4x4x4 parity algorithms

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Revision as of 19:32, 21 April 2012 by ThomasJE (talk | contribs) (Added OLL and PLL parity sections at the top, and used the 'Alg' template to link to alg.garron. The other algorithms listed could possibly be sorted into the new sections and methods.)

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).

OLL Parity

Alg Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
Alg Rw U2 Rw U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' Rw' U2 Rw'

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
Alg Lw' U2 Lw U2 Lw' U2 Lw' U2 Rw U2 Lw' U2 Lw U2 x' U2 Lw2


PLL Parity

Alg Uw2 Rw2 U2 r2 U2 Rw2 Uw2
Alg r2 U2 r2 Uw2 r2 Uw2


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

  • 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

  • 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)

Alg r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
  • r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'
  • r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2
  • r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
  • l2 B2 l U2 l U2 x' U2 l U2 l' U2 l U2 l2 U2 x U2
  • r' U2 r U2 r' F2 r2 U2 r U2 r' U2 x U2 r2 U2
  • r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 r2 F2
  • r2 U2 l' U2 r U2 r' U2 r U2 r' x' U2 r' U2 r2 F2 r
  • 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
  • r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r'

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
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