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Heise method

2019-07-25T14:36:53Z

Wuigukin:

{{Method Infobox
|name=Heise
|image=Heise_method.gif
|proposers=[[Ryan Heise]]
|year=2003
|anames
|variants
|steps=4
|algs=0
|moves=40-
|purpose=<sup></sup>
* [[Fewest Moves]]
* [[Speedsolving]]
}}
The '''Heise method''', invented by [[Ryan Heise]], is an intuitive [[method]] which requires no [[algorithm]]s. It uses extremely few moves, but it may be difficult to get fast times using this method.

==Steps==

# Create four 1x2x2 blocks (also called [[Heise blocks]]), making sure that one color appears on none of the blocks. This color will be the color of the last layer. Note that these blocks do not necessarily have to be paired together when they are built. One of these blocks should be just two centers and an edge.
# Pair up the 1x2x2 blocks, while simultaneously orienting the last-layer edges. Note that you will now have all of F2L minus a corner/edge pair finished.
# Create two corner-edge pairs, and then solve all of the edges and two corners. This is typically a very difficult step for beginners to solve.
# Solve the final three corners with a commutator.

==Pros==
This method is more efficient than any of the main three speedcubing methods, and therefore it's also very good for fewest moves solving. Because there are no algorithms at all, users of this method generally become very good at intuitive blockbuilding and develop a high-level understanding of the cube.

==Cons==
Every turn has to be planned out because there are no algorithms, so fast turners will be disappointed. Some of the steps, especially the third step, can be very difficult to get used to, and beginning cubers might not understand enough cube theory to be able to use this method at all.

==Strategies==
===Step 1===
The first step is [[blockbuilding]]. Knowledge of [[F2L]] can help here, but it is important not to treat the step as just F2L minus a pair. If possible, you should try to plan the first two blocks during inspection. The second block will normally be the inner square, and it can help if the colours match the first block which will give a maximum range of possibilities for the third block. However, you should always be prepared to do things differently.

===Step 2===
Step 2 seeks to orient edge the upper edges while rotating the blocks into an F2L-1 state. Although not compulsory, orienting the edges now makes step 3 easier.

===Step 3===
The third step is the hardest stage to master, particularly the "two pairs" approach which seeks to simultaneously solve the last 5 edges and 2 corners. Ryan Heise's advice is:
<blockquote>First, master solving the 5 edges on their own (ignoring the corners), which you can do using only R-U moves (assuming the edges are already oriented). The last three moves will always be R-U*-R' with U* being one of U, U2 or U'. ... Then, you can try the same with two corners attached to two of the edges. You just try the same strategy as above, treating the corner/edge pairs as just elongated pieces that need to be kept intact. It is rarely possible to do this just using R-U moves.[http://twistypuzzles.com/~sandy/forum/viewtopic.php?f=1&t=6012]</blockquote>

===Step 4===
Step 4 is the 3-corner solve. Ryan Heise explains the 'intuitive' approach using [[commutators]].[http://www.ryanheise.com/cube/corner_3_cycles.html] Alternatively, there are [[Last Three Corners]] algorithm sets available.

==Variants==
===Old Heise===
[[Ryan Heise]] published an earlier version of his method in 2003/4. This early method used a different sequence of steps and made use of algorithms. The method averaged under 45 moves and was also a viable speedcubing method. The steps were:

# Create the four [[Heise blocks]] and join the blocks together (intuitive).
# Insert the remaining middle edge and simultaneously orient the top edges (Mostly intuitive).
# Insert the last corner on the bottom and simultaneously permute the top edges. 17 cases (or 28? including mirrors).
# Solve the [[Last Four Corners]]. 42 cases (or 84 including mirrors).

A notable proponent of this method was [[Andy Camann]] who adopted this method in 2004. He was able to achieve sub-17-second averages, which was close to his [[CFOP]] average.

Internet Archive links:
*[https://web.archive.org/web/20040803122903/http://www.progsoc.uts.edu.au:80/~rheise/cube/ Ryan Heise's 2004 page] (broken applets)
*[https://web.archive.org/web/20100326084444/http://s92824201.onlinehome.us/RyanMethod.htm Andy Camann's Heise pages] (broken images, but there are algorithms for step 3)

===Speed-Heise===
[[Speed-Heise]] is an algorithm set developed by Matt DiPalma. It seeks to systemize step 3 of the Heise method similar to [[ZZ]]. After step 2 the final F2L pair is created in the upper layer and fed to the Front-Right as in the [[Winter Variation]]. An algorithm from a 72-algorithm set (or a 24-algorithm simplified set) is then selected to solve all 4 LL-edges and 1 LL-corner, leaving just the last three corners unsolved.

===FLFL ===
The [[FLFL Method]] simplifies step 3 of Heise. It provides a few algorithms to separately solve the final bottom corner, leaving the [[Last Four Corners]] to solve.

===Heise as a beginner's method===
Since basically all 4 steps of a standard Heise method might be extremely hard for beginners, they could proceed as follows:

# Solve a layer without a corner.
# Solve two layers without an edge-corner pair by means of the working corner.
# Solve remaining edges by means of the working edge.
# Solve remaining corners.

If needed, see "External links" section bellow for details.

== See also ==
* [[Commutators]]
* [[L3C]]
* [[Snyder Method]]

==External links==

* [http://www.ryanheise.com/cube/heise_method.html Ryan Heise's tutorial]
* [http://hlavolam.maweb.eu/rubiks-cube-3x3x3#intuitive-puzzle-solving-method Simplified Heise-like solving approach] especially suitable for beginners

[[Category:3x3x3 methods]]
[[Category:Fewest Moves Methods]]
[[Category:3x3x3 speedsolving methods]]

PLL

2019-07-23T14:38:55Z

Wuigukin: /* V Permutation */

<seo title="PLL Algorithms - CFOP Speedcubing Cases" metak="pll algs, pll, pll algorithms, speedcubing" metad="Permutation of the last layer algorithms for the CFOP speedsolving method." />
{{Substep Infobox
|name=PLL
|image=PLLinfo.jpg
|proposers=[[Hans Dockhorn]], [[Anneke Treep]], [[Jessica Fridrich]]
|year=
|anames=
|variants=
|subgroup=<nowiki></nowiki>
|algs=21
|moves=11.8 [[HTM]]
|purpose=<sup></sup>
* [[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 ==

* [http://algdb.net/puzzle/333/pll AlgDB PLL Page]
* [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 recognizing 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]
*[https://www.speedcubingtips.eu/pll/ speedcubingtips.eu PLL algs]

=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|y L R2 U R U R2 U' R' U' R2 U' R U2 L' U R'|cube=3x3x3&stage=PLL}}
{{Alg|(y) R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R|PLL|cube=3x3x3&stage=PLL|}}
{{Alg|y2 R' U2 R' d' R' F' R2 U' R' U R' F R U' F |PLL|cube=3x3x3&stage=PLL|}}
{{Alg|R' U R U' R2 F' U' F U R F R' F' R2|PLL|cube=3x3x3&stage=PLL|}}
{{Alg|M' U2 L F' R U2 r' U r' R2 U2 R2|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|(R' U R U') R2 (F' U' F U) (R F R' F') R2 U'|Alg.1|cube=3x3x3&stage=PLL|}}
{{Alg|y2 R U' R' U R U F R U R' U' x' D' R2 D R D' |Alg.1(svn)|cube=3x3x3&stage=PLL|}}
{{Alg|y2 R U' R' U R U F R U R' U' x U' R2 U R U' |Alg.1(svn1)|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|(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}}
{{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|}}
{{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}}
{{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}}
{{Alg|L F R' F' L' F' D2 B' L' B D2 F' R F2|Alg.9|cube=3x3x3&stage=PLL}}

===G Permutation : a===
{{case
|image=g3.gif
|name=G-PLL a
|methods=PLL, [[ZBLL]]
|optimal=12 [[HTM]]
|text=
}}
{{Alg|(y) 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 U D' R2 U R' U R U' R U' R2 D|PLL|vidurl=http://www.youtube.com/watch?v=M6RDFenst9g}}
{{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 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 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|B2 L2 U' B2 D B2 D' R2 U M2 F2 (x2)|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' U' D R2 U' R U' R' U R' U R2 D'|PLL}}
{{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|(y2) L U' R' U L' U2 R U' R' U2 R|Alg.7|cube=3x3x3&stage=PLL|vidurl=http://www.youtube.com/watch?v=0Q0aiSuVxe8}}
{{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|L' U R' U2 L U' R U L' U R' U2 L U' R|Alg.3|cube=3x3x3&stage=PLL}}
{{Alg|y2 R' U2 R U R' U2 L U' R U L'|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{Alg|y2 x R2 F R F' R U2 r' U r U2 x'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R' U L') U2 (R U' R') U2 R L|Alg.1(v2)|cube=3x3x3&stage=PLL}}
{{Alg|(y2) F U' R U' R' U' R U R' F' R U R' U' R' F R U F'|Alg.2|cube=3x3x3&stage=PLL|}}
{{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|(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|R' L' U2 L U L' U2 R U' L U|Alg.8|cube=3x3x3&stage=PLL}}

===J Permutation : b===
{{case
|image=j.gif
|name=J-PLL b
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|(y2) R' U L U' R U2' L' U L U2 L'||cube=3x3x3&stage=PLL}}
{{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}}
{{Alg|R U2 R' U' R U2 L' U R' U' r x|Alg.1|cube=3x3x3&stage=PLL}}
{{Alg|R U2 (R' U' R) U2 L' (U R' U') L|Alg.2|cube=3x3x3&stage=PLL}}
{{Alg|(y) (R U' L) U2 (R' U R) U2 L' R'|Alg.1(v3)|cube=3x3x3&stage=PLL}}
{{Alg|L' U R U' L U2 R' U R U2 R'|Alg.1(v4)|cube=3x3x3&stage=PLL}}
{{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|R U' L U2 R' U L' U' R U' L U2 R' U L'|Alg.3|cube=3x3x3&stage=PLL}}
{{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|R2 U F U F' R2 F U' F' R2 U' R2 U'|Alg.13|cube=3x3x3&stage=PLL}}

===N Permutation : a===
{{case
|image=n1.gif
|name=N-PLL a
|methods=PLL, [[ZBLL]], [[ZZLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|r' D r U2 r' D r U2 r' D r U2 r' D r U2 r' D r |PLL|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(L U' R U2 L' U R')2 U|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U R' D R2 U' R D')2 (z')|PLL|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}}

===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|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(z) (D' R U' R2' D R' U)2 (z')|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U R U' R' F' U' F R U R' F R' F' R U' R |PLL|cube=3x3x3&stage=PLL}}
{{Alg|z D' R U' R2 D R' U D' R U' R2 D R' U z'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(z) (U' R D' R2' U R' D)2 (z')|PLL|cube=3x3x3&stage=PLL}}
{{Alg|z U' R D' R2 U R' D U' R D' R2 U R' D z'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|L' U R' d2 R U' L R' U L' U2 l F' r|PLL|cube=3x3x3&stage=PLL}}

===R Permutation : a===
{{case
|image=r1.gif
|name=R-PLL a
|methods=PLL, [[ZBLL]]
|optimal=14 [[HTM]]
|text=
}}
{{Alg|(y') R U' R' U' R U R D R' U' R D' R' U2 R'|PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U R B R2 U|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' U2 R B' R' U' R U l U R2 (x)|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y2 z) U R2 U' R2 U F' U' R' U R U F U2 (z')|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L U2 L' U2 L F' L' U' L U L F L2|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 B' R' U' R' U R B R' U2 R U2 R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y) L2 F' L' U' L' U L F L' U2 L U2 L'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|F2 R' F' U' F' U F R F' U2 F U2 F'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y' x') R2 U' l' U' R' U l U l' U2 R U2 R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y') R l U' l' U' R' U l U l' U2 R U2' R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|F2 L2 U F U F' U' F' U' L2 F' U F' U'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R U' R F2 U R U R U' R' U' F2 R2 U|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 F2 U R U R' U' R' U' F2 R' U R'|PLL|cube=3x3x3&stage=PLL}}

===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'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F (R U R' U') l' U' R2 (x')|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(z') U' L2 U L2 U' F U L U' L' U' F' U2 (z)|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R U2 R' F R U R' U' R' F' R2|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U2 R' D' R U' R' D R U R U' R' U' R|PLL|cube=3x3x3&stage=PLL}}
{{Alg|y' R U2 R' U2 R' F R2 U' R' U' R U R' F' R U R' U R U2 R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|y R2 F R U R U' R' F' R U2 R' U2 R|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y x) R2 U l U R U' l' U' l U2 R' U2 R|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y') r' L' U r U L U' r' U' r U2 L' U2 L|PLL|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'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|F R U' R' U R U R2 F' R U R U' R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R U R' U' R' F R2 U' R' U F' L' U L|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R2 U R2 U' R2 U' D R2 U' R2 U R2 D' |PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y2) L' U' L U L F' L2 U L U L' U' L F|PLL|cube=3x3x3&stage=PLL}}

===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|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' d' R' F' R2 U' R' U R' F R F|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' y R' F' R2 U' R' U R' F R F|PLL|cube=3x3x3&stage=PLL}}
{{Alg|z D' R2 D R2 U R' D' R U' R U R' D R U'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R U2 R' D R U' R U' R U R2 D R' U' R D2|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U R' U' R D' R' D R' U D' R2 U' R2 D R2|PLL|cube=3x3x3&stage=PLL}}

===Y Permutation===
{{case
|image=Y.gif
|name=Y-PLL
|methods=PLL, [[ZBLL]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
{{Alg|R' U' R U' L R U2 R' U' R U2 L' U R2 U R|PLL}}
{{Alg|F R U' R' U' R U R' F' (R U R' U') (R' F R F')|PLL|vidurl=http://www.youtube.com/watch?v=-RKtMhtrd3Y}}
{{Alg|R2 U' R' U R U' x D' R' U R' U' R' D R |PLL|cube=3x3x3&stage=PLL}}
{{Alg|F R' F R2 U' R' U' R U R' F' R U R' U' F'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R' U' R F2 R' U R d R2 U' R2' U' R2|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 U R' F' R U R2 U' R' F R |PLL|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 d R U R' B2 R U' R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|R2 U' R2 U' R2 U y' R U R' B2 R U' R'|PLL|cube=3x3x3&stage=PLL}}
{{Alg|F2 D R2 U R2 D' R' U' R F2 R' U R|PLL|cube=3x3x3&stage=PLL}}
{{Alg|(y') R2 u R2' U R2 D' R' U' R F2' R' U R|PLL|cube=3x3x3&stage=PLL}}

{{PLL}}

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

__NOTOC__