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| {{Alg| r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2 |cube=4x4x4¬ation=WCA}} | | {{Alg| r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2 |cube=4x4x4¬ation=WCA}} |
| {{Alg| z d' m D l' u' 2R' u l u' l'2 b' 2R' b r' R' 2U y' m' u x2 z' // (SiGN) |cube=4x4x4}} | | {{Alg| z d' m D l' u' 2R' u l u' l'2 b' 2R' b r' R' 2U y' m' u x2 z' // (SiGN) |cube=4x4x4}} |
− | ===Impure Edge Flips (For Reduction) (SiGN)=== | + | ===Impure Edge Flips (SiGN notation)=== |
| {{Alg| r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' |cube=4x4x4}} | | {{Alg| r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' |cube=4x4x4}} |
| {{Alg| r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r' |cube=4x4x4}} | | {{Alg| r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r' |cube=4x4x4}} |
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| {{Alg| r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2 |cube=4x4x4}} | | {{Alg| r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2 |cube=4x4x4}} |
| {{Alg| r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r' |cube=4x4x4}} | | {{Alg| r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r' |cube=4x4x4}} |
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| ===Algorithms that solve OLL and PLL parity simultaneously:=== | | ===Algorithms that solve OLL and PLL parity simultaneously:=== |
| {{Alg| Rw2 B2 Rw' U2 Rw' U2 x' U2 Rw' U2 Rw U2 Rw' U2 Rw2 U2 (x) |cube=4x4x4¬ation=WCA}} | | {{Alg| Rw2 B2 Rw' U2 Rw' U2 x' U2 Rw' U2 Rw U2 Rw' U2 Rw2 U2 (x) |cube=4x4x4¬ation=WCA}} |
Revision as of 11:30, 5 June 2012
Parity (also known as Orientation Parity and Permutation Parity) on the 4x4x4 is a common situation (occurring in 3/4 of all solves) where two or four edge pieces need to be cycled. This is considered difficult because in most methods the centers are solved before the edges, and there is no efficient or intuitive way to swap those edges (and no others) without affecting the centers. Because of how common and difficult this case is, many algorithms have been developed. This page attempts to list all efficient algorithms.
NOTE: Alg template (and alg.garron itself) are completely useless for 4x4x4 so I'll just paste algs here.
ALSO: This really needs editing! I just dumped a lot of algorithms here but this could look pretty nice once someone goes over it.
MORE ALSO: Once the lists are made prettier, feel free to give them HTM/BTM counts and names/authors (e.g. lucasparity, cmowlaparity, etc).
A more comprehensive list of ELL algs for the 4x4x4 cube can be found here: Kirjava's K4 ELL page
OLL Parity (WCA notation)
Pure edge flips:
Impure Edge Flips (SiGN notation)
Algorithms that solve OLL and PLL parity simultaneously:
PLL Parity (WCA Notation)
Pure Edge Flips
- F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l'
- r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2
- r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2
- z d' m D l' u' 2R' u l u' l'2 b' 2R' b r' R' 2U y' m' u x2 z' (SiGN)
Other ELL Cases
double parity
- r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l
- r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2
- l2 F2 l' U2 l' U2 F2 l' F2 l F2 l' F2 l2 F2
4-cycles (Checkerboard pattern_
- r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'
- r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r
- l U2 l2 U2 l' U2 l U2 l' U2 l2 U2 l
adjacent 2-swap
- r2 D2 r' D2 l D2 l' D2 B2 l' B2 r'
- l' U2 l' U2 (l' r) U2 l' U2 l U2 r' U2 l2
- r U2 r U2 (r l') U2 r U2 r' U2 l U2 r2
- r U2 r U2 x U2 r U2 l' x' U2 l U2 r2
- l' U2 l' U2 x U2 l' U2 r x' U2 r' U2 l2
opposite/diagonal 2-swap
- l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r
- r S2 U2 r' U2 r U2 l' U2 l F2 r' B2 l'
- l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r
- l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2
- r2 B2 U2 r' U2 r2 B2 r' U2 r2 U2 B2 r' B2
- r U2 r' U2 r' U2 l U2 r' U2 r U2 F2 r2 F2 l'
bowtie (adj. 2-swap + Pll Parity)
- F2 l2 F2 l F2 l' F2 r U2 l U2 r' U2 l U2 l'
- F2 r2 F2 r' F2 r F2 l' U2 r' U2 l U2 r' U2 r
- r U2 l' U2 r U2 r U2 r' U2 r U2 r2 U2 l r' U2 r'
- r U2 r l' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r'
Impure Edge Flips (For Reduction) (SiGN)
algs that don't preserve F2L
- u B' L2 B u B2 u R2 u R F2 R' u
- r2 B2 r' U2 r2 B R' B U' r B2 U2 r
- r B' U2 B r B2 l B2 r B D2 B' r
dump of more parity algs
- long list at http://www.speedsolving.com/forum/showthread.php?26564-4x4x4-edge-parity-is-there-a-shorter-alg-that-doesn-t-preserve-corners&p=531938&viewfull=1#post531938
- Fw (lr') R B R' Uw d (lr') b' (l'r) Uw u (fb') D Lw (x' y') (WCA notation)
- Rw B' u (l'r) l' F' u F r' u2 Rw (f'b) U' Rw (z' y) (WCA notation)
- { Uw, u, d } (lr') R D R' Fw f (ud') l' (u'd) Fw b (u'd) F { Lw, l, r } (WCA notation, choose any one from the brackets)
- { Uw, u, d } R' b (ud') d' L' b L u' b2 Uw (l'r) B' { Uw, u, d } (WCA notation, choose any one from the brackets)
- { Uw, u, d } (fb') L B' R u d f' u d L B' R (fb') { Uw, u, d } (WCA notation, choose any one from the brackets)
- { Uw, u, d } (fb') L' F R' u d f' u d L' F R' (fb') { Uw, u, d } (WCA notation, choose any one from the brackets)
- r B' U2 B r B2 l B2 r B D2 B' r (WCA notation)
- r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r' (WCA notation)
- r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r' (WCA notation)
- u B L2 B' u B2 d B2 u B' R2 B u (WCA notation)
- u B' L2 B u B2 d B2 u B R2 B' u (WCA notation)
- u B L2 B' u B2 u R2 d B R2 B' u (WCA notation)
- u B' L2 B u B2 u R2 d B' R2 B u (WCA notation)
- u F2 L2 d F L' U L' u2 B2 u' B2 u2 (WCA notation)
- u F2 L2 d F' L D' L u2 B2 u' B2 u2 (WCA notation)
- u F2 L2 d F L' (U D') L' u2 B2 u' B2 u2 (WCA notation)
- u F2 L2 d F' L (U D') L u2 B2 u' B2 u2 (WCA notation)
- x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'
- x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'
- x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x
- r U F2 U' l F2 2r U2 r U B2 U' r
- r U' F2 U l F2 2r U2 r U' B2 U r
- l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'
- l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'
- r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'
- r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'
- x' r2 U2 l' U2 r U2 l x U2 x' U r U' F2 U r' U r2 x
- more in this topic? http://www.speedsolving.com/forum/showthread.php?22969-Methods-for-Forming-2-Cycle-Odd-Parity-Algorithms-for-Big-Cubes