# List of Rubik's Cube Commutators



## dChan (Jun 8, 2007)

Just thought it would be nice to have a list of commutators for reference. I am very interested in solving the cube using purely commutators(e.g. Heise method) and intuition. So it would be col if you guyscould post up the commutators you know and their effects. You can even give some for big cubes if you like.

Please write them down like such:
Commutator Sequence (commutator effect)

3x3x3 Commutators
[(R' F R F')x3 U2] x2 (cycles 3 corners 'diagonally') 

4x4x4 Commutators

5x5x5 Commutators


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## joey (Jun 9, 2007)

[R L F B U D] x2 Isn't a commutator. It isn't X Y X' Y'.


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## dChan (Jun 9, 2007)

Fixed.


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## pjk (Jun 9, 2007)

There is basically an infinite amount of commutators. I'd recommend reading up on Joels guide at solvethecube.co.uk . He talks about them a lot in his tutorial.


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## dChan (Jun 9, 2007)

lol. Again with the printale problem!


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## dbeyer (Jun 9, 2007)

Dude ... check on Chris' guide. He covers a lot of them and explains them very well!

Seriously!
Consider different wings on the 4x4 being like the different stickers on the 3x3.

You can take what you've learned from one piece-type and pretty fluently transpose it to the others!

Centers are indiviual pieces
Centrals (3x3 edges) are a double-faceted and some tricks that would work on the centrals wouldn't work on centers (Direct insertions come to mind)
Wings (the 4x4 edges) again certain things that work on wings have a different effect on centrals.

Such as a drop and slide.

M'D2M U' M'D2M U
compared to wings
l'D2l U' l'D2l U
it's just a slightly different effect because of the pieces being multi faceted.

Wings have two stickers, but each wing is distinct. 
there is an FR wing ... and an RF wing just like you can see the FR edge and the RF edge. With an understanding of the cube you can discern which is which 

Corners are very interesting there are so many angles for corners!
A conjugation of a commutator is used for the A-perm (corner cycle for PLL)

A: R'B'R
B: F2
S: R2 

SABA'B'S' == [R2 + R'] ->>R B'RF2R'BRF2 R2
and of course it's inverse
SABA'B'S']' == SBAB'A'S'
R2F2R'B'RF2R'BR'
Let A be the action, B be the interchanging, S the setup.

Good stuff


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## pjk (Jun 9, 2007)

If you can't print, write down ideas, or just read it off the computer.


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## AvGalen (Jun 9, 2007)

Very old method. Technically not fully commutator based, but they are what I call "pretty algs":

Middle layer:
Up-Left to Right-Front: (RU)+- (FU)-+ or (R U R' U') (F' U' F U)
Up-Back to Front-Right: (FU)-+ (RU)+- or (F' U' F U) (R U R' U')

Orient edges:
9-12: F (UR)+- F' or F (U R U' R') F'
9-3: F (RU)+- F' or F (R U R' U') F'

Permutate edges:
12-6-3: ((R2U2)3 (B'UB))+- or (R2 U2 R2 U2 R2 U2) (B' U B) (R2 U2 R2 U2 R2 U2) (B' U' B)
12-6 3-9: ((R2U2)3 U)+- or (R2 U2 R2 U2 R2 U2) U (R2 U2 R2 U2 R2 U2) U'

Permutate corners:
Clockwise: (UR+-)L' (RU+-)L or (U R U' R') L' (R U R' U') L
Counterclockwise: (RU+-)L' (UR+-)L or (R U R' U') L' (U R U' R') L
Swap: F (RU+-)3 F' or F (R U R' U') (R U R' U') (R U R' U') F'

Orient corners:
Clockwise: ((FD)+-)2 or (F D F' D') (F D F' D') 
Counterclockwise: ((DF)+-)2 or (D F D' F') (D F D' F')


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