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3-cycle Freestyle Commutators and Algorithms for BLD Edges
Lucas Garron; March 2, 2008
Below are all the useful algs I know that can be used for freestyle BLD edges. You cycle stickers by setting up into one of these. I don't want to discourage anyone, but you should only try freestyle if you know what you are doing, in which case you shouldn't need an explanation of how to use these: think of this as a collecetion of algs, and hunt through them to find something you micht not have thought of.

  • I use UF as my buffer, but I've consider UR, UL, and maybe DF (to go with M2), possibly even UB (free buffer on U is also not unlikely).
  • {U} represents either U, U2, or U'. I'm using this notation to represent a class of commutators.
  • A lot of these either work or have variations (try doubling an alg, with cancellations) that work on big cube wings and midges.
  • Although I haven't made it obvious, note that all of these are at worst convoluted conjugates of commutators.

3x3x3 Edges / Big(Odd)-Cube Midges

R2 U R U R' U' R' U' R' U R' (UF UL UR)
L2 U' L' U' L U L U L U' L (UF UR UL)
R U' R U R U R U' R' U' R2 (UF UR UL)
2-gen U-Perm/Allan. I suggest you try to get used to all 8 inverses and mirrors on U.
R2 U R U R2' U' R' U' R' U2 R' (UF UB UR)
L2 U' L' U' L2 U L U L U2' L (UF UB UL)
R2 U' R' U' R2 U R U R U2' R (UF UR UB)
This variant differs in exactly 2 twists. It's also good to know it from different angles. I don't use the inverse (R' U2 R' U' R' U' R2 U R U R2), but you might like it better.
U R U R' U' R' U' R' U R (DR UF UL)
R' U' R U R U R U' R' U'(UL UF DR)
Another variant. Good to know the 8 mirrors/inverses/angles each.
U R U R2' U' R' U' R' U2 R (DR UF UB)
Combination of two variants. Good to know, but less useful.
R2 U R U R U' R' U' R' U' R' (UF FR UR)
R U R U R U R' U' R' U' R2 (UF UR FR)
Yet another way to avoid setups.
U x U' M2' ULU' M2' Ur'U' (UF LU FR)
U r U' M2' U L' U' M2' F x' U' (UF FR LU)
Whenever the previous is inapplicable around a corner.
M' U2 M U2 (DF UF UB)
U2 M' U2 M (UB UF DF)
R U2' M' U2 R' (UB UF DF)
u2 M' u2 M' (UF DF DB)
Whenever the previous is inapplicable around a corner.
F2 U' M' U2 M U' F2 (UF UR UL)
F2 U M' U2 M U F2 (UF UL UR)
Petrus Allan / Conjugate.
M2 U' M U2' M' U' M2' (UF UL UR)
M2 U M U2' M' U M2' (UF UR UL)
M2 U' M' U2' M U' M2' (UB UR UL)
R U R U R U' R' U' R' U' (UF UR BR)
Pure form of the 2-gen Allan. Can be written as [RURUR,y2z].
M U M' U2 M U M' (UL UR FU)
M' U' M U2 M' U' M (UL UR BU)
M U' M' U2 M U' M' (UR UL FU)
M' U M U2 M' U M (UR UL BU)
Deals with non-Allans on U.
[M' U2 M , {D}] (UF DF D_)
[M' D2 M , {D}] (DB UB U_)
[M D2 M' , {D}] (DF UF U_)
I think Hardwick calls this "tossing".
[{M'}, U' {R} U]
[U' {M'} U, {R}]
There are insanely many variations on this, and I'm not even going to try listing them. M and R can be any amount, you can use the L face, too, RU'R'U/etc. work for setups, any inverses & rotations/angles & mirrors of these work... but these all basically involve exchanges on a middle and outer layer.