4x4x4 parity algorithms

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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)

Speedsolving Logo tiny.gif Alg Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw' U2 Rw U2 Lw' U2 Rw U2 Rw' U2 x' Rw' U2 Rw'

Pure edge flips:

Speedsolving Logo tiny.gif Alg F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l'
Speedsolving Logo tiny.gif Alg r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2
Speedsolving Logo tiny.gif Alg r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2
Speedsolving Logo tiny.gif 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)

Algorithms that solve OLL and PLL parity simultaneously:

Speedsolving Logo tiny.gif Alg Rw2 B2 Rw' U2 Rw' U2 x' U2 Rw' U2 Rw U2 Rw' U2 Rw2 U2 (x)
Speedsolving Logo tiny.gif Alg Lw' U2 Lw U2 Lw' U2 Lw' U2 Rw U2 Lw' U2 Lw U2 x' U2 Lw2


PLL Parity (WCA Notation)

Speedsolving Logo tiny.gif Alg Uw2 Rw2 U2 (Rw2 R2') U2 Rw2 Uw2
Speedsolving Logo tiny.gif Alg Uw2 Rw2 U2 r2 U2 Rw2 Uw2
Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 u2
Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 Uw2
Speedsolving Logo tiny.gif Alg (Rw2 R2') U2 (Rw2 R2') Uw2 (Rw2 R2') Uw2
Speedsolving Logo tiny.gif Alg Rw2 B2 U2 r2 U2 B2 Rw2


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)

Speedsolving Logo tiny.gif Alg r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
Speedsolving Logo tiny.gif Alg r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'
Speedsolving Logo tiny.gif Alg r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2
Speedsolving Logo tiny.gif Alg r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
Speedsolving Logo tiny.gif Alg l2 B2 l U2 l U2 x' U2 l U2 l' U2 l U2 l2 U2 x U2
Speedsolving Logo tiny.gif Alg r' U2 r U2 r' F2 r2 U2 r U2 r' U2 x U2 r2 U2
Speedsolving Logo tiny.gif Alg r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 r2 F2
Speedsolving Logo tiny.gif Alg r2 U2 l' U2 r U2 r' U2 r U2 r' x' U2 r' U2 r2 F2 r
Speedsolving Logo tiny.gif Alg F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l'
Speedsolving Logo tiny.gif Alg r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2
Speedsolving Logo tiny.gif Alg r' U2 x l U2 l' U2 x' r2 U2 r U2 r' U2 F2 r2 F2
Speedsolving Logo tiny.gif Alg 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