Difference between revisions of "4x4x4 parity algorithms"

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{{Alg|(r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)/(22,13)|cube=4x4x4&notation=WCA}}
 
{{Alg|(r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)/(22,13)|cube=4x4x4&notation=WCA}}
 
{{Alg|R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2/(26,14)|cube=4x4x4&notation=WCA}}
 
{{Alg|R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2/(26,14)|cube=4x4x4&notation=WCA}}
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{{Alg|Uw2 F2 U R2 F2 R2 U R2 F2 Uw2 R2 F2 Uw2 R2/(26,14)|cube=4x4x4&notation=WCA}}
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{{Alg|R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2/(21,16)|cube=4x4x4&notation=WCA}}
  
 
==Two Corner Swaps==
 
==Two Corner Swaps==

Revision as of 17:52, 1 March 2013

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. Solutions listed which are not as efficient as others in their categories are at least relatively efficient for their specific effect on the cube or for the move set they are confined to.

Introduction

  • The shortest odd parity fix (PLL Parity algorithms are even parity fixes for wing edges) algorithm which preserves the colors of the centers is simply:
Speedsolving Logo tiny.gif Alg (r U2)4 r/(13,9)

For those who are familiar with commutators and conjugates, this quick parity fix can be represented as [r: [U2, r] [r2 U2: r] ]. In fact, we can do the same 4-cycle of wing edges with just one conjugate [r2 d' r2 Uw2 S': r'].

The phrase "there is more than one way to solve any given problem" holds true with tackling 4x4x4 parity situations. In fact, there are different categories of parity algorithms, and algorithms can consist of different move patterns (the move set of one algorithm might be entirely different than the algorithm above and/or below it).

This page not only contains commonly practiced speedsolving algorithms, but it also contains algorithms which illustrate the veracity of the 4x4x4 cube parity algorithm domain.


NOTES

  • The algorithms below each case image solve the permutation in the case image.
  • All algorithms can be applied to the 6x6x6 if instead of turning the outer 2 layers, turn the outer 3 layers; instead of turning 1 inner layer slice, turn 2 inner layer slices.
  • All algorithms' lengths are written next to them (slice quarter turn, slice half turn).
Algorithms with fewer slice half turns (STM) are listed first in each category.
Algorithms which have fewer slice quarter turn moves (SQTM) are listed before other algorithms which have the same number of STM as them.
  • Most of these algorithms affect centers on the 4x4x4 supercube: not all algorithms affect the supercube centers in the same manner.

Contents

PLL Parity (WCA Notation)

Dedges

  • Algorithms marked as "Safe" are supercube safe.

Two Dedges (Oriented)

Opposite

Opppllparity.png

Speedsolving Logo tiny.gif Alg_1(v1) r2 U2 r2 Uw2 r2 u2/(12,6)
Speedsolving Logo tiny.gif Alg_1(v2) r2 U2 r2 Uw2 r2 Uw2 U2/(12,6)
Speedsolving Logo tiny.gif Alg_1(v3) (Rw2 R2') U2 (Rw2 R2') Uw2 (Rw2 R2') Uw2 U2/(12,6)
Speedsolving Logo tiny.gif Alg_2(v1) Uw2 Rw2 U2 r2 U2 Rw2 Uw2/(14,7)
Speedsolving Logo tiny.gif Alg_2(v2) Uw2 Rw2 U2 (Rw2 R2') U2 Rw2 Uw2/(14,7)
Speedsolving Logo tiny.gif Alg Rw2 B2 U2 r2 U2 B2 Rw2/(14,7)
Speedsolving Logo tiny.gif Alg r2 U2 B2 l r U2 M' U2 r2 B2 U2/Safe(19,11)
Speedsolving Logo tiny.gif Alg r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2/Safe(22,12)
Speedsolving Logo tiny.gif Alg r' F U' R F' U l r U' F R' U F' l'/Safe(14,14)


Adjacent

Oadjpllparity.png

Speedsolving Logo tiny.gif Alg (R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2)/(18,10)
Speedsolving Logo tiny.gif Alg (R2 D' x) Rw2 F2 U2 r2 U2 F2 Rw2 (x' D R2)/(20,11)
Speedsolving Logo tiny.gif Alg (F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2)/(20,11)
Speedsolving Logo tiny.gif Alg y' R' F l E F2 E' l' r' E F2 E' r F' R y/Safe(16,14)
Speedsolving Logo tiny.gif Alg y' R' F l E' F2 E l' r' E' F2 E r F' R y/Safe(16,14)
Speedsolving Logo tiny.gif Alg (R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R')/(20,14)
Speedsolving Logo tiny.gif Alg (R2 D' x) r2 U2 B2 l r U2 M' U2 r2 B2 U2 (x' D R2)/Safe(24,15)
Speedsolving Logo tiny.gif Alg (Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw)/(22,17)


Two Dedges (Unoriented)

Opposite

Uopppllparity.png

Speedsolving Logo tiny.gif Alg F2 l E F2 E' l' r' E F2 E' r F2/Safe(16,12)
Speedsolving Logo tiny.gif Alg F2 l E' F2 E l' r' E' F2 E r F2/Safe(16,12)
Speedsolving Logo tiny.gif Alg (y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y')/(18,12)
Speedsolving Logo tiny.gif Alg r U2 l D2 l' U2 M U2 r D2 r' U2 l'/Safe(19,13)
Speedsolving Logo tiny.gif Alg (y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y)/(20,13)
Speedsolving Logo tiny.gif Alg (y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y')/(20,13)


Adjacent

Uoadjpllparity.png

Speedsolving Logo tiny.gif Alg (R B) r2 U2 r2 Uw2 r2 u2 (B' R')/(16,10)
Speedsolving Logo tiny.gif Alg (R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R')/(18,11)
Speedsolving Logo tiny.gif Alg ((Lw r') U Rw2 U2 F2) r2 (F2 U2 Rw2 U' (Lw' r))/(18,11)
Speedsolving Logo tiny.gif Alg R B U2 r2 U2 B2 l r U2 M' U2 r2 B R'/Safe(21,14)


Four Dedges (Oriented)

Circular 4-cycle of Dedges

Circ4cy.png

Speedsolving Logo tiny.gif Alg r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2/(20,11)
Speedsolving Logo tiny.gif Alg Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2/(22,13)
Speedsolving Logo tiny.gif Alg M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2/(23,14)
Speedsolving Logo tiny.gif Alg l r (U' y) L R u' L' R' (U y') M2 (U y') L' R' u' L R (U' y) l r/Safe(20,19)
Speedsolving Logo tiny.gif Alg l' r' (U' y) L' R' u L R (U y') M2 (U y') L R u L' R' (U' y) l' r'/Safe(20,19)
Speedsolving Logo tiny.gif Alg l r (U y') L R u L' R' (U' y) M2 (U' y) L' R' u L R (U y') l r/Safe(20,19)
Speedsolving Logo tiny.gif Alg l' r' U y L' R' u' L R (U' y) M2 (U' y) L R u' L' R' U y l' r'/Safe(20,19)


Zigzag 4-cycle of Dedges

Zigzag4cycdedges.png

Speedsolving Logo tiny.gif Alg (r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)/(22,13)
Speedsolving Logo tiny.gif Alg R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2/(26,14)
Speedsolving Logo tiny.gif Alg Uw2 F2 U R2 F2 R2 U R2 F2 Uw2 R2 F2 Uw2 R2/(26,14)
Speedsolving Logo tiny.gif Alg R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2/(21,16)


Two Corner Swaps

Adjacent

Adj2crnrsp.png

Speedsolving Logo tiny.gif Alg R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2/(25,16)
Speedsolving Logo tiny.gif Alg y' B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 y/(25,16)/(25,16)
Speedsolving Logo tiny.gif Alg z r2 U2 R' U2 R' U2 R x U2 Rw2 U2 B2 L U2 L' U2 Rw2 U2 z' y'/(29,17)
Speedsolving Logo tiny.gif Alg z' Rw2 x U2 R' U2 x' U2 R' U2 R U2 L' x U2 Rw2 U2 Rw2 U2 Rw2 x' U2 Rw2 z U/(33,19)
Speedsolving Logo tiny.gif Alg r2 U2 r2 Uw2 r2 u2 y' R U R' U' R' F R2 U' R' U' R U R' F' y/(27,20)
Speedsolving Logo tiny.gif Alg z' x Rw2 R' U2 Rw' U2 Rw2 U2 Rw2 U2 L Rw' U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z/(35,22)
Speedsolving Logo tiny.gif Alg z' x Rw2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z/(35,22)


Opposite/Diagonal

Diag2cornerswap.png

Speedsolving Logo tiny.gif Alg Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U/(27,15)
Speedsolving Logo tiny.gif Alg Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U/(27,16)
Speedsolving Logo tiny.gif reParity y' z (R2' Uw2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' Uw2' R2 (Dw' u) R2) Uw2 U2 x/(29,16)
Speedsolving Logo tiny.gif Alg y' r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 y/(30,17)
Speedsolving Logo tiny.gif Alg y' r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2 y/(31,17)
Speedsolving Logo tiny.gif Alg y' r2 U2 r2 Uw2 r2 Uw2 L' U R' U2 L U' L' R U R' U2 L U' R U y/(29,21)
Speedsolving Logo tiny.gif Alg Rw2 R U2 R U2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' Rw2/(35,22)
Speedsolving Logo tiny.gif Alg l2 U2 F2 l R U2 R' U2 L2 F2 L F2 Lw F2 U2 Lw2 U2 F2 U2 F2 L' U2/(38,22)


Two Corner Swaps (Only 2 X-center Piece Exchange on the Supercube)

Adjacent

Adj2crnrsp.png

Speedsolving Logo tiny.gif Alg U Rw2 Bw2 Rw F Rw' Bw2 Rw F' L2 r U' b2 U L' F' L U' b2 U L' F M x/(29,23)
Speedsolving Logo tiny.gif Alg z' Fw' L2 Uw F' U R U' F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L z/(27,24)
Speedsolving Logo tiny.gif Alg z' Fw' L2 Uw r2 F' U R U' F r2 F' U R' U' F Fw Uw' L Uw Fw' Uw' L Fw L z/(27,24)
Speedsolving Logo tiny.gif Alg y' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' Rw' F Rw2 U' Rw' U' y/(28,26)
Speedsolving Logo tiny.gif Alg y' Rw' U' R U r U' R' U R2 U R' U' r U r' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' y/(28,26)
Speedsolving Logo tiny.gif Alg y' Rw' U' R U r U' R' U R2 U R' U' r U R U' Lw Uw2 Rw' U' Rw Dw2 Rw' U Rw' F' x y'/(29,26)
Speedsolving Logo tiny.gif Alg U Rw2 Bw2 Rw F Rw' Bw2 Rw F' D' f' D F2 D' f D F2 Rw L F' L' f' L F L' f/(31,26)
Speedsolving Logo tiny.gif Alg y' Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' R' F' r' F R F' r2 B' R B r' B' R' B y/(29,27)
Speedsolving Logo tiny.gif Alg y' Rw U R' U' r' U R U' R2 U' R U r' U' R' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U y/(29,28)


Opposite/Diagonal

Diag2cornerswap.png

Speedsolving Logo tiny.gif Alg F r2 F' U R' U' F r2 Fw Uw' L Uw Fw' Uw' L Fw L Fw' L2 Uw F' U R U'/(27,24)
Speedsolving Logo tiny.gif Alg F Rw' F Rw2 U' Rw' U' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' F'/(30,28)


Two X-Center Piece Swap Algorithms

  • These algorithms, and other algorithms like them, are used to make two corner swap algorithms which only swap two X-center pieces on the 4x4x4 supercube.

2xcentpswp.png

Speedsolving Logo tiny.gif Alg y Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U y'/(13,10)
Speedsolving Logo tiny.gif Alg Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U'/(13,12)
Speedsolving Logo tiny.gif Alg Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'/(15,14)
Speedsolving Logo tiny.gif Alg Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U/(15,15)



Pure Flips (WCA Notation)

  • OLL parity algorithms in this section preserve more than any other OLL parity algorithm form, escpecially algorithms marked as "Safe", which are also supercube safe.
  • Algorithms in SiGN Notation are labeled.

One Dedge Flip

One Dedge Flip.png

Speedsolving Logo tiny.gif cmowlaparity x' Rw2 U2 Lw' U2 r U2 Rw U2 x' U r U' F2 U r' U Rw2 x/(23,16)
Speedsolving Logo tiny.gif Alg x' Rw2 U2 Lw' U2 r U2 Rw U2 x' U' r U F2 U' r' U' Rw2 x/(23,16)
Speedsolving Logo tiny.gif Alg y' Rw Uw2 x' U D r y Uw2 Rw2 Uw r Uw' Rw2 Dw r' u D' x Uw2 Rw' y/(22,17)
Speedsolving Logo tiny.gif Alg Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw'/(23,17)
Speedsolving Logo tiny.gif Alg Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw'/(23,17)
Speedsolving Logo tiny.gif lucasparity Rw U2 Rw U2 r' U2 r U2 l' U2 l F2 r' F2 Rw' U2 Rw'/(25,17)
Speedsolving Logo tiny.gif Holy_Grail z Dw' M D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' M' Uw x2 z'/(19,18) Cube Camera Icon.png[1]
Speedsolving Logo tiny.gif Alg Rw' E Uw2 Fw Uw Rw' r' Fw' r Fw Rw Uw' Fw' Uw r Uw E' Rw/(19,18)
Speedsolving Logo tiny.gif Alg Lw' S Bw2 Dw r Dw' Bw Dw r' Dw' r' Bw' r Bw r Bw S' Lw/(19,18)
Speedsolving Logo tiny.gif Alg Lw' F' b' Rw' Bw' Rw u Rw' Bw Rw u2 Bw' u Bw u b F Lw/(19,18)
Speedsolving Logo tiny.gif Alg Rw2 B r' U R' U r U' R U' r B U2 r U2 r' B2 Rw2/(23,18)
Speedsolving Logo tiny.gif Alg z r f2 3u U y' 2R' u2 y' l2 u' 2R' u l2 u' 2R 3u' u' U' x' u2 r' z/(23,18)(SiGN)
Speedsolving Logo tiny.gif Alg Rw2 B2 U' b' U r U2 r' U' b U' Rw' U2 r' U2 Rw B2 Rw2/(25,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U2 x' U r U' F2 U r' U' Lw' U2 r U2 Rw' U2 Rw'/(25,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U2 x' U' r U F2 U' r' U Lw' U2 r U2 Rw' U2 Rw'/(25,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 r' U2 Rw U2 l' U2 r U2 r' U2 (l Rw') Rw' U2 Rw'/(27,18)
Speedsolving Logo tiny.gif Alg r2 U2 r2 U2 r U2 r U2 r' U2 B2 U' r' U B2 U' r U'/(27,18)
Speedsolving Logo tiny.gif Alg r2 U2 r2 U2 r U2 r U2 r' U2 B2 U r' U' B2 U r U/(27,18)
Speedsolving Logo tiny.gif Alg Rw' E Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw E' Rw/(19,19)
Speedsolving Logo tiny.gif Alg Rw' E Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw r Rw Fw' Uw Lw E' Rw/(19,19)
Speedsolving Logo tiny.gif Alg Rw' D' u' Uw' Rw f Rw' Uw Rw f' Rw' f' Uw' f Uw f u D Rw/(19,19)
Speedsolving Logo tiny.gif Alg Rw' E R Uw' Fw' u' Fw Uw2 Bw' Uw Fw' u' Fw U' Bw Uw' R' E' Rw/(20,19)
Speedsolving Logo tiny.gif Alg Dw' F' z Rw2 B2 x' l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l u' U Rw2 D Rw z'/(24,19)
Speedsolving Logo tiny.gif Alg Rw' E r' f' Dw' f' Dw Fw Lw' f Fw Dw' f' Dw Fw' Lw F' r E' Rw/(20,20)
Speedsolving Logo tiny.gif Alg Uw Fw' D r' Dw b Dw b' Dw' r Dw b' Dw' b Dw b Dw2 D' Fw Uw'/(21,20)
Speedsolving Logo tiny.gif Alg Fw' U' l u2 Lw Bw' Lw' u Lw Uw Bw u' Bw' Uw' Bw Lw' u l' U Fw/(21,20)
Speedsolving Logo tiny.gif Alg Rw U L F' U l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l Uw' U' F L' U' Rw'/(23,20)
Speedsolving Logo tiny.gif Alg Bw' R' u Rw' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' Rw u' R Bw/(21,21)
Speedsolving Logo tiny.gif Alg Bw' R' u Rw' l' Dw Bw' Dw' l Dw Lw Bw l' Bw' Lw' Bw Dw' Rw u' R Bw/(21,21)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw' U L u l Uw' r' Uw l' u' L' U' Fw r2 Uw' z/(23,22)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw' f' U L U' f r' f' U L' U' f Fw r2 Uw' z/(23,22)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw' f' L Fw R' F' r' F R Fw' L' f Fw r2 Uw' z/(23,22)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r U2 r U r U r U2 r2 U2 r U2 r U r' U' r2 U2/(31,22)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r U2 r U' r U' r U2 r2 U2 r U2 r U' r' U r2 U2/(31,22)
Speedsolving Logo tiny.gif Alg r2 U r' U' r U2 r U2 r2 U2 r U' r U' r U2 r U2 r' U2 r U2/(31,22)
Speedsolving Logo tiny.gif Alg r2 U' r' U r U2 r U2 r2 U2 r U r U r U2 r U2 r' U2 r U2/(31,22)
Speedsolving Logo tiny.gif Alg r' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U r/Safe(27,23)
Speedsolving Logo tiny.gif Alg Rw2 U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw2 x'/Safe(33,23)
Speedsolving Logo tiny.gif Alg z' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' U L U' r' U L' U' Fw Rw Uw' r2 z/(25,24)
Speedsolving Logo tiny.gif Alg y' Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U' Rw U Rw' U' Rw U2 Rw' U2 y/(34,26)
Speedsolving Logo tiny.gif Alg y' Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U Rw U Rw' U' Rw U2 Rw' U2 y/(34,26)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U Rw U2 Rw U2 Rw' U2 Rw' U r' U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw' U2 Rw'/(37,27)


One Dedge Flip + PLL Parity (Double Parity)

DblParity.png

Speedsolving Logo tiny.gif Alg x r F2 Lw' F' r' F U2 F' r F U2 Lw x' E2 l' U2 l y2/(21,16)
Speedsolving Logo tiny.gif Alg x r F2 Lw' F r' F' U2 F r F' U2 Lw x' E2 l' U2 l y2/(21,16)
Speedsolving Logo tiny.gif Alg Rw2 B2 l F2 r' F2 U2 r' U2 r U2 M' r U2 B2 Rw2/(26,16)
Speedsolving Logo tiny.gif Alg r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 U2 r' U2 r/(26,17)
Speedsolving Logo tiny.gif Alg r2 U2 M U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r/(26,17)
Speedsolving Logo tiny.gif Alg_1(v1) Rw2 U B2 U' r' U B2 U' Rw r U B2 U r' U' B2 U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg_1(v2) r2 3d L2 3d' 2R' 3d L2 3d' r 2R 3d L2 3d 2L' 3d' L2 3d' r/(23,18)(SiGN)
Speedsolving Logo tiny.gif Alg_2(v1) r2 U' B2 U r' U' B2 U r2 U' B2 U' r' U B2 U r/(23,18)
Speedsolving Logo tiny.gif Alg_2(v2) 2R2 3d' R2 3d 2R' 3d' R2 3d 2R2 3d' R2 3d' 2L' 3d R2 3d 2R/(23,18)(SiGN)
Speedsolving Logo tiny.gif Alg (F d' S r F Rw2 f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 Rw2 F' r' S' d F')/(31,23)
Speedsolving Logo tiny.gif Alg (B Lw2 U' L' U r u2 b' r2 Bw2 E) r' (E' Bw2 r2 b u2 r' U' L U Lw2 B')/(31,23)
Speedsolving Logo tiny.gif Alg r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2/(29,24)


One Dedge Flip + Adjacent PLL Parity (Adjacent Double Parity)

Adj.dblparity.png

Speedsolving Logo tiny.gif Alg (y' r2 F Rw' F') r2 U2 r' U2 r' U2 r' U2 (F Rw F' r2 y)/(23,16)
Speedsolving Logo tiny.gif Alg (y Rw' z' L' U r F) r2 U2 r' U2 r' U2 r' U2 (F' r' U' L z Rw y') /(23,18)
Speedsolving Logo tiny.gif Alg (x' r2 U' Rw U) M' U2 r' U2 r' U2 r' U2 l r (U' Rw' U r2 x)/(24,18)
Speedsolving Logo tiny.gif Alg R B y2 r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l B' R'/(25,18)
Speedsolving Logo tiny.gif Alg (R B' r2 B2) r B2 r' B2 r B2 U2 r U2 r (B2 r2 B' R')/(27,18)
Speedsolving Logo tiny.gif Alg Rw U2 x U' Rw R U r2 U2 r' U2 r' U2 r' U Rw' R' U x' U2 Rw'/(25,19)
Speedsolving Logo tiny.gif Alg y Rw2 U x' l U' L' U' l' U L U F2 l' F2 r U2 r' U2 x U' Rw2 y'/(25,19)
Speedsolving Logo tiny.gif Alg r2 F' Rw' F' U2 F r F l D2 r' D2 F2 l' U2 F R F r2/(26,19)
Speedsolving Logo tiny.gif Alg r' B L' B l' B' L B' l U l B2 l' F2 l' F2 l B2 U' M'/(24,20)
Speedsolving Logo tiny.gif Alg (y Rw2 U x') l U' L' U' l' U L U M' U2 l' U2 l U2 r' U2 (x U' Rw2 y')/(26,20)
Speedsolving Logo tiny.gif Alg (y Rw2 F L) F U2 l F2 D2 r D2 l' F r' F U2 F' r (L' F' Rw2 y')/(27,20)
Speedsolving Logo tiny.gif Alg (z' Rw' U' Rw' l' U L') U' r2 U2 r' U2 r' U2 r' U' (L U' l Rw U Rw z)/(25,21)
Speedsolving Logo tiny.gif Alg (Lw2 B' R B l b2 u' l2 Uw2 S) l' (S' Uw2 l2 u b2 l' B' R' B Lw2)/(29,21)
Speedsolving Logo tiny.gif Alg (y x' Lw2 F' L2 F r f2 u' r2 Uw2 S') r' (S Uw2 r2 u f2 r' F' L2 F Lw2 x y')/(31,21)
Speedsolving Logo tiny.gif Alg x Uw F U r S' L2 S r S' L2 S r U R' U r U' R U' r U' F' Uw' x'/(25,23)
Speedsolving Logo tiny.gif Alg x2 r U2 l U2 r' F R F' U l' F2 l U B2 l B2 l' U' F2 U' F R' F' x2/(29,23)
Speedsolving Logo tiny.gif Alg (y Bw' R U b' R' Bw' Uw2 Rw' u2 l2 S') u (S l2 u2 Rw Uw2 Bw R b U' R' Bw y')/(29,23)
Speedsolving Logo tiny.gif Alg (r2 z B' Uw R Uw M' Uw2 l' u2 Rw2 S) u (S' Rw2 u2 l Uw2 M Uw' R' Uw' B z' r2)/(31,23)
Speedsolving Logo tiny.gif Alg (Lw U Rw2 F Rw U' Rw U' F2 U Rw2 U' R' U') r (U R U Rw2 U' F2 U Rw' U Rw' F' Rw2 U' Lw')/(35,29)
Speedsolving Logo tiny.gif Alg Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' B' L B U' L U l U' L' U B' L' B L Uw R Uw2 l2 Bw/(33,30)
Speedsolving Logo tiny.gif Alg Uw Bw' l Bw Uw' Bw' l Uw2 R' Uw' L' U' B' L B L U l U' L' B' L' B U L Uw R Uw2 l2 Bw/(33,30)
Speedsolving Logo tiny.gif Alg (Lw' Uw2 U Lw' U2 Rw U Lw' U' L U B' U' R' B U') l (U B' R U B U' L' U Lw U' Rw' U2 Lw U' Uw2 Lw)/(37,33)
Speedsolving Logo tiny.gif Alg (Rw Uw2 Lw Rw Uw2 Rw2 U2 Rw U' Lw U2 F L2 U F' U') l' (U F U' L2 F' U2 Lw' U Rw' U2 Rw2 Uw2 Lw' Rw' Uw2 Rw')/(45,33)


Three Flips

OLL Parity (Only)

Ollpo3flip.png

Speedsolving Logo tiny.gif Alg y M U l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2 U' M' y'/(29,19)
Speedsolving Logo tiny.gif Alg Rw U Rw U2 Rw U2 Rw U Rw' U2 r' U2 Rw' U Rw U2 Rw U2 Rw U Rw/(27,21)
Speedsolving Logo tiny.gif Alg Uw2 F2 Lw' U' L U Lw U2 Lw' U' L' U' l' U2 Lw' F2 l F2 Lw' U2 Lw' l' F2 Uw2/(33,24)
Speedsolving Logo tiny.gif Alg Uw2 B2 Lw U L' U' Lw' U2 Lw U L U l U2 Lw B2 l' B2 Lw U2 Lw l B2 Uw2/(33,24)

Other Cases

Speedsolving Logo tiny.gif Alg (Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw) (D' F2 D) (r' F2 r F2) (F2 r2 F2 r2 F2 r2 F2) (D' F2 D)/(39,29)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw U R U Rw U2 Rw' U' R' U' Rw' R' U R U Rw U2 Rw' U' R' U' Rw U2 Rw' U2 Rw'/(36,30)
Speedsolving Logo tiny.gif Alg (Rw' U' F' R' F R2 U' Lw' E' R2 E) r' (E' R2 E Lw U R2 F' R F U Rw) (r U2 r' U2) (U2 r2 U2 r2 U2 r2 U2) /(41,31)
Speedsolving Logo tiny.gif Alg (Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw) (D' U' F2 U D) (r' F2 r F2) (F2 r2 F2 r2 F2 r2 F2) (D' U' F2 U D) /(43,33)


OLL Parity + PLL Parity (Double Parity)

Dp3flip.png

Speedsolving Logo tiny.gif Alg Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw R U2 x/(24,19)
Speedsolving Logo tiny.gif Alg y M U r U2 r2 U2 r' U2 F2 r' F2 r2 U2 l F2 l' F2 r2 U' M' y'/(31,20)

Other Cases

Speedsolving Logo tiny.gif Alg (r' U' F' R' F R2 U' Lw2 E L2 E') r' (E L2 E' Lw2 U R2 F' R F U r) (r U2 r' U2)/(35,26)
Speedsolving Logo tiny.gif Alg (r' U2 M l U) (r' U' F' R' F R2 U') r' (U R2 F' R F U r) r U2 r' U2 (U' M' l' U2 r)/(33,27)


Pure Flips/OLL Parity Algorithms which Don't Preserve the Last Layer

  • The algorithms are linked with SiGN Notation (where lowercase = wide turn). However, if the following group of algorithms is executed using WCA notation (where lowercase = inner layer turns), pure one dedge flips will result.

OLL Parity (Only)

One Dedge Flip.png and ImpurededgeFlip.PNG

  • Note that all 26 possible (25,15) solutions (excluding mirrors and inverses) of this category are listed.
Speedsolving Logo tiny.gif Frédérick_Badie(v1) r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2/(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v2) r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2/(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v3) r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2/(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v4) r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2/(25,15)
Speedsolving Logo tiny.gif Frédérick_Badie(v5) r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2/(25,15)
Speedsolving Logo tiny.gif Alg.2(v1) r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2/(25,15)
Speedsolving Logo tiny.gif Alg.2(v2) r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2/(25,15)
Speedsolving Logo tiny.gif Alg.2(v3) r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2/(25,15)
Speedsolving Logo tiny.gif Alg.2(v4) r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2/(25,15)
Speedsolving Logo tiny.gif Alg.2(v5) r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v1) r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v2) r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v3) r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v4) r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v5) r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v6) r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v7) r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.3(v8) r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v1) r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v2) r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v3) r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v4) r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v5) r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v6) r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v7) r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2/(25,15)
Speedsolving Logo tiny.gif Alg.4(v8) r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2/(25,15)
Speedsolving Logo tiny.gif cmowlaparity x' r2 U2 l' U2 r U2 l F2 U r U' F2 U r' U r2 x/(23,16)
Speedsolving Logo tiny.gif Alg r U2 F2 D' r' D F2 D' r D r F2 r' F2 r' U2 r'/(23,17)
Speedsolving Logo tiny.gif lucasparity r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r'/(25,17)
Speedsolving Logo tiny.gif Alg r2 U2 l' U2 r U2 r' U2 r U2 r' x' U2 r' U2 r2 F2 l x/(27,17)
Speedsolving Logo tiny.gif Alg r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r'/(27,18)
Speedsolving Logo tiny.gif Alg r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l/(27,18)


OLL Parity + PLL Parity (Double Parity)

DblParity.png and ImpurededgeFlip.PNG

Speedsolving Logo tiny.gif Alg r U2 r' e2 F2 l F2 l' F2 r F2 r' D2 l y2/(21,14)
Speedsolving Logo tiny.gif Alg r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x/(25,15)
Speedsolving Logo tiny.gif Alg x r F2 l' F' r' F U2 F' r F U2 l x' e2 l' U2 l y2/(21,16)
Speedsolving Logo tiny.gif Alg x' F2 U2 r2 U2 x U2 r U2 r' U2 x' r U2 r' U2 r' U2 r U2 r' x/(29,18)


OLL Parity algorithms Which Don't Preserve the Last Layer (SiGN Notation)

ImpurededgeFlip.PNG

  • Algorithms in WCA notation are labeled.

OLL Parity (Only)

1 Flip

Speedsolving Logo tiny.gif cmowlaparity x' r2 U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r2 x/(23,16)
Speedsolving Logo tiny.gif Alg r U2 x U2 F' r' F U2 F' r F r U2 r' U2 x' r' U2 r'/(23,17)
Speedsolving Logo tiny.gif lucasparity r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'/(25,17)
Speedsolving Logo tiny.gif lucasparity r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'/(25,17)
Speedsolving Logo tiny.gif Alg r U2 r2 U2 x' U r U' F2 U r' U' l' U2 r U2 r' U2 r'/(25,18)
Speedsolving Logo tiny.gif Alg r2 B2 3d' r' 3d r U2 r' 3d' r U' y' r' U2 r' U2 r B2 r2/(25,18)
Speedsolving Logo tiny.gif Alg r' U' r2 U' r' U r' U' r' U2 r U r U' r U r2 U r2 U2 r U2 r2 U2 r/(33,25)
Speedsolving Logo tiny.gif Alg r' U2 r' U2 r U r' U r' U2 r2 U r2 U' r2 U' r' U' r U r' U2 r2 U2 r/(34,25)
Speedsolving Logo tiny.gif Alg r' U2 r' U2 r U r' U r U' r2 U' r2 U2 r2 U' r U' r U r' U2 r2 U2 r/(34,25)
Speedsolving Logo tiny.gif Alg r' U2 r' U2 r U r' U r U r2 U2 r2 U' r2 U r U' r U r' U2 r2 U2 r/(34,25)
Speedsolving Logo tiny.gif Alg r' U r' U' r' U2 r2 U2 r2 U' r U2 r U2 r' U2 r' U' r2 U r2 U r' U2 r/(35,25)
Speedsolving Logo tiny.gif Alg r' U r' U' r' U2 r2 U2 r2 U r U2 r U2 r' U2 r' U r2 U r2 U r' U2 r/(35,25)
Speedsolving Logo tiny.gif Alg r' U r' U' r' U2 r2 U2 r2 U r U2 r U2 r' U2 r U' r2 U' r2 U' r U2 r/(35,25)
Speedsolving Logo tiny.gif Alg r' U r' U' r U' r2 U2 r2 U2 r' U2 r U2 r' U2 r' U' r2 U r2 U r' U2 r/(35,25)
Speedsolving Logo tiny.gif Alg r' U r' U' r U r2 U2 r2 U2 r' U2 r U2 r' U2 r' U r2 U r2 U r' U2 r/(35,25)
Speedsolving Logo tiny.gif Alg r' U r' U' r U r2 U2 r2 U2 r' U2 r U2 r' U2 r U' r2 U' r2 U' r U2 r/(35,25)

3 Flip

Speedsolving Logo tiny.gif Alg Rw F U2 F' Rw U2 Rw U2 Rw U' L' U2 L F (Lw' r) U' R U' x' U F Rw/(25,21)(WCA)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' R' U2 R' U2 R U' Rw/(28,22)(WCA)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U2 R' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw/(28,22)(WCA)
Speedsolving Logo tiny.gif Alg Rw U' Rw U2 R' U2 Rw' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw/(28,22)(WCA)


OLL Parity + PLL Parity (Double Parity)

1 Flip

Speedsolving Logo tiny.gif Alg_1(v1) r' U2 r' U2 l U2 r' U2 r U2 x U2 r2 U2 r' U2 r/(25,16)
Speedsolving Logo tiny.gif Alg_1(v2) l U2 l U2 r' U2 l U2 l' U2 x U2 l2 U2 l U2 l'/(25,16)
Speedsolving Logo tiny.gif Alg_2(v1) r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2/(25,16)
Speedsolving Logo tiny.gif Alg_2(v2) l' U2 l U2 l' U2 l' U2 r U2 l' U2 l U2 x' U2 l2/(25,16)
Speedsolving Logo tiny.gif Alg_3(v1) r2 U2 x' U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r/(25,16)
Speedsolving Logo tiny.gif Alg_3(v2) l2 U2 x' U2 l U2 l' U2 r U2 l' U2 l' U2 l U2 l'/(25,16)
Speedsolving Logo tiny.gif Alg_4(v1) r U2 r' U2 r2 U2 x U2 r U2 r' U2 l U2 r' U2 r'/(25,16)
Speedsolving Logo tiny.gif Alg_4(v2) l' U2 l U2 l2 U2 x U2 l' U2 l U2 r' U2 l U2 l/(25,16)
Speedsolving Logo tiny.gif Alg_5(v1) Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U Rw2 R U Rw U' Rw/(23,19)(WCA)
Speedsolving Logo tiny.gif Alg_5(v2) Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' Rw2 R' U' Rw' U Rw'/(23,19)(WCA)
Speedsolving Logo tiny.gif Alg Rw' U2 Rw' U2 Rw R U Rw2 R' U2 Rw' R' U R U Rw' U2 Rw2 U' Rw2/(26,20)(WCA)
Speedsolving Logo tiny.gif Alg z' U2 Lw' R2 x U' F2 U Lw' U2 r' U2 Rw F' L2 F r2 U2 x' U' F2 U x U2 Lw' U2 z/(32,22)(WCA)
Speedsolving Logo tiny.gif Alg r' U' r' U' r U r U2 r2 U2 r U2 r U r' U r U r2 U2 r' U2 r U2 r'/(33,25)
Speedsolving Logo tiny.gif Alg r' U r2 U r2 U2 r U2 r' U2 r U r U r U2 r' U2 r' U2 r2 U' r2 U r'/(35,25)

3 Flip

Speedsolving Logo tiny.gif Alg r U' r U' r2 U r' U2 r U2 r' U r' U' r U2 r U2 r U2 r U' r' U2 r' U2 r/(35,27)


  • You can make a 3 flip from a one flip, for example, by conjugating a 1 flip with B' R'. For example,
Speedsolving Logo tiny.gif Alg B' R' x' r2 U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r2 x R B


OLL Parity Algorithms Which Don't Preserve F3L (WCA Notation)

  • One advantage to having access to algorithms which don't preserve the first three layers of the 4x4x4 is that the shortest algorithms that this category of algorithms has to offer have fewer moves than algorithms which preserve the first three layers, which might be of interest to certain cubers.
  • Unlike algorithms which preserve the first three layers, which are at minimum 14 block half turns (double parity) and 19 block quarter turns (one dedge flip), some algorithms in this section are just 13 block half turns and some are just 15 block quarter turns.
  • A few of the algorithms are in SiGN Notation: they are labeled.

Just Corners are Permuted (Most are also Just FR F3L Slot Destroyers)

CrnersParity.png

OLL Parity (Only)

Speedsolving Logo tiny.gif Alg r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r'/(21,15)
Speedsolving Logo tiny.gif Alg l U2 F' U2 F U2 l U2 l U2 l F' U2 F l/(21,15)
Speedsolving Logo tiny.gif Alg r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'/(21,17)
Speedsolving Logo tiny.gif Alg l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l'/(21,17)
Speedsolving Logo tiny.gif Alg r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2/(21,17)
Speedsolving Logo tiny.gif Alg r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2/(21,17)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2/(22,18)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw/(22,18)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw/(22,18)
Speedsolving Logo tiny.gif Alg Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw/(24,18)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw/(24,19)


FR F3L Slot Destroyers

FRF3Lslot.png

OLL Parity (Only)

Speedsolving Logo tiny.gif Alg l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F/(22,17)
Speedsolving Logo tiny.gif Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F/(22,17)
Speedsolving Logo tiny.gif Alg Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw/(24,19)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw/(21,18)


Petrus (They Destroy 2 Adjacent Faces)

Pparity.png

OLL Parity (Only)

Speedsolving Logo tiny.gif Alg_1 r B' U2 B r B2 l B2 r B D2 B' r/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v2) x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v3) x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v4) x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'/(20,16)
Speedsolving Logo tiny.gif Alg Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'/(20,16)
Speedsolving Logo tiny.gif Alg Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x'/(21,16)
Speedsolving Logo tiny.gif Alg Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'/(21,17)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw/(21,17)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw/(21,17)
Speedsolving Logo tiny.gif Alg Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw'/(21,17)
Speedsolving Logo tiny.gif Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F/(22,17)
Speedsolving Logo tiny.gif Alg Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw/(23,17)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'/(25,17)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw'/(25,17)
Speedsolving Logo tiny.gif Alg Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw/(25,17)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw'/(21,18)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R' U' R U2 R' U Rw'/(22,18)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw/(23,18)
Speedsolving Logo tiny.gif Alg Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'/(24,18)
Speedsolving Logo tiny.gif Alg Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw/(22,19)
Speedsolving Logo tiny.gif Alg Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw/(22,19)
Speedsolving Logo tiny.gif Alg Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw/(22,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw/(23,19)
Speedsolving Logo tiny.gif Alg Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw/(23,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U' R' U2 r U2 Rw U2 r U R' U2 R U' Rw/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R U2 R' U' R' U2 r U2 Rw U2 r U R U2 R' U' Rw/(24,19)
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 Rw U2 Rw U R U2 R' U R' U2 Rw/(24,19)
Speedsolving Logo tiny.gif Alg Rw U R' U2 R' U2 R U Rw R U2 Rw U2 Rw U R U2 R' U' Rw/(25,20)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg_1(v2) l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg_1(v3) l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg_2(v2) r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg_2(v3) r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'/(20,14)(SiGN)
Speedsolving Logo tiny.gif Alg r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw/(21,17)
Speedsolving Logo tiny.gif Alg Rw' U Rw' U' Rw2 R' U' Rw' U' R U2 Rw' U' Rw' U2 Rw' U2 Rw'/(21,18)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2/(24,18)
Speedsolving Logo tiny.gif Pochmann Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'/(24,19)


More than 1 F3L Slot Destroyed (Not Petrus)

MoreT1F3Lslot.png

OLL Parity (Only)
Speedsolving Logo tiny.gif Alg r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r'/(21,15)(SiGN)
Speedsolving Logo tiny.gif Alg Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw/(22,16)
Speedsolving Logo tiny.gif Alg Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r/(22,16)
Speedsolving Logo tiny.gif Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z'/(20,17)
Speedsolving Logo tiny.gif Alg Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x'/(22,18)
Speedsolving Logo tiny.gif Alg Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R/(23,19)


Affect M Layer Only

MLyrparity.png

OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg r U2 r' U2 r' D2 r D2 r' B2 r B2 r'/(19,13)
Speedsolving Logo tiny.gif Alg r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l'/(20,14)
Speedsolving Logo tiny.gif reParity(v2) r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2/(23,15)


Complete 3x3x3 Scrambles

Pseudo3.png

OLL Parity (Only)

Speedsolving Logo tiny.gif Alg Rw B U2 B' r B2 l B2 r B' D2 B Rw/(17,13)
Speedsolving Logo tiny.gif Alg r U F2 U' l F2 2R U2 r U B2 U' r/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg r U' F2 U l F2 2R U2 r U' B2 U r/(17,13)(SiGN)
Speedsolving Logo tiny.gif Alg Uw M R D R' Bw f M d' M' Fw b M' F Uw/(15,15)
Speedsolving Logo tiny.gif Alg Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'/(20,16)
Speedsolving Logo tiny.gif Alg Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'/(20,16)
Speedsolving Logo tiny.gif Alg r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r/(21,16)(SiGN)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg_1 r F2 U2 l F U' R U' r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif Alg_2 r F2 U2 l F' U L' U r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif Alg r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif Alg r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2/(19,13)(SiGN)
Speedsolving Logo tiny.gif reParity r U2 l' U2 x' (r' U2 l U2)2 l'/(19,13)
Speedsolving Logo tiny.gif Alg Rw U' b M r' D' b D l' b2 Lw E' B' Rw/(15,14)
Speedsolving Logo tiny.gif Alg Uw M F R' B u d l' u d F R' B M Uw/(15,15)
Speedsolving Logo tiny.gif Alg Uw M F' L B' u d l' u d F' L B' M Uw/(15,15)
Speedsolving Logo tiny.gif Alg Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw x/(21,17)



Non Dedge-Preserving Last Layer 2-Cycle Cases

  • This section contains all of the 2-cycle cases that can occur in the last layer besides the one dedge flip.
  • These are additional cases which arise in the K4 Method and other direct-solving methods.
  • Algorithms marked as "Safe" are supercube safe.

In Opposite Dedges

Adjacent 2-Swap

Adj2swap.png

Speedsolving Logo tiny.gif Alg_1(v1) r U2 r U2 x U2 r U2 l' x' U2 l U2 r2/(19,12)
Speedsolving Logo tiny.gif Alg_1(v2) l' B2 r' B2 D2 r' D2 r D2 l' D2 l2/(19,12)
Speedsolving Logo tiny.gif Alg r U2 r U2 M' U2 r U2 r' U2 l U2 r2/(20,13)
Speedsolving Logo tiny.gif Alg Rw' U2 r' U2 (Rw' l) U2 r' U2 r U2 l' U2 Rw2/(20,13)
Speedsolving Logo tiny.gif Alg z Rw' U l' Uw' Rw Uw l' Fw' l' Fw l2 Uw' Rw' u Rw z'/(16,15)
Speedsolving Logo tiny.gif Alg l F2 r F2 l D f' D r D2 r' D' f D l2/(19,15)
Speedsolving Logo tiny.gif Alg b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b'/(17,16)
Speedsolving Logo tiny.gif Alg Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F'/(23,16)
Speedsolving Logo tiny.gif Alg l' B2 l D2 r' D2 l' B2 l' D2 r' D2 l2 D2 r D2/(25,16)
Speedsolving Logo tiny.gif Alg l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D'/(21,17)
Speedsolving Logo tiny.gif Alg r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D'/(21,17)
Speedsolving Logo tiny.gif Alg r' U2 l D2 l' U2 l D2 l' U2 r' U2 r' U2 r' U2 r'/(25,17)
Speedsolving Logo tiny.gif Alg Dw' Fw l' Fw' Uw Fw l' Uw' u' R u l' u' R' Uw u l2 Fw' y'/(19,18)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw2 L f L F r' F' L' f' L' Fw2 r2 Uw' z/(23,20)
Speedsolving Logo tiny.gif Alg l U l U' l' U' l U l U l' D' b2 l b2 l' U2 D l' U/Safe(23,20)
Speedsolving Logo tiny.gif Alg r' U' R U r' U R' U' r U R U2 R' U' r' U2 r' U2 r' U2 r'/(25,21)
Speedsolving Logo tiny.gif Alg U2 l' U2 r U2 r' U2 x' U2 r' U2 r' U' l r u2 l' r' U l r u2 x/Safe(29,21)
Speedsolving Logo tiny.gif Alg x' l Uw' Rw' Uw l2 Fw2 Rw Fw' U L' U' l U L U' Fw Rw' Fw2 l Uw' Rw Uw x/(25,22)
Speedsolving Logo tiny.gif Alg Rw U' R U Rw U2 Rw' U' R' U' r U R U Rw U2 Rw' U' R' U' r2 U2 Rw'/(27,23)


Opposite/diagonal 2-Swap

Diag.opp.png

Speedsolving Logo tiny.gif Alg l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2/(21,14)
Speedsolving Logo tiny.gif Alg l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2/(25,14)
Speedsolving Logo tiny.gif Alg r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2/(25,14)
Speedsolving Logo tiny.gif Alg Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw'/(16,15)
Speedsolving Logo tiny.gif Alg Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw'/(16,15)
Speedsolving Logo tiny.gif Alg Uw Lw' Bw' r' Bw Lw2 Bw' Rw Fw' r' Fw R' Bw Lw' Uw'/(16,15)
Speedsolving Logo tiny.gif Alg Fw' L2 Uw b' Uw' Lw2 Uw L' Uw b' Uw' Lw Uw' l2 Fw/(18,15)
Speedsolving Logo tiny.gif Alg Fw' Uw B2 Rw' u Rw Bw2 Lw2 d Lw d' Lw b2 Uw' Fw/(19,15)
Speedsolving Logo tiny.gif Alg Uw Rw' F2 Rw' f Rw Bw2 Lw2 u Lw u' Rw u2 Rw Uw' y2/(19,15)
Speedsolving Logo tiny.gif Alg Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x'/(25,15)
Speedsolving Logo tiny.gif Alg Fw' L U' f Uw2 Lw2 Dw r Dw' Lw2 Uw f' Uw U L' Fw/(19,16)
Speedsolving Logo tiny.gif Alg l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r/(25,16)
Speedsolving Logo tiny.gif Alg l' F2 D2 r' D2 F' l2 U2 l2 F' l F l2 U2 l2 F'/(25,16)
Speedsolving Logo tiny.gif Alg Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw/(26,17)
Speedsolving Logo tiny.gif Alg Uw Rw Fw' L Fw d Fw' L' Fw Rw2 Fw2 Lw u Lw' Fw2 Rw b' Uw'/(21,18)
Speedsolving Logo tiny.gif Alg x' l' Uw Rw' Uw' l Uw Fw Uw B' l2 B r' B' l2 B Uw' Fw' Rw Uw' x/(21,19)
Speedsolving Logo tiny.gif Alg x' U2 r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r U x/Safe(25,21)
Speedsolving Logo tiny.gif Alg z Fw Uw' l Uw Fw' Uw' l Fw2 R' Fw' F' L2 F l F' L2 Fw F R Fw2 l2 Uw z'/(27,22)
Speedsolving Logo tiny.gif Alg x l U2 l' U2 l U2 l2 U' l' U l U2 l U2 l2 U2 l U l U l U2 x'/(31,22)
Speedsolving Logo tiny.gif Alg x l U2 l' U2 l U2 l2 U l' U' l U2 l U2 l2 U2 l U' l U' l U2 x'/(31,22)
Speedsolving Logo tiny.gif Alg Rw2 U2 r' U R U r U2 r' U' R' U' r2 U R U r U2 r' U' R' U Rw2/(29,23)
Speedsolving Logo tiny.gif Alg Lw' U2 l U2 l U l' r' u2 l r U' l' r' u2 x U2 r U2 l' U2 l U2 Lw x'/Safe(31,23)
Speedsolving Logo tiny.gif Alg Rw' U' Rw U2 Rw U2 Rw' U2 Rw' U' r U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U2 Rw/(31,23)
Speedsolving Logo tiny.gif Alg Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw2 U' Rw2 U2 Rw U2 Rw' U2 Rw U2 Rw U'/(34,26)
Speedsolving Logo tiny.gif Alg Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U/(34,26)


In Adjacent Dedges

Case 1 (Close Adjacent Unoriented)

Adj.case1.png

Speedsolving Logo tiny.gif Alg l2 U Lw U2 r' U2 Rw' U2 F' r' F U2 F' M' l' x/(20,15)
Speedsolving Logo tiny.gif Alg x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x/(23,15)
Speedsolving Logo tiny.gif Alg r U2 r U2 F' L F' r F L' F l' U2 l U2 r2/(21,16)
Speedsolving Logo tiny.gif Alg x' l2 F U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F' l2 x/(24,16)
Speedsolving Logo tiny.gif Alg z F' Rw2 b' Uw Lw' Uw' b Uw b Lw b' Lw' b' Lw Uw' Rw2 F z'/(19,17)
Speedsolving Logo tiny.gif Alg z F' Lw2 Uw Bw' l Bw Uw' Bw' Lw Uw l Uw' Lw' l' Bw Lw2 F z'/(19,17)
Speedsolving Logo tiny.gif Alg z F' Rw2 z' Rw Bw' l Bw Rw' Bw' Lw Dw l Dw' Lw' l' Fw Rw2 F z'/(19,17)
Speedsolving Logo tiny.gif Alg Lw' b Uw2 Lw Uw f' Uw' Lw' Uw f' Lw f' Lw' f2 Uw b' Lw/(19,17)
Speedsolving Logo tiny.gif Alg r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2/(23,17)
Speedsolving Logo tiny.gif Alg l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2/(25,17)
Speedsolving Logo tiny.gif Alg l U l U l' U' l' U' l D f2 l' f2 l U2 D' l U' l' U' l2/Safe(25,21)
Speedsolving Logo tiny.gif Alg x' l' Rw' U2 Rw U' L' U' r' U L U Rw' U2 Rw U' L' U' r2 U L U l x/(25,22)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R2 U r' U' R2 U Fw' L' Fw2 r2 Uw' z/(27,22)
Speedsolving Logo tiny.gif Alg l' F2 l F2 U' Rw U2 l U2 Rw' B' M U' Lw2 F2 r2 F2 Lw2 U M' B U/(31,22)


Case 2 (Far Adjacent Unoriented)

Adjcase2.png

Speedsolving Logo tiny.gif Alg l2 U' Lw U2 r' U2 Rw' U2 F r' F' U2 F M' l' x/(20,15)
Speedsolving Logo tiny.gif Alg x Rw2 F' U2 l U2 r' U2 r U2 F2 r F2 l' F Rw2 x'/(23,15)
Speedsolving Logo tiny.gif Alg r U2 r U2 F R' F r F' R F' l' U2 l U2 r2/(21,16)
Speedsolving Logo tiny.gif Alg x Rw2 F' U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F Rw2 x'/(24,16)
Speedsolving Logo tiny.gif Alg Rw r z l Fw' Uw Fw l' Fw' l' Uw' l Uw l Uw' Fw z' Rw' r'/(17,17)
Speedsolving Logo tiny.gif Alg Rw r y Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Uw' Rw' r'/(17,17)
Speedsolving Logo tiny.gif Alg Lw r Uw' Fw l' Fw' Uw Fw Lw' Uw' l' Uw Lw l Fw' Lw' r'/(17,17)
Speedsolving Logo tiny.gif Alg Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw/(21,17)
Speedsolving Logo tiny.gif Alg r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2/(23,17)
Speedsolving Logo tiny.gif Alg Lw2 U' M U2 l U2 r' U2 r U2 M' U2 r U2 l' U Lw2/(25,17)
Speedsolving Logo tiny.gif Alg y z Dw' (M R') D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' (M' R) Uw y x/(19,18)
Speedsolving Logo tiny.gif Alg x' U2 l' U2 l U2 r' U2 r B2 r' F D2 F' l' F D2 F' r B2 x/(27,19)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw2 U L U' Fw r' Fw' U L' U' Fw2 r2 Uw' z/(23,20)
Speedsolving Logo tiny.gif Alg Rw' U R U r2 U' R' U' Rw' U2 Rw U R U r U' R' U' Rw' U2 Rw2/(25,21)
Speedsolving Logo tiny.gif Alg l U' l U' l' U l' U l D' b2 l' b2 l U2 D l U l' U l2/Safe(25,21)
Speedsolving Logo tiny.gif Alg z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw U' R U r' U' R' U Fw' L' Fw2 r2 Uw' z/(25,22)
Speedsolving Logo tiny.gif Alg Rw r U' R' U r' U' R U2 R' U r U2 r U2 r U2 r2 U R U' Rw'/(27,22)
Speedsolving Logo tiny.gif Alg Rw2 R U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw' U2 Rw' R'/(30,23)


Case 3 (Oriented Case)

Adjcase3.png

Speedsolving Logo tiny.gif Alg y' Fw2 l Uw' Bw Uw l' Uw' l' Bw' l Bw l Bw' Uw Fw2 y/(17,15)
Speedsolving Logo tiny.gif Alg Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2/(17,15)
Speedsolving Logo tiny.gif Alg y' z' Fw2 Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Dw' Fw2 z y/(17,15)
Speedsolving Logo tiny.gif Alg Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2/(17,15)
Speedsolving Logo tiny.gif Alg y' z' Fw' l' Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 l Fw z y/(19,15)
Speedsolving Logo tiny.gif Alg Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw'/(16,16)
Speedsolving Logo tiny.gif Alg y' Bw' R Dw r' Dw' Rw' Bw Rw' R' Dw r' Dw' Rw2 Fw' u Fw y/(17,16)
Speedsolving Logo tiny.gif Alg y' Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw' y/(19,16)
Speedsolving Logo tiny.gif Alg r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw'/(19,16)
Speedsolving Logo tiny.gif Alg z x2 Rw' Uw l' Uw' Rw Uw l' Fw2 R Fw l' Fw' R' Fw2 l2 Uw' x2 z'/(19,16)
Speedsolving Logo tiny.gif Alg y' Bw' Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r Bw y/(19,16)
Speedsolving Logo tiny.gif Alg y' l' r' U Rw U2 l' U2 Lw' U2 x' U' l' U F2 U' M' l' y/(20,16)
Speedsolving Logo tiny.gif Alg z Uw' Rw Uw2 l' Uw r' Uw' l Uw2 R' Uw Bw2 Uw' r' Uw Bw2 z'/(20,16)
Speedsolving Logo tiny.gif Alg x l' U L U l' U' L' U' F2 l' F2 r U2 r' U2 l2 x'/(21,16)
Speedsolving Logo tiny.gif Alg L' B' l' U2 l' U2 x U2 l' U2 x' r U2 r' U2 l2 B L/(23,16)
Speedsolving Logo tiny.gif Alg x l' U L U l' U' L' U' x U2 l' U2 l U2 r' U2 l r x2/(21,17)
Speedsolving Logo tiny.gif Alg x l' U L U l' U' L' U' M' U2 l' U2 l U2 r' U2 l2 x'/(22,17)
Speedsolving Logo tiny.gif Alg x' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' r' Fw Rw Uw' r2 x/(19,18)
Speedsolving Logo tiny.gif Alg y' l U F2 U' l U F2 l F L F l F' L' F' l' U' l2 y/(21,18)
Speedsolving Logo tiny.gif Alg z' r' Uw Bw Uw' Bw L Bw r Bw' L' Bw' Uw Bw' Lw Uw' r Uw Lw' Uw' z/(19,19)
Speedsolving Logo tiny.gif Alg r Uw' Lw Uw r' Uw' Fw' Uw' B Rw2 B' l B Rw2 B' Uw Fw Lw' Uw/(21,19)
Speedsolving Logo tiny.gif Alg y' x Lw' U' R' U' l2 U R U Lw' U2 Lw U' R' U' l U R U Lw' U2 Lw2 x' y/(25,21)
Speedsolving Logo tiny.gif Alg r' U' r U' r' D b2 r b2 r' U2 D' r' U' r U' r U r' U r2/Safe(25,21)
Speedsolving Logo tiny.gif Alg x l2 U2 Lw U l U' Lw' U2 Lw' U2 Lw U2 Lw U l2 U' Lw' U2 Lw' U2 Lw' L2 x'/(30,22)
Speedsolving Logo tiny.gif Alg Rw2 U Rw' U Rw' U Rw U2 Rw U2 Rw' U Rw U' Rw' U' Rw' U2 Rw' U2 Rw U2 Rw' U Rw2 U2/(34,26)
Speedsolving Logo tiny.gif Alg y Rw' U2 r' Rw2 U2 Rw U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw r U2 Rw y'/(37,27)


Non Dedge-Preserving Last Layer 4-Cycle Cases in Two Dedges

  • These are all of the other 4-cycles that can occur in two dedges in the last layer besides double parity and adjacent double parity.
  • These are additional cases which arise in the K4 Method and other direct-solving methods.

In Opposite Dedges

Checkerboard

Chkbrd.png

Speedsolving Logo tiny.gif Alg (f2 u' r2 Uw2 S') r (S Uw2 r2 u f2)/(17,11)
Speedsolving Logo tiny.gif Alg r2 U2 r S2 r S2 r' U2 l2 f2 M2 f2/(21,12)
Speedsolving Logo tiny.gif Alg r S' L2 S r U2 r U2 r S' L2 S r/(17,13)
Speedsolving Logo tiny.gif Alg r S R2 S' r U2 r U2 r S R2 S' r/(17,13)
Speedsolving Logo tiny.gif Alg Rw2 S r' U2 r' U2 r' U2 r' U2 r' S' Rw2/(19,13)
Speedsolving Logo tiny.gif Alg Rw2 S' r' U2 r' U2 r' U2 r' U2 r' S Rw2/(19,13)
Speedsolving Logo tiny.gif Alg_(v1) r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'/(21,13)
Speedsolving Logo tiny.gif Alg_(v2) l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l'/(21,13)


Bowtie/Hourglass

Hourglass.png

Speedsolving Logo tiny.gif Alg r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2/(25,15)
Speedsolving Logo tiny.gif Alg r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2/(25,16)
Speedsolving Logo tiny.gif Alg (B' R Uw' u' r' f2 Rw2 E) f' (E' Rw2 f2 r u Uw R' B)/(21,17)
Speedsolving Logo tiny.gif Alg r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r'/(26,17)


In Adjacent Dedges

Checkboard

Adjchkbd.png

Speedsolving Logo tiny.gif Alg (R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2)/(21,15)
Speedsolving Logo tiny.gif Alg (Rw' F2 M2 F) U2 l U2 l2 U2 l U2 l (F' M2 F2 Rw)/(25,16)
Speedsolving Logo tiny.gif Alg (Lw' U2 M2 U) M U2 l U2 l2 U2 l U2 r (U' M2 U2 Lw)/(26,17)
Speedsolving Logo tiny.gif Alg R B r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' B' R'/(30,21)


Bowtie/Hourglass

Ahourglass.png

Speedsolving Logo tiny.gif Alg (R Fw f r u2 Rw2 S) u' (S' Rw2 u2 r' Fw' f' R')/(19,15)
Speedsolving Logo tiny.gif Alg (Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw)/(25,16)
Speedsolving Logo tiny.gif Alg R B r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r B' R'/(25,17)
Speedsolving Logo tiny.gif Alg (r U2 M2 U') M' U2 l' U2 l2 U2 l' U2 r' (U M2 U2 r')/(26,17)
Speedsolving Logo tiny.gif Alg y2 Fw' r2 Uw2 L' Uw' U' R U F' R' F r' F' R F U' R' Uw U L Uw2 r' Fw Uw Fw' r' Fw Uw' y2/(31,28)


Summary of Last Layer 2-cycles and 4-cycles (in two dedges) Movecounts

  • Since there is disagreement among cubers about whether lowest slice quarter turn moves (SQTM) or lowest slice half turn moves (STM) defines the "optimal algorithm", the table below categorizes all 2-cycle and 4-cycle cases (in two dedges) on the 4x4x4 by the average of the two.
  • Algorithms optimal in STM need not be the algorithm with the lowest average of SQTM and STM, and algorithms optimal in SQTM turns need not be the algorithm with the lowest average of SQTM and STM. Therefore the average for a given case might be from an algorithm optimal in SQTM moves, optimal in STM moves or optimal in both.
  • Of course this ranking is based off of required moves. It is not based off of the amount of time it takes to solve a case.
  • These results will change in the future if shorter algorithms are found for any of these cases.
  • The table shows that the "worst case" is Adjacent Double Parity, and that the "easiest case" is the Checkerboard Pattern (in two opposite edges).

Algorithms Which Don't Preserve the Centers (WCA Notation)

  • These algorithms are for fixing the wing edges, but they do not preserve the centers. Many of these algorithms can be used in solving methods such as the Cage Method.

One Dedge Flip

COneDedge Flip.png

Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r' U2 B2 Rw2/(17,12)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2/(17,12)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U y r U2 F2 Rw2/(17,12)
Speedsolving Logo tiny.gif Alg Lw2 (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw2/(17,13)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U B2 D2 l D2 Rw2/(19,13)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw2/(19,13)
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2/(21,13)
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2/(21,13)
Speedsolving Logo tiny.gif Alg l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2/(21,13)
Speedsolving Logo tiny.gif Alg r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r/(15,14)
Speedsolving Logo tiny.gif Alg r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r/(21,14)
Speedsolving Logo tiny.gif Alg r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r/(21,14)
Speedsolving Logo tiny.gif Alg x r R' U' Rw U' r U Rw' r' U R U' r U r' x'/(15,15)


One Dedge Flip + PLL Parity (Double Parity)

CDoubleParity.png

  • Most of these algorithms are exactly the same as the one dedge flip ones except that the extra quarter turn is inverted.
Speedsolving Logo tiny.gif Alg Rw' F' u F' D2 F u' F' l D2 F2 Rw/(15,12)
Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r U2 B2 Rw2/(17,12)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r U2 B2 Rw2/(17,12)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U y r' U2 F2 Rw2/(17,12)
Speedsolving Logo tiny.gif Alg Lw2 (Dw' u) r' U L2 U' r D' r U D L2 y' Lw2/(17,13)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U B2 D2 l' D2 Rw2/(19,13)
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l' D2 F2 Rw2/(19,13)
Speedsolving Logo tiny.gif Alg x' Rw2 F2 r F2 r U2 l' U2 l U2 r' U2 Rw2 x/(21,13)
Speedsolving Logo tiny.gif Alg l' y' Uw2 Rw2 Uw' l' Uw Rw2 Uw' l u' U y l U2 l'/(18,14)
Speedsolving Logo tiny.gif Alg Rw2 b2 D' f' D B2 D' f U' f U D Bw2 Rw2/(19,14)
Speedsolving Logo tiny.gif Alg l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2/(21,14)
Speedsolving Logo tiny.gif Alg r U2 r' U2 Bw' r Fw r' Bw Rw2 Fw' r Fw Rw2 Fw'/(19,15)


One Dedge Flip + Adjacent PLL Parity (Adjacent Double Parity)

Cadj.dblparity.png

Speedsolving Logo tiny.gif Alg (r2 U' Rw U' R' U') r' (U R U Rw' U r2)/(15,13)
Speedsolving Logo tiny.gif Alg (r2 U F2 U' r' F2) r (F2 r U F2 U' r2)/(19,13)
Speedsolving Logo tiny.gif Alg Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw/(16,14)
Speedsolving Logo tiny.gif Alg x' r2 U' Rw U' l' U2 l' U2 l' U2 l2 U' Rw' U r2 x/(21,15)


Three Flips

OLL Parity (Only)

Collpo3flip.png

Speedsolving Logo tiny.gif Alg (r2 F2 U) r U2 r' U2 r U2 r' U2 r (U' F2 r2)/(23,15)
Speedsolving Logo tiny.gif Alg (r2 U2 F' M' U) r U2 r' U2 r U2 r' U2 r (U' M F U2 r2)/(27,19)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg (r' U' F' R' F R2 U') r' (U R2 F' R F U r) (r U2 r' U2)/(23,18)


2-Cycles In Two Adjacent Edges (in the M ring)

Adjacent 2-Swap

Cadj.2swap.png

Speedsolving Logo tiny.gif Alg l U' l' U' F2 U l U' F2 U2/(13,10)
Speedsolving Logo tiny.gif Alg l U l' U F2 U' l U F2 U2/(13,10)
Speedsolving Logo tiny.gif Alg z2 y' U2 R2 U l U' R2 U l' U y r z2/(13,10)
Speedsolving Logo tiny.gif Alg l F2 r' U2 l U2 l' U2 r U2 F2/(17,11)
Speedsolving Logo tiny.gif Alg l' U Lw' U L U' l' U L' U' Lw l U'/(13,13)


Opposite/Diagonal 2-Swap

CDiag.opp.png

  • Some of these are nearly the same as the one dedge flip algorithms.
Speedsolving Logo tiny.gif Alg Lw' U' l U B2 U' l' U' l U2 B2 Lw/(15,12)
Speedsolving Logo tiny.gif Alg Lw' U l U' B2 U l' U l U2 B2 Lw/(15,12)
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r U' y' l' U2 F2 Lw/(17,12)
Speedsolving Logo tiny.gif Alg x' U Rw' U r' U' Rw r U' R' U r' U' R x/(13,13)
Speedsolving Logo tiny.gif Alg x' R U Rw' U r' U' Rw r U' R' U r' U' x/(13,13)
Speedsolving Logo tiny.gif Alg x' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' x/(13,13)
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw/(15,13)
Speedsolving Logo tiny.gif Alg Lw' U l U' B2 U l' U' B2 D2 r' D2 Lw/(17,13)
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r U D2 y' r' D2 F2 Lw/(17,13)
Speedsolving Logo tiny.gif Alg (x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x)/(19,13)
Speedsolving Logo tiny.gif Alg Lw' U2 l' U2 r U2 r' U2 l F2 l' F2 Lw/(19,13)
Speedsolving Logo tiny.gif Alg Lw' U2 l' U2 r U2 r' U2 l B2 r' B2 Lw/(21,13)
Speedsolving Logo tiny.gif Alg M' l' U2 l' U2 l U2 r' U2 l U2 l' U2 l/(20,14)


2-Cycles In Two Opposite Edges (in the M Ring)

Adjacent 2-Swap

A2spnM.png

Speedsolving Logo tiny.gif Alg y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw/(13,12)
Speedsolving Logo tiny.gif Alg U' Rw' U r' U' Rw r U' R' U r' U' R U2/(15,14)


Opposite/Diagonal 2-Swap

OppdiagnM.PNG

  • These are the same as the one dedge flips but without first and last moves.
Speedsolving Logo tiny.gif Alg U r' U' B2 U r U r' U2 B2/(13,10)
Speedsolving Logo tiny.gif Alg U' r' U B2 U' r U' r' U2 B2/(13,10)
Speedsolving Logo tiny.gif Alg (Dw u') l U' R2 U l' D l U' D' R2 y/(13,11)
Speedsolving Logo tiny.gif Alg U' r' U B2 U' r U B2 D2 l D2/(15,11)
Speedsolving Logo tiny.gif Alg (Dw u') l U' R2 U l' U' D2 y l D2 F2/(15,11)
Speedsolving Logo tiny.gif Alg x' U2 l U2 r' U2 r U2 l' F2 r F2 x/(17,11)
Speedsolving Logo tiny.gif Alg U2 r U2 l' U2 l U2 r' F2 r F2/(17,11)
Speedsolving Logo tiny.gif Alg U2 r U2 l' U2 l U2 r' B2 l B2/(17,11)


4-Cycles in Adjacent Edges (in the M ring)

Checkboard

Cchkbrd.png

Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 Rw2/(9,5)


Bowtie/Hourglass

Chrglass.png

Speedsolving Logo tiny.gif Alg r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x/(19,12)
Speedsolving Logo tiny.gif Alg r2 U2 r U2 x' D2 r' U2 r D2 r' U2 r' x/(19,12)


Parity Algorithms Which Don't Preserve F3L or the Colors of the Centers (WCA Notation)

  • These algorithms are least practical when it comes to use of parity algorithms, and therefore they are mentioned here for theoretical purposes only. They have fewer moves than any other OLL Parity algorithm forms.

OLL Parity (Only)

Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r' B2 Rw2/(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r' B2 Rw2/(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U f U' B2 U f' U l B2 Rw2/(15,11)
Speedsolving Logo tiny.gif Alg r' U' R U' r U2 r U2 r U' R' U' r'/(15,13)


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg Rw U R B R' l Fw2 r' Fw2 U' Rw2 x/(14,11)
Speedsolving Logo tiny.gif Alg Rw U R B l Fw2 r' Fw2 R' U' Rw2 x/(14,11)
Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r B2 Rw2/(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r B2 Rw2/(15,11)
Speedsolving Logo tiny.gif Alg Rw2 U f U' B2 U f' U l' B2 Rw2/(15,11)
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2/(21,15)
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw'/(21,15)


Either OLL Parity (Only) or Double Parity

  • The following list of algorithms can be considered either OLL Parity (Only) or Double Parity. Just exchange the last move Rw' with Lw', Rw with Lw, etc.
Speedsolving Logo tiny.gif Alg Rw' U' R' U' Rw F' R' F' Rw'/(9,9)
Speedsolving Logo tiny.gif Alg Rw' U' R U' Rw F' R F' Rw'/(9,9)
Speedsolving Logo tiny.gif Alg Rw U' R U' r' D' R D' Rw/(9,9)
Speedsolving Logo tiny.gif Alg Rw' U R' U Rw U F2 U Rw'/(10,9)
Speedsolving Logo tiny.gif Alg Rw U' R U' Rw' D' R2 D' Lw/(10,9)
Speedsolving Logo tiny.gif Alg Rw' U' F2 U' r B' R B' Lw'/(10,9)
Speedsolving Logo tiny.gif Alg Rw U' L U' F2 Lw U' R U' Rw'/(11,10)
Speedsolving Logo tiny.gif Alg Rw U' L' U' F2 l U L U Rw'/(11,10)
Speedsolving Logo tiny.gif Alg Rw' U' L' U' Rw F2 U L U Rw/(11,10)
Speedsolving Logo tiny.gif Alg Rw' U' L' U' B2 Rw' B R B Rw/(11,10)
Speedsolving Logo tiny.gif Alg Rw' U R2 U Rw F2 U L' U Rw/(12,10)
Speedsolving Logo tiny.gif Alg Rw' U F' U l U2 F' U2 F Rw'/(12,10)
Speedsolving Logo tiny.gif Alg Rw U' R' U' Rw' D' L D L' D' Lw/(11,11)
Speedsolving Logo tiny.gif Alg Rw B U F' R b' M R E' R Bw/(11,11)
Speedsolving Logo tiny.gif Alg Rw U R' U R r' U2 B' L' B' Rw'/(12,11)
Speedsolving Logo tiny.gif Alg l' B' u B' D2 B u' B' l D2 l'/(13,11)
Speedsolving Logo tiny.gif Alg Rw F U' R U Rw' F U R F' U Rw/(12,12)
Speedsolving Logo tiny.gif Alg Rw' U F' L F Rw F R B' E y B Rw'/(12,12)
Speedsolving Logo tiny.gif Alg Rw S' F L F' U b' U E M U Bw/(12,12)
Speedsolving Logo tiny.gif Alg Rw' U' F R' F' Rw F' U' F2 R U Rw'/(13,12)


2-Cycles

  • Although the following list of algorithms is not "OLL Parity", where dedge preservation is important, they are the briefest 2-cycle algorithms yet to be found. They do not preserve F3L or the centers.
  • These algorithms are nothing more than 2-cycle algorithms which don't preserve centers with beginning and ending outer layer turns omitted.
Speedsolving Logo tiny.gif Alg r' U' B2 U r U r'/(8,7)
Speedsolving Logo tiny.gif Alg r' U B2 U' r U' r'/(8,7)
Speedsolving Logo tiny.gif Alg r' U L2 U' r D' r'/(8,7)
Speedsolving Logo tiny.gif Alg r' U' R2 U r D r'/(8,7)


External Links

OLL Parity Algorithms

OLL Parity Algorithms which don't preserve F3L

PLL Parity Algorithms

SuperCube Parity Algorithms

Miscellaneous