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Last Three Corners

2015-12-24T14:17:32Z

Zombiedude347: /* External links */ fixed a,an error

{{Substep Infobox
|name=Last Three Corners
|image=L3C.png
|proposers=[[Anthony Snyder]], [[Ryan Heise]]
|anames=L3C
|variants=[[L4C]], [[CxLL]]
|subgroup=
|algs=24
|moves=~10 [[HTM]]
|purpose=
* [[Speedsolving]], [[FMC]], [[BLD]]
|previous=[[L3C cube state]]
|next=[[Solved cube state]]
}}

'''Last three corners''', abbrevaited '''L3C''' (or 3LC), is a [[method]] that solves three of the [[last layer]] corners preserving all the rest, a sub group of [[L4C]], [[ZBLL]] and [[ZZLL]].

'''Usage:''' besides L4C, [[CxLL]], ZBLL and ZZLL it is useful for [[FMC]] and the 3-cycles are nice for [[Freestyle BLD]]. L3C is the final stage in the [[Snyder Method]].

'''See also:'''
* [[Last Four Corners]]
* [[Beyer-Hardwick Method]]

== External links ==
* [http://www.ryanheise.com/cube/corner_3_cycles.html] Ryan Heise explains an intuitive approach to solve the last three corners.

=L3C Cases=
The group have 27 cases including solved, 3*3 orientations and 3 permutations. Most of the cases (18) are pure [[3-cycle]]s, the rest are pure twists U, T, L, S and -S. Some of the twist occures 2 times (U, T and L) and the T-twist is the same as the U-twist if the puzzle is reoriented. Subtracting the duplicates and solved it will be 22 cases left. 16 of them are pure L3C cases and listed at this page, the rest are in one of two sub groups.

===Sub groups===
*'''Pure twists''' you can find at the [[Corner orientation|Corner orientation page]].
*'''Only permutation''', see [[CPLL]], corner permutation of the last layer.''

The '''naming system''' used here is adapted to BLD, the ULB corner is always the solved one and URF is the 'buffer' with U as the buffer sticker. The piece in the buffer will go to two places, either URB or UFL and the sticker in U will go to any of the three stickers on each goal position and that sticker is in uppercase, the other two letters will be in lowercase. The second half of the name is the same but from the goal position of the first. The last piece will always go to the first buffer position so that will not be in the name.

Example: CW A-PLL is Ufl-Urb and CCW A-PLL is Urb-Ufl.

==Algorithms==
{{Algnote}}
----

{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|
=== uFl-Urb ===
{{case |image=L3C case1(a).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2 D R' U2 R D' R' U2 R'}}

|
=== uRb-Ufl ===
{{case
|image=L3C case1(b).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y) L2 D' L U2 L' D L U2 L}}

|-valign="top"
|
=== Ufl-uRb ===
{{case |image=L3C case1(c).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y) L' U2 L' D' L U2 L' D L2}}

|
=== Urb-uFl ===
{{case |image=L3C case1(d).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R D R' U2 R D' R2}}

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|
=== ufL-uRb ===
{{case |image=L3C case2(a).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y x) R2 D2 R U2 R' D2 R U2 l}}

|

=== urB-uFl ===
{{case |image=L3C case2(b).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(x) L2 D2 L' U2 L D2 L' U2 r'}}

|-valign="top"
|

=== uFl-urB ===
{{case |image=L3C case2(c).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|r U2 L D2 L' U2 L D2 L2 (x')}}

|
=== uRb-ufL ===
{{case |image=L3C case2(d).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y) l' U2 R' D2 R U2 R' D2 R2 (x')}}

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|
=== ufL-Urb ===
{{case |image=L3C case3(a).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(y) r' U' R U L U' R' U (x)}}
{{Alg|(x') R U R' D R U' R' D' (x)}}
|
=== urB-Ufl ===
{{case |image=L3C case3(b).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(y2) l U L' U' R' U L U' (x)}}
{{Alg| r U R' U' r' F R F'}}
|-valign="top"
|
=== Ufl-urB ===
{{case |image=L3C case3(c).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(x') U L' U' R U L U' l'}}

|
=== Urb-ufL ===
{{case |image=L3C case3(d).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(y x') U' R U L' U' R' U r}}
{{Alg|(x') D R U R' D' R U' R' (x)}}
|-valign="top"
|
=== ufL-urB ===
{{case |image=L3C case4(a).jpg
|name=Niklas
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R' U L U' R U L' U'}}

|
=== urB-ufL ===
{{case |image=L3C case4(b).jpg
|name=Niklas b
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|U L U' R' U L' U' R}}

|-valign="top"
|
=== uFl-uRb ===
{{case |image=L3C case5(a).jpg
|name=Anti Niklas a
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B L' U2 L B' L' B U2 B' L}}
{{Alg|(y2 x') U2 R2 D R U2 R' D' R U2 R U2 (x y2)}}
{{Alg|(y' x) R2 U2 L U R2 U' L' U R2 U R2 (x' y)}}
|
=== uRb-uFl ===
{{case |image=L3C case5(b).jpg
|name=Anti Niklas b
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|L' B U2 B' L B L' U2 L B'}}
{{Alg|(y2 x') U2 R' U2 R' D R U2 R' D' R2 U2 (x y2)}}
{{Alg|(y' x) R2 U' R2 U' L U R2 U' L' U2 R2 (x' y)}}
|}

[[Category:3x3x3 methods]]
[[Category:3x3x3 last layer methods]]

__NOTOC__

User:Zombiedude347

2015-12-23T20:18:37Z

Zombiedude347: /* 3x3x3 */

Hi, I am Zombiedude347, I am a cubing enthusiast (as is obvious by me having an account on this wiki). I personally have owned several 3x3x3s, a 4x4x4 (which sadly fell out of my backpack while in a parking lot and it got ran over by a car), and a 7x7x7. I plan on posting my methods during my free time.

* My [[User:Zombiedude347/2x2x2|2x2x2]] method.
* My [[User:Zombiedude347/3x3x3|3x3x3]] method.

== Example Solves==
===3x3x3===
Example Solve 1
*Cross
**U' R F L U'
*F2L
**F D F' R' D2 R D2 R' D' R - [[F2L#Reposition_Edge_and_Flip_Corner|F2L 13]]
**D' L' D' L2 B' L' B - [[F2L#Pair_Made_on_Side|F2L 22]]
**F' D2 F D' F L' F' L - [[F2L#Reposition_Edge|F2L 8]]
**D R' D' S D2 S' D' R - [[F2L#Corner_in_Place.2C_Edge_in_U_Face|F2L 25]]
*CLL Permutation
**B' D' B R D R' B' D B - [[CLL_algorithms_(3x3x3)#T_cases|T L]]
*CLL Orientation
**R D R' D R D2 R' - [[CLL_algorithms_(3x3x3)#S_cases|S U]]
*ELL
**M D' M' D M D M' D M D2 M' D2 - [[ELL#B_edge_solved_.283-cycles.29|RF-flip U-PLL b]]
65 Moves (ATM), 66 moves (STM), 74 Moves (SQTM), 74 Moves (HTM), 82 Moves (QTM)

== Patterns (algs in SiGN) ==
* Cube in a Cube in a Cube in a Cube in a corner (9x9x9) (can't think of a better name for the pattern)
[[[4r,4u]3:4f2][[3r,3u]3:4f2][[r,u]3:f2][[R,U]3:f2]:y2]
* 7x7x7
[[[3r,3u]3:3f2][[r,u]3:3f2][[R,U]3:F2]:s2 y2]
* 5x5x5
[[[r,u]3:f2][[R,U]3:f2]:y2]
* 3x3x3
[[[R,U]3:F2]:s2 y2]

Talk:Sexy Move

2015-12-22T18:21:54Z

Zombiedude347:

About this article, the sexy move is so much more than Arnuds tutorial and the remix, that should be a passage in the lower part of the page and at top it should be a description of the move and how it is used. //[[User:Kenneth|Kenneth]] 16:40, 15 July 2010 (UTC)

The youtube video has been removed and the link to the original mp3 doesn't work -[[User:Erzz|Erzz]] 17:59, 15 June 2011 (EDT)

This page should probably contain a list of common algorithms that use the sexy move. [[User:Zombiedude347|Zombiedude347]] ([[User talk:Zombiedude347|talk]]) 18:21, 22 December 2015 (UTC)

User:Zombiedude347

2015-12-22T05:13:54Z

Zombiedude347: /* Patterns */

Hi, I am Zombiedude347, I am a cubing enthusiast (as is obvious by me having an account on this wiki). I personally have owned several 3x3x3s, a 4x4x4 (which sadly fell out of my backpack while in a parking lot and it got ran over by a car), and a 7x7x7. I plan on posting my methods during my free time.

* My [[User:Zombiedude347/2x2x2|2x2x2]] method.
* My [[User:Zombiedude347/3x3x3|3x3x3]] method.

== Example Solves==
===3x3x3===
Example Solve 1
*Cross
**U' R F L U'
*F2L
**F D F' R' D2 R D2 R' D' R
**D' L' D' L2 B' L' B
**F' D2 F D' F L' F' L
**D R' D' S D2 S' D' R
*CLL Permutation
**B' D' B R D R' B' D B
*CLL Orientation
**R D R' D R D2 R' - Corner Orientation
*ELL
**M D' M' D M D M' D M D2 M' D2
65 Moves (ATM), 66 moves (STM), 74 Moves (SQTM), 74 Moves (HTM), 82 Moves (QTM)

== Patterns (algs in SiGN) ==
* Cube in a Cube in a Cube in a Cube in a corner (9x9x9) (can't think of a better name for the pattern)
[[[4r,4u]3:4f2][[3r,3u]3:4f2][[r,u]3:f2][[R,U]3:f2]:y2]
* 7x7x7
[[[3r,3u]3:3f2][[r,u]3:3f2][[R,U]3:F2]:s2 y2]
* 5x5x5
[[[r,u]3:f2][[R,U]3:f2]:y2]
* 3x3x3
[[[R,U]3:F2]:s2 y2]

User:Zombiedude347

2015-12-22T00:41:04Z

Zombiedude347:

Hi, I am Zombiedude347, I am a cubing enthusiast (as is obvious by me having an account on this wiki). I personally have owned several 3x3x3s, a 4x4x4 (which sadly fell out of my backpack while in a parking lot and it got ran over by a car), and a 7x7x7. I plan on posting my methods during my free time.

* My [[User:Zombiedude347/2x2x2|2x2x2]] method.
* My [[User:Zombiedude347/3x3x3|3x3x3]] method.

== Example Solves==
===3x3x3===
Example Solve 1
*Cross
**U' R F L U'
*F2L
**F D F' R' D2 R D2 R' D' R
**D' L' D' L2 B' L' B
**F' D2 F D' F L' F' L
**D R' D' S D2 S' D' R
*CLL Permutation
**B' D' B R D R' B' D B
*CLL Orientation
**R D R' D R D2 R' - Corner Orientation
*ELL
**M D' M' D M D M' D M D2 M' D2
65 Moves (ATM), 66 moves (STM), 74 Moves (SQTM), 74 Moves (HTM), 82 Moves (QTM)

== Patterns ==
* Cube in a Cube in a Cube in a corner. (can't think of a better name for the pattern)
[[[3r,3u]3:3f2][[r,u]3:3f2][[R,U]3:F2]:s2 y2], in simplified general notation (SiGN).

PLL

2015-10-04T02:09:36Z

Zombiedude347: /* See also */

{{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}}

===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}}
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}}

===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)] ] ]

===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')] ] ]
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')

===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__

User:Zombiedude347

2015-10-03T18:23:45Z

Zombiedude347:

Talk:PLL

2015-10-02T04:19:24Z

Zombiedude347: /* Aa Perm */

Just learned the N(a) and N(b) perms and they were written as L U' R U2 L' U R' L U' R U2 L' U R' U' and R' U L' U2 R U' L R' U L' U2 R U' L U respectively. I noticed that they were actually two repetitions of a shorter algorithm so I changed it so other cubers will have an easier time learning those perms. I turned N(a) into (L U' R U2 L' U R')2 U' and N(b) into (R' U L' U2 R U' L)2 U.

~ Eleredo

----

Quick question: Is a Ja Perm same as a L perm and if it is, maybe a alternate name block on that PLL? [[User:MaeLSTRoM|MaeLSTRoM]] 17:40, 14 January 2011 (EST)

==Templates==
I'm thinking it might be good to have each case in a template, aspecially the PLLs, then you can put the cases at other pages too but still all algs added will go to the same place, no matter if it is edited on page x or y.

But I'm not sure it is doable, have to test it a little...

// [[User:Kenneth|Kenneth]] 09:36, 25 August 2010 (UTC)

It works, but after edit you will be at the template page and not at the page you started from, a smaller problem I think...

I think I got it, a little menu in top of the pic that have links to the pages the template is used on =)

{{H-PLL}}

=Old talk=
It is possible to remove the huge table of contents and make links to the sections in a nice table instead, it looks much better.

Open the editor and look at the next line after this, it removes the table, the next line removes the section edit tabs if one likes that (removed it again becuse it took away the tabs from this page)

__NOTOC__

// [[User:Kenneth|Kenneth]] 21:14, 30 August 2008 (UTC)

I made an example image that shows how LL cases can be displayed, this is right side J-PLL

[[image:R J PLL.gif]]

Looking good? I think it does, maybe a little higher side pices and roundes stickers would be nice.

If anyone can make nicer looking images than mine then things is good (I used pain(t) and that is not a good tool)

// [[User:Kenneth|Kenneth]] 05:18, 31 August 2008 (UTC)

EDIT: I skiped that image idéa if someone wonders what happend =) // [[User:Kenneth|Kenneth]] 14:41, 1 October 2008 (UTC)

=== Table of contents ===

Here is a example of how to solve the problem with that disturbing TOC

Edit:
Remade it, tiny:

{{PLL}}

Bah! I put it on the page and remove the TOC :)

// [[User:Kenneth|Kenneth]] 08:38, 1 September 2008 (UTC)

I think we should color code (if possible) the algorithms that are most commonly used for OH. Or maybe put them in a seperate section if possible. What do you guys think?

[[User:Rubik's Cube Fan|Rubik's Cube Fan]] 18:44, 30 September 2008 (UTC)

: In that case I think it is better to make sub pages under BLD for recommnded OLL's and PLL'. It is pretty easy to colour code but it makes the wiki code messy with all those "font" tags and colour codes. I make an example here, click edit to see how it looks:

* R U R' U R U2 R'

// [[User:Kenneth|Kenneth]] 14:41, 1 October 2008 (UTC)

== Aa Perm ==

[http://alg.cubing.net/?stage=PLL&type=alg&view=playback&alg=%28y-%29_r_U_r-_U-_r-_F_r2_U-_r-_U-_r_U_r-_F- (y') r U r' U' r' F r2 U' r' U' r U r' F'] doesn't seem to be an A perm. The scrambled view on alg.cubing doesn't look like one... [[User:Randomno|Randomno]] ([[User talk:Randomno|talk]]) 23:06, 12 September 2014 (UTC)

* it is an A-perm, the top layer is just rotated a quarter turn. You can tell that it is an a-perm because it containes a 1x2x2 block surrounded by 2 stickers of the same color. [[User:Zombiedude347|Zombiedude347]] ([[User talk:Zombiedude347|talk]]) 04:19, 2 October 2015 (UTC)

Parity

2015-09-27T23:18:10Z

Zombiedude347: Added paragraph explaining the correct definition of parity, modified first sentence of original paragraph to make it a transition from first paragraph

'''Parity''' in a puzzle describes whether a move or sequence of moves swaps pieces an even or odd amount of times. If a puzzle is described as having '''Even Parity''', only moves with even-parity are possible. If a puzzle is described as having '''Odd Parity''' then it can perform both Odd and Even parity moves. For example, a standard 3-cycle (ABC -> BCA) would have Even parity because it is actually 2 swaps A<->B and A<->C. Orientation of pieces is ignored when considering swapped pieces.

The term Parity is often misused in cubing. It is used colloquially to describe an odd permutation of pieces within a certain defined [[orbital]]. It is most commonly used to refer to certain situations that can arise on the [[4x4x4]] and [[5x5x5]] cubes when solving with the [[reduction method]]. The most commonly known example is referred to as OLL Parity, and comes about on cubes of size 4x4x4 and larger. OLL Parity on a 4x4x4 cube happens when two adjacent wing edges are interchanged with each other. When solving with the reduction method these two interchanged wing edges give the two piece edge group the appearance of being a flipped [[3x3x3]] edge. This leads to a case that is impossible to solve using outer layer turns only, and must be solved by performing an odd number of inner slice quarter turns to return the wing edge orbital back to an even permutation.

== See also ==
* [[Permutation Parity]]
* [[4x4x4 Parity Algorithms]]

== External links ==
Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=19800 Understanding Parity]

[[Category:Puzzle theory]]

{{Stub}}

User:Zombiedude347/2x2x2

2015-09-24T23:56:50Z

Zombiedude347: /* OLLs */ modified algorithms to use only D & R turns, making them quicker to perform, fixed errors, added a few alternate algorithms

Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use {{Alg|(R' D' R)(F D F')(R' D R)}}
*If the two corners that need switched are diagonal from each other, then use {{Alg|(R' D' R)(F D2 F')(R' D R)}}

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || {{Alg|R D R' D R D2 R'}}
|-
| [[File:2x2AS.gif]] || {{Alg|D' R' D' R D' R' D2 R}}
|-
| [[File:2x2Bo.gif]] || {{Alg|R D R' D R D2 R' D R' D' R D' R' D2 R}}{{Alg|R' D' R D' R' D2 R D2 R' D' R D' R' D2 R}}{{Alg|D' R' D' R D' R' D2 R D' R D R' D R D2 R'}}
|-
| [[File:2x2He.gif]] || {{Alg|D R D R' D R D2 R2 D' R D' R' D2 R}}{{Alg|D' R' D' R D' R' D2 R2 D R' D R D2 R'}}
|-
| [[File:2x2H.gif]] || {{Alg|D R' D' R D' R' D R D' R' D2 R}}{{Alg|D' R' D' R D' R' D R D' R' D2 R}}{{Alg|D R D R' D R D' R' D R D2 R'}}{{Alg|D' R D R' D R D' R' D R D2 R'}}
|-
| [[File:2x2T.gif]] || {{Alg|R D R' D R D2 R' D2 R' D' R D' R' D2 R}}{{Alg|R' D' R D' R' D2 R D2 R D R' D R D2 R'}}
|-
| [[File:2x2Pi.gif]] || {{Alg|D R' D' R D' R' D2 R D R' D' R D' R' D2 R}}{{Alg|R' D' R D' R' D2 R D' R' D' R D' R' D2 R}}{{Alg|D2 R D R' D R D2 R' D R D R' D R D2 R'}}{{Alg|D R D R' D R D2 R' D' R D R' D R D2 R'}}
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/3x3x3

2015-09-11T23:01:58Z

Zombiedude347: /* Bottom Layer */

==Top Layer==
* Solve the cross, done intuitively.
* Place Top Corners
** Find a corner on the D face that belongs on the U face. Rotate the cube so that the correct location of the piece is at the UFR corner. Rotate the D face so that the piece is in the DFR corner.
** If the white sticker is on the D face, use {{Alg|R' D2 R D R' D' R}}
** If the white sticker is on the F face, use {{Alg|F D F'}}
** If the white sticker is on the R face, use {{Alg|R' D' R}}
** If all the top layer corners are on the U face, but 2 or more are incorrect, then rotate the cube so that of these incorrect corners is at the UFR and do move R' D' R to move it to the D face.

==Middle Layer==
*Find a middle layer edge on the bottom layer.
*Rotate the cube so that the correct location of the piece is at the FR edge.
*If the bottom sticker of the piece belongs on the F face, place the piece in the DF position and use {{Alg|R D S D2 S' D R'}}
*If the bottom sticker of the piece belongs on the R face, place the piece in the DR position and use {{Alg|F' D' M D2 M' D' F}}
*If the edge in the FL slot belongs in the FR slot, and could be oriented correctly using the move D2, use {{Alg|M F M' F2 M F M'}}
*If the edge in the FR slot belongs in the FL slot, and could be oriented correctly using the move D2, use {{Alg|M F' M' F2 M F' M'}}
*In any other cases, where FR is incorrectly positioned or oriented, use {{Alg|F' D' M D2 M' D' F}}

==Bottom Layer==
''Note:Correct Orientation for edges is defined such that quarter turns change orientation, and half turns preserve orientation.''

*Solve Corners
**Use the algorithms on my [[User:Zombiedude347/2x2x2|2x2x2]] page.
*ELL
**This method is primarily intuitive, done use combinations of these 4 algorithms and rotations of the cube.
{|
|- {{Alg|M D M' D2 M D M'}} || Rotates DR,DB,DL clockwise, preserves orientation
|- {{Alg|M D' M' D2 M D' M'}} || Rotates DR,DB,DL counterclockwise, preserves orientation
|- {{Alg|M D M' D' M D' M' D' M D2 M'}} || Re-Orients DB,DL, doesn't preserve location (use if no edges being reoriented are correctly positioned or oriented)
|- {{Alg|E R F' U R' F E' F' R U' F R'}} || Re-Orients FL,FR, preserves location (use if 1 or more edges being reoriented are correctly positioned or oriented)
|}

User:Zombiedude347/3x3x3

2015-09-11T22:55:06Z

Zombiedude347: /* Bottom Layer */

==Top Layer==
* Solve the cross, done intuitively.
* Place Top Corners
** Find a corner on the D face that belongs on the U face. Rotate the cube so that the correct location of the piece is at the UFR corner. Rotate the D face so that the piece is in the DFR corner.
** If the white sticker is on the D face, use {{Alg|R' D2 R D R' D' R}}
** If the white sticker is on the F face, use {{Alg|F D F'}}
** If the white sticker is on the R face, use {{Alg|R' D' R}}
** If all the top layer corners are on the U face, but 2 or more are incorrect, then rotate the cube so that of these incorrect corners is at the UFR and do move R' D' R to move it to the D face.

==Middle Layer==
*Find a middle layer edge on the bottom layer.
*Rotate the cube so that the correct location of the piece is at the FR edge.
*If the bottom sticker of the piece belongs on the F face, place the piece in the DF position and use {{Alg|R D S D2 S' D R'}}
*If the bottom sticker of the piece belongs on the R face, place the piece in the DR position and use {{Alg|F' D' M D2 M' D' F}}
*If the edge in the FL slot belongs in the FR slot, and could be oriented correctly using the move D2, use {{Alg|M F M' F2 M F M'}}
*If the edge in the FR slot belongs in the FL slot, and could be oriented correctly using the move D2, use {{Alg|M F' M' F2 M F' M'}}
*In any other cases, where FR is incorrectly positioned or oriented, use {{Alg|F' D' M D2 M' D' F}}

==Bottom Layer==
''Note:Correct Orientation for edges is defined such that quarter turns change orientation, and half turns preserve orientation.''

*Solve Corners
**Use the algorithms on my [[User:Zombiedude347/2x2x2|2x2x2]] page.
*ELL
**This method is primarily intuitive, done use combinations of these 4 algorithms and rotations of the cube.
{|
|- {{Alg|M D M' D2 M D M'}} || Rotates DR,DB,DL clockwise, preserves orientation
|- {{Alg|M D' M' D2 M D' M'}} || Rotates DR,DB,DL counterclockwise, preserves orientation
|- {{Alg|M D M' D' M D' M' D' M D2 M'}} || Re-Orients DB,DL, doesn't preserve location (use if no edges are correctly positioned or oriented)
|- {{Alg|E R F' U R' F E' F' R U' F R'}} || Re-Orients FL,FR, preserves location (use if 1 or more edges are correctly positioned or oriented)
|}

User:Zombiedude347/2x2x2

2015-09-01T17:37:48Z

Zombiedude347: /* PLLs */ added alg template

Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use {{Alg|(R' D' R)(F D F')(R' D R)}}
*If the two corners that need switched are diagonal from each other, then use {{Alg|(R' D' R)(F D2 F')(R' D R)}}

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || {{Alg|(y2) L D L' D L D2 L'}}
|-
| [[File:2x2AS.gif]] || {{Alg|(y) R' D' R D' R' D2 R}}
|-
| [[File:2x2Bo.gif]] || {{Alg|(y) R' D' R D' R' D2 R y' L D L' D L D2 L'}}
|-
| [[File:2x2He.gif]] || {{Alg|(y) R' D' R D' R' D2 R y2 L D L' D L D2 L'}}
|-
| [[File:2x2H.gif]] || {{Alg|(y) R' D' R D' R' D R D' R' D2 R}}
|-
| [[File:2x2T.gif]] || {{Alg|R' D' R D' R' D2 R L D L' D L D2 L'}} or {{Alg|(y')R' D' R D' R' D2 R(y)R' D' R D' R' D2 R}}
|-
| [[File:2x2Pi.gif]] || {{Alg|(y') R' D' R D' R' D2 R (y') R' D' R D' R' D2 R}}
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/2x2x2

2015-09-01T17:35:35Z

Zombiedude347: /* OLLs */ used alg template

Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || {{Alg|(y2) L D L' D L D2 L'}}
|-
| [[File:2x2AS.gif]] || {{Alg|(y) R' D' R D' R' D2 R}}
|-
| [[File:2x2Bo.gif]] || {{Alg|(y) R' D' R D' R' D2 R y' L D L' D L D2 L'}}
|-
| [[File:2x2He.gif]] || {{Alg|(y) R' D' R D' R' D2 R y2 L D L' D L D2 L'}}
|-
| [[File:2x2H.gif]] || {{Alg|(y) R' D' R D' R' D R D' R' D2 R}}
|-
| [[File:2x2T.gif]] || {{Alg|R' D' R D' R' D2 R L D L' D L D2 L'}} or {{Alg|(y')R' D' R D' R' D2 R(y)R' D' R D' R' D2 R}}
|-
| [[File:2x2Pi.gif]] || {{Alg|(y') R' D' R D' R' D2 R (y') R' D' R D' R' D2 R}}
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/3x3x3

2015-09-01T17:28:39Z

Zombiedude347: /* Bottom Layer */

==Top Layer==
* Solve the cross, done intuitively.
* Place Top Corners
** Find a corner on the D face that belongs on the U face. Rotate the cube so that the correct location of the piece is at the UFR corner. Rotate the D face so that the piece is in the DFR corner.
** If the white sticker is on the D face, use {{Alg|R' D2 R D R' D' R}}
** If the white sticker is on the F face, use {{Alg|F D F'}}
** If the white sticker is on the R face, use {{Alg|R' D' R}}
** If all the top layer corners are on the U face, but 2 or more are incorrect, then rotate the cube so that of these incorrect corners is at the UFR and do move R' D' R to move it to the D face.

==Middle Layer==
*Find a middle layer edge on the bottom layer.
*Rotate the cube so that the correct location of the piece is at the FR edge.
*If the bottom sticker of the piece belongs on the F face, place the piece in the DF position and use {{Alg|R D S D2 S' D R'}}
*If the bottom sticker of the piece belongs on the R face, place the piece in the DR position and use {{Alg|F' D' M D2 M' D' F}}
*If the edge in the FL slot belongs in the FR slot, and could be oriented correctly using the move D2, use {{Alg|M F M' F2 M F M'}}
*If the edge in the FR slot belongs in the FL slot, and could be oriented correctly using the move D2, use {{Alg|M F' M' F2 M F' M'}}
*In any other cases, where FR is incorrectly positioned or oriented, use {{Alg|F' D' M D2 M' D' F}}

==Bottom Layer==
*Solve Corners
**Use the algorithms on my [[User:Zombiedude347/2x2x2|2x2x2]] page.
*ELL
**This method is primarily intuitive, done use combinations of these 4 algorithms and rotations of the cube.
{{Alg|M D M' D2 M D M'}}
{{Alg|M D' M' D2 M D' M'}}
{{Alg|M D M' D' M D' M' D' M D2 M'}}
{{Alg|E R F' U R' F E' F' R U' F R'}}

User:Zombiedude347/3x3x3

2015-09-01T17:27:51Z

Zombiedude347: /* Middle Layer */ added missing algs

==Top Layer==
* Solve the cross, done intuitively.
* Place Top Corners
** Find a corner on the D face that belongs on the U face. Rotate the cube so that the correct location of the piece is at the UFR corner. Rotate the D face so that the piece is in the DFR corner.
** If the white sticker is on the D face, use {{Alg|R' D2 R D R' D' R}}
** If the white sticker is on the F face, use {{Alg|F D F'}}
** If the white sticker is on the R face, use {{Alg|R' D' R}}
** If all the top layer corners are on the U face, but 2 or more are incorrect, then rotate the cube so that of these incorrect corners is at the UFR and do move R' D' R to move it to the D face.

==Middle Layer==
*Find a middle layer edge on the bottom layer.
*Rotate the cube so that the correct location of the piece is at the FR edge.
*If the bottom sticker of the piece belongs on the F face, place the piece in the DF position and use {{Alg|R D S D2 S' D R'}}
*If the bottom sticker of the piece belongs on the R face, place the piece in the DR position and use {{Alg|F' D' M D2 M' D' F}}
*If the edge in the FL slot belongs in the FR slot, and could be oriented correctly using the move D2, use {{Alg|M F M' F2 M F M'}}
*If the edge in the FR slot belongs in the FL slot, and could be oriented correctly using the move D2, use {{Alg|M F' M' F2 M F' M'}}
*In any other cases, where FR is incorrectly positioned or oriented, use {{Alg|F' D' M D2 M' D' F}}

==Bottom Layer==
*Solve Corners
**Use the algorithms on my [[User:Zombiedude347/2x2x2|2x2x2]] page.
*ELL
**This method is primarily intuitive, done use combinations of these 4 algorithms
{{Alg|M D M' D2 M D M'}}
{{Alg|M D' M' D2 M D' M'}}
{{Alg|M D M' D' M D' M' D' M D2 M'}}
{{Alg|E R F' U R' F E' F' R U' F R'}}

User:Zombiedude347/3x3x3

2015-09-01T17:10:21Z

Zombiedude347: /* Top Layer */

User:Zombiedude347/3x3x3

2015-09-01T17:07:28Z

Zombiedude347:

User:Zombiedude347/3x3x3

2015-09-01T17:05:56Z

Zombiedude347: added ELL algorithms

User:Zombiedude347/3x3x3

2015-08-25T17:36:12Z

Zombiedude347: Created page with "==Top Layer== * Solve the cross, done intuitively. * Place Top Corners ** Find a corner on the D face that belongs on the U face. Rotate the cube so that the correct location..."

User:Zombiedude347/2x2x2

2015-08-25T16:57:31Z

Zombiedude347: /* OLLs */

Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || (y2) L D L' D L D2 L'
|-
| [[File:2x2AS.gif]] || (y) R' D' R D' R' D2 R
|-
| [[File:2x2Bo.gif]] || (y) R' D' R D' R' D2 R y' L D L' D L D2 L'
|-
| [[File:2x2He.gif]] || (y) R' D' R D' R' D2 R y2 L D L' D L D2 L'
|-
| [[File:2x2H.gif]] || (y) R' D' R D' R' D R D' R' D2 R
|-
| [[File:2x2T.gif]] || R' D' R D' R' D2 R L D L' D L D2 L' or (y')R' D' R D' R' D2 R(y)R' D' R D' R' D2 R
|-
| [[File:2x2Pi.gif]] || (y') R' D' R D' R' D2 R (y') R' D' R D' R' D2 R
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/2x2x2

2015-08-23T19:29:08Z

Zombiedude347: /* OLLs */ fixed slight error in an algorithm

Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || (y2) L D L' D L D2 L' (d2)
|-
| [[File:2x2AS.gif]] || (y) R' D' R D' R' D2 R (d2)
|-
| [[File:2x2Bo.gif]] || (y) R' D' R D' R' D2 R y' L D L' D L D2 L'
|-
| [[File:2x2He.gif]] || (y) R' D' R D' R' D2 R y2 L D L' D L D2 L'
|-
| [[File:2x2H.gif]] || (y) R' D' R D' R' D R D' R' D2 R
|-
| [[File:2x2T.gif]] || R' D' R D' R' D2 R L D L' D L D2 L' or (y')R' D' R D' R' D2 R(y)R' D' R D' R' D2 R
|-
| [[File:2x2Pi.gif]] || (y') R' D' R D' R' D2 R (y') R' D' R D' R' D2 R
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/2x2x2

2015-08-23T19:24:26Z

Zombiedude347:

Here's my 2x2x2 method. All of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || (y2) L D L' D L D2 L' (d2)
|-
| [[File:2x2AS.gif]] || (y) R' D' R D' R' D2 R (d2)
|-
| [[File:2x2Bo.gif]] || (y) R' D' R D' R' D2 R y' L D L' D L D2 L'
|-
| [[File:2x2He.gif]] || (y) R' D' R D' R' D2 R y2 L D L' D L D2 L'
|-
| [[File:2x2H.gif]] || (y) R' D' R D' R' D R D' R' D2 R
|-
| [[File:2x2T.gif]] || R' D' R D' R' D2 R L D L' D L D2 L' or (y')R' D' R D' R' D2 R(y)R' D' R D' R' D2
|-
| [[File:2x2Pi.gif]] || (y') R' D' R D' R' D2 R (y') R' D' R D' R' D2 R
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/2x2x2

2015-08-23T16:40:38Z

Zombiedude347:

Here's my 2x2x2 method. Some of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

Create a matching 1x1x2 then combine it with the other 1x1x2 block to create a 1x2x2 block.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
{| border=1
|-
| [[File:2x2Su.gif]] || (y2) L D L' D L D2 L' (d2)
|-
| [[File:2x2AS.gif]] || (y) R' D' R D' R' D2 R (d2)
|-
| [[File:2x2Bo.gif]] || (y) R' D' R D' R' D2 R y' L D L' D L D2 L'
|-
| [[File:2x2He.gif]] || (y) R' D' R D' R' D2 R y2 L D L' D L D2 L'
|-
| [[File:2x2H.gif]] || (y) R' D' R D' R' D R D' R' D2 R
|-
| [[File:2x2T.gif]] || R' D' R D' R' D2 R L D L' D L D2 L' or (y')R' D' R D' R' D2 R(y)R' D' R D' R' D2
|-
| [[File:2x2Pi.gif]] || (y') R' D' R D' R' D2 R (y') R' D' R D' R' D2 R
|-
| <colspan="2"> | Note That all algorithms are with the Down face as the Last Layer
|}

User:Zombiedude347/2x2x2

2015-08-23T15:06:36Z

Zombiedude347:

Here's my 2x2x2 method. Some of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==First Layer==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

The second step is to expand 2 corners into a 1x2x2 block. This is done by intuition.

==Last Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
{| border=1
|-
! R' D' R D' R' D2 R !! L D L' D L D2 L'
|-
| images to be added || images to be added
|-
| colspan="2" | note D can be changed to F, U, or B, whichever is being used as the last layer.
|}

User:Zombiedude347/2x2x2

2015-08-23T06:04:59Z

Zombiedude347:

User:Zombiedude347

2015-08-23T04:13:13Z

Zombiedude347: fixed broken link

User:Zombiedude347

2015-08-23T04:12:20Z

Zombiedude347:

User:Zombiedude347/2x2x2

2015-08-23T04:09:51Z

Zombiedude347: Created page with "Here's my 2x2x2 method. Some of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method. ==Top== The first step is to put any 2 co..."

Here's my 2x2x2 method. Some of these algorithms are applicable to the 3x3x3 as well, as I adapted this method from my 3x3x3 method.

==Top==
The first step is to put any 2 corners in a 1x1x2 block. ~48% of the time, this is already done on a scrambled cube.(146/306 from my tests using a random scramble generator).

The second step is to expand 2 corners into a 1x2x2 block. This is done by intuition.

==Bottom Layer==
====PLLs====
Look at all the unsolved corners, look if 2 corners need to be switched.
*If the two that need switched are adjacent. Position the cube so that the two faces needing switched are on the front face then use the algorithm (R' D' R)(F D F')(R' D R).
*If the two corners that need switched are diagonal from each other, then do the move (R' D' R)(F D2 F')(R' D R).

====OLLs====
to be done.

User:Zombiedude347

2015-08-23T03:00:44Z

Zombiedude347: Created page with "Hi, I am Zombiedude347, I am a cubing enthusiast (as is obvious by me having an account on this wiki). I personally have owned several 3x3x3s, a 4x4x4 (which sadly fell out of..."

4LLL

2015-08-17T04:27:34Z

Zombiedude347:

The '''4-Look Last Layer''' involves completing the last layer in four steps or ''looks''. It is an intermediate step between the [[beginner LBL]] method and learning [[Fridrich|full Fridrich]]. It is generally broken down into [[2-look OLL]] (orientation of edges, followed by orientation of corners) and [[2-look PLL]] (permutation of corners, followed by permutation of edges). Achieving 4LLL requires knowledge of 16 algorithms or 14 excluding mirrors. While progressing from '''4LLL''' to [[2LLL]] a speedcuber will typically learn all 21 [[PLL]]s first, to achieve a [[3-look last layer]]. Eventually, learning the final 57 [[OLL]] cases will achieve the 2-look last layer used in full [[Fridrich]].

Another possible breakdown is to use 2-look [[CLL]] ([[CO]]-[[CP]]) and 2-look [[ELL]] ([[EO]]-[[EP]]). This can later become three different 3-looks, full CLL and 2-look ELL, 2-look CLL and full ELL but also CO, [[CPEOLL]] and [[EPLL]]. This suggestion only uses 26 algorithms in total, the drawback is that the mid step is not of much use when expanding to 2-look.

Both the 2-Look CLL and ELLs can also be done with permutations before orientations. This takes learning 14 algorithms (or 16 if including mirrored algorithms). Splitting CLL into 4-look reduces the algorithms needed for permutation from 2 to 1, and the number needed for corner orientation to 1 (or 2 including its mirror). Splitting ELL into 4-look reduces the number of required algorithms for permutation from 4 to 1 (or 2 including its mirror) and reduces the permutation to 1 algorithm.

Another breakdown is [[BLL]], which uses a 2-Look [[LLEF]] and 2-Look [[CLL]] ([[Corner_Orientation#OCLL-EPP|OCLL-EPP]] - [[CPLL]]) that respects the edges. This can develop into a [[3LLL]] by perform the [[LLEF]] in one step. This 3LLL method uses only 24 algorithms (26 including reuses), and can be later expanded to a [[2LLL]] that uses 98 algorithms (exactly 100 including reuses).

== See also ==
* [[2-Look OLL]]
* [[2-Look PLL]]
* [[BLL]]
* [[Last Layer]]
* [[Layer By Layer]]
* [[Fridrich Method]]
* [[1LLL]]
* [[2LLL]]
* [[3LLL]]

== External links ==
* [http://cubefreak.net/speed/fourlook.html cubefreak.net 4 Look Last Layer]
* YouTube: [http://www.youtube.com/watch?v=DTYvklyOpVM Badmephisto's 2-Look OLL Guide]
* [http://www.freewebs.com/kaixax555/4lll.htm Kaixax555's 4LLL Guide]
* [http://thomasje.webs.com/4lll-tutorial-2 ThomasJE's 4LLL Guide]

[[Category:3x3x3 methods]]
[[Category:3x3x3 beginner methods]]

Talk:4LLL

2015-08-15T19:17:58Z

Zombiedude347: Created page with "The method I originally learned to solve the rubik's cube uses a 4LLL method using Corner Permutation->Corner Orientation->Edge Permutation->Edge Orientation. Is this a common..."

The method I originally learned to solve the rubik's cube uses a 4LLL method using Corner Permutation->Corner Orientation->Edge Permutation->Edge Orientation. Is this a common enough (beginners) LL method that it would deserve mention on this page? [[User:Zombiedude347|Zombiedude347]] ([[User talk:Zombiedude347|talk]]) 19:17, 15 August 2015 (UTC)