3-cycle Freestyle Commutators and Algorithms for BLD Edges

weekend

三循环法盲拧换棱公式

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.


Notes:

• 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' M(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) ...	MU-version.
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.

来源：http://cube.garron.us/BLD/freestyle/index.htm
不过国内不能直接访问这个网页。

[ 本帖最后由 weekend 于 2009-6-6 08:42 编辑 ]

weekend

CO	Straight Execution
[1 4 3] Allan (Three-Cycle) PLL	L2 U' L' U' L U L U L U' L
[1 3 4] Allan (Three-Cycle) PLL	R2' U R U R' U' R' U' R' U R'
[1 3][2 4] Arne Parity	M2' U' M2' U2' M2' U' M2'
[1 4][2 3] Bert Other parity; note the direction of the last "U" (found this one in chemistry class during Study Session)	M2' U' M' U2' M2' U2' M' U M2'
[1 2 5] Allan variant Has a nice rhythm to it; also found this one myself. Make sure to perform it on two unrestricted faces (like U and F)	(R2 U R U R) U' (R' U' R' U' R') Here, with the F face being used as R.
[2 3 4] Allan Yet another variant	R2 U R U R2' U' R' U' R' U2 R'

[ 本帖最后由 weekend 于 2009-6-2 20:29 编辑 ]

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R U2' M' U2 R'应该为R U2' M' U2 R' M