{{case
|image=H.gif
|name=H-PLL, X-PLL
|methods=[[EPLL]], [[CPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=X-PLL is H-PLL + U2.
}}
{{Alg|M2' U M2' U2 M2' U M2'|PLL|vidurl=http://www.youtube.com/watch?v=eRsxqjJN3WA}}
{{Alg|M2' U' M2' U2' M2' U' M2'|PLL|vidurl=http://www.youtube.com/watch?v=4YqOYb6pHSs}}
{{Alg|M2' U2 M2' U' M2' U2 M2' U|PLL}}
{{Alg|M2' U2 M2' U M2' U2 M2' U'|PLL}}
{{Alg|R2 U2 R U2 R2 U2 R2 U2 R U2 R2|PLL}}
{{Alg|R2' U2 R' U2 R2' U2' R2' U2 R' U2 R2'|PLL|vidur2=http://www.youtube.com/watch?v=HI9ff1ACklU}}
{{Alg|R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2|PLL}}
{{Alg|R U2' R' U' R' U' R2 U' R2' U2' R2 U2' R' (U)|PLL}}
{{Alg|L2 U2 L' U2 L2 U2 L2 U2 L' U2 L2|PLL}}
{{Alg|L R U2 L' R' F' B' U2 F B|PLL}}
{{Alg|L R U2 L' R' (y) L' R' U2 L R|PLL}}
{{Alg|(M2' U)6 U2|PLL}}
{{Alg|(M2' U')6 U2|PLL}}
{{Alg|(R' S R u)6|PLL}}
{{Alg|S R U2 R2 U2 R2 U2 R S'|PLL}}
{{Alg|F2 M2' F2 U' F2 M2' F2|PLL}}
{{Alg|(x) U2 M2' U2 B' U2 M2' U2 (x')|PLL}}
{{Alg|L R U2 L' l' U' u' L2 U (z) L|PLL}}
{{Alg|M2' u M2' u2 M2' u M2'|PLL}}
{{Alg|M2' u' M2' u2' M2' u' M2'|PLL}}
{{Alg|z2 (R U R' U' D)30|PLL}}

Template:H-PLL

2016-02-13T15:41:36Z

Addons zz: Fixed broken algoritm

===H Permutation===
{{case
|image=H.gif
|name=H-PLL, X-PLL
|methods=[[EPLL]], [[CPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=X-PLL is H-PLL + U2.
}}
{{Alg|M2' U M2' U2 M2' U M2'|PLL|vidurl=http://www.youtube.com/watch?v=eRsxqjJN3WA}}
{{Alg|M2' U' M2' U2' M2' U' M2'|PLL|vidurl=http://www.youtube.com/watch?v=4YqOYb6pHSs}}
{{Alg|M2' U2 M2' U' M2' U2 M2' U|PLL}}
{{Alg|M2' U2 M2' U M2' U2 M2' U'|PLL}}
{{Alg|R2 U2 R U2 R2 U2 R2 U2 R U2 R2|PLL}}
{{Alg|R2' U2 R' U2 R2' U2' R2' U2 R' U2 R2'|PLL|vidur2=http://www.youtube.com/watch?v=HI9ff1ACklU}}
{{Alg|R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2|PLL}}
{{Alg|R U2' R' U' R' U' R2 U' R2' U2' R2 U2' R' (U)|PLL}}
{{Alg|L2 U2 L' U2 L2 U2 L2 U2 L' U2 L2|PLL}}
{{Alg|L R U2 L' R' F' B' U2 F B|PLL}}
{{Alg|L R U2 L' R' (y) L' R' U2 L R|PLL}}
{{Alg|(M2' U)6|PLL}}
{{Alg|(M2' U')6|PLL}}
{{Alg|(R' S R u)6|PLL}}
{{Alg|S R U2 R2 U2 R2 U2 R S'|PLL}}
{{Alg|F2 M2' F2 U' F2 M2' F2|PLL}}
{{Alg|(x) U2 M2' U2 B' U2 M2' U2 (x')|PLL}}
{{Alg|L R U2 L' l' U' u' L2 U (z) L|PLL}}
{{Alg|M2' u M2' u2 M2' u M2'|PLL}}
{{Alg|M2' u' M2' u2' M2' u' M2'|PLL}}
{{Alg|z2 (R U R' U' D)30|PLL}}