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. 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) author Cube Camera Icon.png [X]

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 r2 U2 r2 Uw2 r2 u2 (12,6) Chris Hardwick Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif SP01 (Uw2 Rw2 U2) r2 (U2 Rw2 Uw2) (14,7) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw2 F2 U2) r2 (U2 F2 Rw2) (14,7) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw2 B2 U2) r2 (U2 B2 Rw2) (14,7) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 B2 l r U2 M' U2 r2 B2 U2/Safe (19,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2/Safe (22,12) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' F U' R F' U l r U' F R' U F' l'/Safe (14,14) author Cube Camera Icon.png [X]


Adjacent

Oadjpllparity.png

Speedsolving Logo tiny.gif Alg (R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2) (18,10) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif SP02 (R2 D' x Uw2 Rw2 U2) r2 (U2 Rw2 Uw2 x' D R2) (20,11) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif FB02 (R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2) (20,11) Frédérick Badie Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2) (20,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (R2 D' x Rw2 F2 U2) r2 (U2 F2 Rw2 x' D R2) (20,11) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (R2 D' x Rw2 B2 U2) r2 (U2 B2 Rw2 x' D R2) (20,11) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y' R' F l E F2 E' l' r' E F2 E' r F' R y/Safe (16,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y' R' F l E' F2 E l' r' E' F2 E r F' R y/Safe (16,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R') (20,14) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw) (22,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y Rw' U2 Rw U2 Rw' U2 Rw' U' Rw U' Rw U Rw' U' Rw U Rw2 U Rw U' Rw U Rw' U Rw U y' (30,26) Ben Whitmore Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg F2 l E' F2 E l' r' E' F2 E r F2/Safe (16,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y') (18,12) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 l D2 l' U2 M U2 r D2 r' U2 l'/Safe (19,13) Kenneth Gustavsson Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y) (20,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y') (20,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l U2 M l U2 M' l' U2 M' U2 Rw M' U2 M r' U2 Rw'/Safe (23,17) Kenneth Gustavsson Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (F r U' R U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R' U r' F') (24,19) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw U2 Rw' U l' U' Lw' U2 Rw' U' l2 U') r2 (U l2 U Rw U2 Lw U l U' Rw U2 Rw') (32,25) Christopher Mowla Cube Camera Icon.png [X]


Adjacent

Uoadjpllparity.png

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


Four Dedges (Oriented)

Circular 4-cycle of Dedges (O Perm)

Circ4cy.png

Speedsolving Logo tiny.gif CG03 r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2 (20,11) Clément Gallet Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif PKF03 Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2 (22,13) Per Kristen Fredlund Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2 (23,14) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (F R U R' U' F') (r2 U2 r2 Uw2 r2 Uw2) (R' U' F R' F' R U R) U2 (28,21) Antoine Cantin Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (F2 U2 M U Fw2 r2 u S' Rw2 u2) M' (u2 Rw2 S u' r2 Fw2 U' M' U2 F2) (33,21) Christopher Mowla Cube Camera Icon.png [X]


Zigzag 4-cycle of Dedges (8 Perm)

Zigzag4cycdedges.png

Speedsolving Logo tiny.gif PKF04 (r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2) (22,13) Per Kristen Fredlund Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif CG04 R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2 (26,14) Clément Gallet Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw2 F2 U R2 F2 R2 U R2 F2 Uw2 R2 F2 Uw2 R2 (26,14) Clément Gallet Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif SP04 R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2 (21,16) Stefan Pochmann Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (M2 U Fw2 r2 u r2 Uw2 S' U' B R B' R2 U) M' (U' R2 B R' B' U S Uw2 r2 u' r2 Fw2 U' M2) (41,29) Christopher Mowla Cube Camera Icon.png [X]


Two Corner Swaps

Adjacent

Adj2crnrsp.png

Speedsolving Logo tiny.gif PKF10 y' B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 y (25,16) Per Kristen Fredlund Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2 (25,16) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


Opposite/Diagonal

Diag2cornerswap.png

Speedsolving Logo tiny.gif CG14 Rw2 f2 U2 Fw2 D Rw2 U2 Fw2 U' Fw2 L2 U2 B2 Lw2 U (27,15) Clément Gallet Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif MF14 Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U (27,15) Michael Fung Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) reThinking the Cube Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif FB14 y' R Rw2 F2 L U L' B D L D' B2 U B r2 U2 F2 Rw2 R' U2 y (25,19) Frédérick Badie Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Robert Yau Cube Camera Icon.png [X]
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) Robert Yau Cube Camera Icon.png [X]
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) Robert Yau Cube Camera Icon.png [X]
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) Chris Hardwick Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) Robert Yau Cube Camera Icon.png [X]


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) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U' (13,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' (15,14) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U (15,15) Christopher Mowla Cube Camera Icon.png [X]



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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw' (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw' (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif lucasparity Rw U2 Rw U2 r' U2 r U2 l' U2 l F2 r' F2 Rw' U2 Rw' (25,17) Lucas Garron & Stefan Pochmann Cube Camera Icon.png [X]
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) Christopher Mowla 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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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/SiGN (23,18) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Per Kristen Fredlund Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Bruce Norskog Cube Camera Icon.png [X]
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) Bruce Norskog Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y r U r2' U' r U' r' U r U' r2' U2' r' U2' r U2' r' U r2' U' r U r' U' r U2' r U2' r2' U r' U' r' y'/SiGN (42,33) Ben Whitmore Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 B2 l F2 r' F2 U2 r' U2 r U2 M' r U2 B2 Rw2 (26,16) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 U2 r' U2 r (26,17) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 M U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r (26,17) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg(v1) Rw2 U B2 U' r' U B2 U' Rw r U B2 U r' U' B2 U' Rw (23,18) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg(v2) r2 3d L2 3d' 2R' 3d L2 3d' r 2R 3d L2 3d 2L' 3d' L2 3d' r/SiGN (23,18) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg(v1) r2 U' B2 U r' U' B2 U r2 U' B2 U' r' U B2 U r (23,18) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg(v2) 2R2 3d' R2 3d 2R' 3d' R2 3d 2R2 3d' R2 3d' 2L' 3d R2 3d 2R/SiGN (23,18) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (z' Lw Uw2 U' Rw L2 U2 Lw' U' Lw R F2 U' R' U) r' (U' R U F2 R' Lw' U Lw U2 L2 Rw' U Uw2 Lw' z) (33,29) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (z' Lw Uw2 U' Rw L2 U2 Lw' U' Rw R U2 (Lw r') U' R2 U) r' (U' R2 U (Lw' r) U2 R' Rw' U Lw U2 L2 Rw' U Uw2 Lw' z) (37,31) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Kenneth Gustavsson Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x Rw F2 U' Rw R U' r U2 r U2 r U2 r2 U' Rw' R' U F2 Rw' x' (25,19) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (z Rw' Uw2 U Lw' R2 U2 Rw U Lw' U2 F' R2 F) l' (F' R2 F U2 Lw U' Rw' U2 R2 Lw U' Uw2 Rw z') (33,27) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


Three Flips

OLL Parity (Only)

Ollpo3flip.png

Speedsolving Logo tiny.gif Alg y M U r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2 U' M' y' (29,19) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y M U r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2 U' M' y' (29,19) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg M2' U' x' r2 U2 M r' U2 r F2 U2 r2 U2 M' r x U2 r U2 r' U' M2' (31,20) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y M U l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r' U' M' y' (27,21) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y M U r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2 U' M' y' (27,21) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg y M U l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r U' M' y' (27,21) Christopher Mowla Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]

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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (y' 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 y) (33,27) Christopher Mowla Cube Camera Icon.png [X]


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.
    • The algorithms below which end with "B2" can be conjugated with B2 to create additional "unique" algorithms, but these were excluded from the list of distinctly unique paths because they are basically the same algorithm.


Speedsolving Logo tiny.gif Alg.1(v1) r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 (25,15) Frédérick_Badie Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.1(v2) r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2 (25,15) Frédérick_Badie Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.1(v3) r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2 (25,15) Frédérick_Badie Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.1(v4) r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2 (25,15) Frédérick_Badie Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.1(v5) r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2 (25,15) Frédérick_Badie Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.2(v1) r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.2(v2) r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.2(v3) r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.2(v4) r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.2(v5) r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v1) r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v2) r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v3) r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v4) r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v5) r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v6) r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v7) r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.3(v8) r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v1) r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v2) r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v3) r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v4) r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v5) r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v6) r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v7) r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg.4(v8) r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2 (25,15) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 F2 D' r' D F2 D' r D r F2 r' F2 r' U2 r' (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif lucasparity r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r' (25,17) Lucas Garron & Stefan Pochmann Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]


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) Kenneth Gustavsson Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x (25,15) Frédérick Badie Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Lucas Garron & Stefan Pochmann Cube Camera Icon.png [X]
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) Lucas Garron & Stefan Pochmann Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]

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/WCA (25,21) Christopher Mowla Cube Camera Icon.png [X]
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/WCA (28,22) Kåre Krig Cube Camera Icon.png [X]
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/WCA (28,22) Kåre Krig Cube Camera Icon.png [X]
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/WCA (28,22) Kåre Krig Cube Camera Icon.png [X]


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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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/WCA (23,19) Kåre Krig Cube Camera Icon.png [X]
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'/WCA (23,19) Kåre Krig Cube Camera Icon.png [X]
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/WCA (26,20) Kåre Krig Cube Camera Icon.png [X]
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/WCA (32,22) Christopher Mowla Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]

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) Kåre Krig Cube Camera Icon.png [X]


  • 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 (SQTM,STM) author Cube Camera Icon.png [X]


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) Christopher Mowla & Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l U2 F' U2 F U2 l U2 l U2 l F' U2 F l (21,15) Christopher Mowla & Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r' (21,17) Christopher Mowla & Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l' (21,17) Christopher Mowla & Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2 (21,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2 (21,17) Christopher Mowla Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (r' U' R U r)(r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r)(r U R' U' r') (31,21) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F (22,17) Christopher Mowla Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]


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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (r' U' R U r)(r2 F2 Uw2 r Uw2 F2 r2)(r U R' U' r')(Fw2 l' Uw2 l r Uw2 r' Fw2) (31,23) Christopher Mowla Cube Camera Icon.png [X]


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/SiGN (17,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_1(v2) x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'/SiGN (17,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_1(v3) x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'/SiGN (17,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_1(v4) x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x/SiGN (17,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw' (20,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw' (20,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x' (21,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw' (21,17) Kåre Krig, Bruce Norskog, & Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw (21,17) Kåre Krig Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw (21,17) Kåre Krig Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw' (21,17) Bruce Norskog & Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F (22,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw (23,17) Kåre Krig Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw' (25,17) Kåre Krig & Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw' (25,17) Kåre Krig & Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw (25,17) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]
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) Kåre Krig Cube Camera Icon.png [X]


OLL Parity + PLL Parity (Double Parity)

Speedsolving Logo tiny.gif Alg_1(v1) l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'/SiGN (20,14) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_1(v2) l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'/SiGN (20,14) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_2(v1) r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'/SiGN (20,14) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_2(v2) r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'/SiGN (20,14) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw (21,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw' (24,19) Stefan Pochmann Cube Camera Icon.png [X]


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'/SiGN (21,15) Bruce Norskog & Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r (22,16) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


Affect M Layer Only

MLyrparity.png

OLL Parity (Only)

Speedsolving Logo tiny.gif Alg r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r' (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2 (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2 (24,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2 (24,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' D2 l2 D2 F2 l' D b D' F2 D b' D M l D2 r2 (24,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 M' r U2 r' B2 U2 r2 U2 M r' B2 r' B2 r B2 (27,17) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 F2 r U2 r U2 F2 r2 U2 F2 r' U2 r U2 F2 r U2 (29,17) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 F2 r U2 F2 r U2 r2 U2 F2 r U2 r F2 r' U2 (29,17) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l' (20,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif reParity(v2) r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2 (23,15) reThinking the Cube Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U F2 U' l F2 2R U2 r U B2 U' r/SiGN (17,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U' F2 U l F2 2R U2 r U' B2 U r/SiGN (17,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw M R D R' Bw f M d' M' Fw b M' F Uw (15,15) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw' (20,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw' (20,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r/SiGN (21,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U' M' U M' U' M' U' M Uw2 r Uw2 U' M' U2 M' U M U2 M U M' U M U M' U' l' (31,28) Christopher Mowla Cube Camera Icon.png [X]


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/SiGN (19,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_2 r F2 U2 l F' U L' U r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_3 r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_4 r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif reParity r U2 l' U2 x' (r' U2 l U2)2 l' (19,13) reThinking the Cube Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' b M r' D' b D l' b2 Lw E' B' Rw (15,14) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw M F R' B u d l' u d F R' B M Uw (15,15) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw M F' L B' u d l' u d F' L B' M Uw (15,15) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U M' U' M' U M' U M Uw2 l' Uw2 M' U M U' M' U M' U M U2 M' U2 r (29,25) Christopher Mowla Cube Camera Icon.png [X]


  • It's interesting to note that the long (Uw,U,r,l,M) algorithms have the same structure as Bruce's (15,15) OLL parity (only) solution.


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) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_1(v2) l' B2 r' B2 D2 r' D2 r D2 l' D2 l2 (19,12) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r U2 M' U2 r U2 r' U2 l U2 r2 (20,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U2 r' U2 (Rw' l) U2 r' U2 r U2 l' U2 Rw2 (20,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg z Rw' U l' Uw' Rw Uw l' Fw' l' Fw l2 Uw' Rw' u Rw z' (16,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l F2 r F2 l D f' D r D2 r' D' f D l2 (19,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b' (17,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F' (23,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' B2 l D2 r' D2 l' B2 l' D2 r' D2 l2 D2 r D2 (25,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D' (21,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D' (21,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U2 l D2 l' U2 l D2 l' U2 r' U2 r' U2 r' U2 r' (25,17) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Per Kristen Fredlund Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Kenneth Gustavsson Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2 (25,14) Nicholas Ho Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2 (25,14) Nicholas Ho Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' (16,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw' (16,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw Lw' Bw' r' Bw Lw2 Bw' Rw Fw' r' Fw R' Bw Lw' Uw' (16,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Fw' L2 Uw b' Uw' Lw2 Uw L' Uw b' Uw' Lw Uw' l2 Fw (18,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Fw' Uw B2 Rw' u Rw Bw2 Lw2 d Lw d' Lw b2 Uw' Fw (19,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw Rw' F2 Rw' f Rw Bw2 Lw2 u Lw u' Rw u2 Rw Uw' y2 (19,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x' (25,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Fw' L U' f Uw2 Lw2 Dw r Dw' Lw2 Uw f' Uw U L' Fw (19,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r (25,16) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' F2 D2 r' D2 F' l2 U2 l2 F' l F l2 U2 l2 F' (25,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw (26,17) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Per Kristen Fredlund Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Bruce Norskog Cube Camera Icon.png [X]
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) Bruce Norskog Cube Camera Icon.png [X]


In Adjacent Dedges

Case 1 (Close Adjacent Unoriented)

Adj.case1.png

Speedsolving Logo tiny.gif Alg l2' U Lw U2 r' U2 Rw' U2 x U' r' U x' U2 x U' M' l' (20,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x (23,15) reThinking the Cube Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r U2 F' L F' r F L' F l' U2 l U2 r2 (21,16) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' b Uw2 Lw Uw f' Uw' Lw' Uw f' Lw f' Lw' f2 Uw b' Lw (19,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2 (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2 (25,17) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x Rw2 F' U2 l U2 r' U2 r U2 F2 r F2 l' F Rw2 x' (23,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r U2 F R' F r F' R F' l' U2 l U2 r2 (21,16) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw r Uw' Fw l' Fw' Uw Fw Lw' Uw' l' Uw Lw l Fw' Lw' r' (17,17) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2 (23,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw2 U' M U2 l U2 r' U2 r U2 M' U2 r U2 l' U Lw2 (25,17) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2 (17,15) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2 (17,15) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw' (16,16) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw' (19,16) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x l U2 l U2 M U L U l U' L' U' l' U2 r U2 l2 x' (22,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 l U2 (L M) U L' U l U' L U' l' U2 r U2 Lw2 x' (22,17) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x Lw' L' U L' U l' U' L U' M' U2 l' U2 l U2 r' U2 Lw2 x' (23,18) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
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) Bruce Norskog Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg U' Rw' U Rw U' Rw2 U2 Rw' U2 Rw U2 Rw' U Rw2 U' Rw U Rw' U' Rw U2 Rw U2 Rw2 U Rw U' Rw (36,28) Ben Whitmore Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (f2 u r2 Uw2 S') r (S Uw2 r2 u' f2) (17,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 r S2 r S2 r' U2 l2 f2 M2 f2 (21,12) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 r S2 r S2 r' U2 l2 b2 M2 b2 (21,12) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r S' L2 S r U2 r U2 r S' L2 S r (17,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r S R2 S' r U2 r U2 r S R2 S' r (17,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw2 Uw U S Lw2 u2) r (u2 Lw2 S' U' Uw' Rw2) (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw2 Uw' U' S Lw2 u2) r (u2 Lw2 S' U Uw Rw2) (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 S r' U2 r' U2 r' U2 r' U2 r' S' Rw2 (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 S' r' U2 r' U2 r' U2 r' U2 r' S Rw2 (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_(v1) r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r' (21,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg_(v2) l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l' (21,13) author Cube Camera Icon.png [X]


Bowtie/Hourglass

Hourglass.png

  • It might be best to think of this case as adjacent 2-swap + PLL Parity, because if we combine the proper algorithms for each, we produce the shortest algorithm in STM.
The algorithms ending in u2 are the result of combing algorithms for those two cases.


Speedsolving Logo tiny.gif Alg r U2 r U2 F2 r F2 l' U2 M r' Uw2 r2 u2 (22,14) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r U2 M' U2 r U2 r' U2 M r' Uw2 r2 u2 (23,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2 (25,15) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2 (25,16) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (B' R Uw' u' r' f2 Rw2 E) f' (E' Rw2 f2 r u Uw R' B) (21,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (B' R Uw' u' r f2 Rw2 E) f' (E' Rw2 f2 r' u Uw R' B) (21,17) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' (26,17) author Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (R2 Uw' u' r f2 Rw2 E) f (E' Rw2 f2 r' u Uw R2) (21,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Rw' F2 M2 F) U2 l U2 l2 U2 l U2 l (F' M2 F2 Rw) (25,16) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Lw' U2 M2 U) M U2 l U2 l2 U2 l U2 r (U' M2 U2 Lw) (26,17) Christopher Mowla Cube Camera Icon.png [X]
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) author Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (R Fw f r' u2 Rw2 S) u' (S' Rw2 u2 r Fw' f' R') (19,15) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg R B r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r B' R' (25,17) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (r U2 M2 U') M' U2 l' U2 l2 U2 l' U2 r' (U M2 U2 r') (26,17) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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.
  • Lastly, note that term "optimal average" below does not necessarily mean the average of the minimum SQTM and STM (if an algorithm has both the fewest SQTM and STM, then yes). It's an average of the SQTM and STM of one algorithm. Should one algorithm have the least SQTM but not the least STM, we do not average the shortest numbers from two different algorithms.
  • 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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2 (17,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U y r U2 F2 Rw2 (17,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw2 (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw2 (17,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U B2 D2 l D2 Rw2 (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw2 (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2 (21,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2 (21,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2 (21,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r (15,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r (21,14) Lucas Garron Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r (21,14) Nicholas Ho Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x r R' U' Rw U' r U Rw' r' U R U' r U r' x' (15,15) author Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r U2 B2 Rw2 (17,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r U2 B2 Rw2 (17,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U y r' U2 F2 Rw2 (17,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw2 (Dw' u) r' U L2 U' r D' r U D L2 y' Lw2 (17,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U B2 D2 l' D2 Rw2 (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l' D2 F2 Rw2 (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' Rw2 F2 r F2 r U2 l' U2 l U2 r' U2 Rw2 x (21,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' y' Uw2 Rw2 Uw' l' Uw Rw2 Uw' l u' U y l U2 l' (18,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 b2 D' f' D B2 D' f U' f U D Bw2 Rw2 (19,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2 (21,14) Nicholas Ho Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r' U2 Bw' r Fw r' Bw Rw2 Fw' r Fw Rw2 Fw' (19,15) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (r2 U F2 U' r' F2) r (F2 r U F2 U' r2) (19,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw (16,14) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (x Uw F U r' U R' U) r (U' R U' r U' F' Uw' x') (15,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' r2 U' Rw U' l' U2 l' U2 l' U2 l2 U' Rw' U r2 x (21,15) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l U l' U F2 U' l U F2 U2 (13,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg z2 y' U2 R2 U l U' R2 U l' U y r z2 (13,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l F2 r' U2 l U2 l' U2 r U2 F2 (17,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' U Lw' U L U' l' U L' U' Lw l U' (13,13) author Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' U l U' B2 U l' U l U2 B2 Lw (15,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r U' y' l' U2 F2 Lw (17,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' U Rw' U r' U' Rw r U' R' U r' U' R x (13,13) Marc Waterman Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' R U Rw' U r' U' Rw r U' R' U r' U' x (13,13) Marc Waterman Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' x (13,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw (15,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' U l U' B2 U l' U' B2 D2 r' D2 Lw (17,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' (Dw' u) r' U L2 U' r U D2 y' r' D2 F2 Lw (17,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x) (19,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' U2 l' U2 r U2 r' U2 l F2 l' F2 Lw (19,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Lw' U2 l' U2 r U2 r' U2 l B2 r' B2 Lw (21,13) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg M' l' U2 l' U2 l U2 r' U2 l U2 l' U2 l (20,14) Nicholas Ho Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg U' Rw' U r' U' Rw r U' R' U r' U' R U2 (15,14) Francois Courtes Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg U' r' U B2 U' r U' r' U2 B2 (13,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Dw u') l U' R2 U l' D l U' D' R2 y (13,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg U' r' U B2 U' r U B2 D2 l D2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (Dw u') l U' R2 U l' U' D2 y l D2 F2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg x' U2 l U2 r' U2 r U2 l' F2 r F2 x (17,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg U2 r U2 l' U2 l U2 r' F2 r F2 (17,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg U2 r U2 l' U2 l U2 r' B2 l B2 (17,11) author Cube Camera Icon.png [X]


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

Checkboard

Cchkbrd.png

Speedsolving Logo tiny.gif Alg Rw2 U2 r U2 Rw2 (9,5) Marc Waterman Cube Camera Icon.png [X]


Bowtie/Hourglass

Chrglass.png

Speedsolving Logo tiny.gif Alg (y L' U B' Rw2 U2) r' (U2 Rw2 B U' L y') (15,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg (y L F' U Rw2 F2) r (F2 Rw2 U' F L' y') (15,11) author Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x (19,12) Nicholas Ho Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r2 U2 r U2 x' D2 r' U2 r D2 r' U2 r' x (19,12) Kenneth Gustavsson Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r' B2 Rw2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U f U' B2 U f' U l B2 Rw2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U' R U' r U2 r U2 r U' R' U' r' (15,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U' R U r' U2 r' U2 r' U R' U' r' (15,13) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U' R U r' F2 U2 r U2 F2 r' U R' U' r' (19,15) Christopher Mowla Cube Camera Icon.png [X]


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) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U R B l Fw2 r' Fw2 R' U' Rw2 x (14,11) Bruce Norskog Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U r' U' B2 U r U r B2 Rw2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U' r' U B2 U' r U' r B2 Rw2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw2 U f U' B2 U f' U l' B2 Rw2 (15,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2 (21,15) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw' (21,15) Kåre Krig & Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' R U' Rw F' R F' Rw' (9,9) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R U' r' D' R D' Rw (9,9) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U R' U Rw U F2 U Rw' (10,9) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R U' Rw' D' R2 D' Lw (10,9) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' F2 U' r B' R B' Lw' (10,9) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' L U' F2 Lw U' R U' Rw' (11,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' L' U' F2 l U L U Rw' (11,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' L' U' Rw F2 U L U Rw (11,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' L' U' B2 Rw' B R B Rw (11,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U R2 U Rw F2 U L' U Rw (12,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U F' U l U2 F' U2 F Rw' (12,10) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U' R' U' Rw' D' L D L' D' Lw (11,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw B U F' R b' M R E' R Bw (11,11) Bruce Norskog & Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw U R' U R r' U2 B' L' B' Rw' (12,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg l' B' u B' D2 B u' B' l D2 l' (13,11) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw F U' R U Rw' F U R F' U Rw (12,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U F' L F Rw F R B' E y B Rw' (12,12) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw S' F L F' U b' U E M U Bw (12,12) Bruce Norskog & Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg Rw' U' F R' F' Rw F' U' F2 R U Rw' (13,12) Christopher Mowla Cube Camera Icon.png [X]


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) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U B2 U' r U' r' (8,7) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U L2 U' r D' r' (8,7) Christopher Mowla Cube Camera Icon.png [X]
Speedsolving Logo tiny.gif Alg r' U' R2 U r D r' (8,7) Christopher Mowla Cube Camera Icon.png [X]


External Links

OLL Parity Algorithms

OLL Parity Algorithms which don't preserve F3L

PLL Parity Algorithms

SuperCube Parity Algorithms

Miscellaneous

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