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:
Alg (r U2)4 r (13,9) author []

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.

PLL Parity (WCA Notation)

Dedges

  • Algorithms marked as "Safe" are supercube safe.

Two Dedges (Oriented)

Opposite

Alg r2 U2 r2 Uw2 r2 u2 (12,6) Chris Hardwick []
SP01 (Uw2 Rw2 U2) r2 (U2 Rw2 Uw2) (14,7) Stefan Pochmann []
Alg (Rw2 F2 U2) r2 (U2 F2 Rw2) (14,7) Stefan Pochmann []
Alg (Rw2 B2 U2) r2 (U2 B2 Rw2) (14,7) Stefan Pochmann []
Alg r2 U2 B2 l r U2 M' U2 r2 B2 U2/Safe (19,11) author []
Alg r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2/Safe (22,12) author []
Alg r' F U' R F' U l r U' F R' U F' l'/Safe (14,14) author []


Adjacent

Alg (R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2) (18,10) author []
SP02 (R2 D' x Uw2 Rw2 U2) r2 (U2 Rw2 Uw2 x' D R2) (20,11) Stefan Pochmann []
FB02 (R2 D' Rw2 U2 F2) r2 (F2 U2 Rw2 D R2) (20,11) Frédérick Badie []
Alg (F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2) (20,11) author []
Alg (R2 D' x Rw2 F2 U2) r2 (U2 F2 Rw2 x' D R2) (20,11) Stefan Pochmann []
Alg (R2 D' x Rw2 B2 U2) r2 (U2 B2 Rw2 x' D R2) (20,11) Stefan Pochmann []
Alg y' R' F l E F2 E' l' r' E F2 E' r F' R y/Safe (16,14) Christopher Mowla []
Alg y' R' F l E' F2 E l' r' E' F2 E r F' R y/Safe (16,14) Christopher Mowla []
Alg (R U R' U') r2 U2 r2 Uw2 r2 Uw2 (U' R U' R') (20,14) author []
Alg (R2 D' x) r2 U2 B2 l r U2 M' U2 r2 B2 U2 (x' D R2)/Safe (24,15) author []
Alg(v1) (Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw) (22,17) Christopher Mowla []
Alg(v2) y' (Rw U' R' U' Rw B2) (Rw B2 r2 B2 Rw') (B2 Rw' U R U Rw') y (22,17) Christopher Mowla []
Alg y2 Rw U Rw' R U' Rw' U' Rw U Rw U' Rw' U' Rw' R U Rw U R' U' R' U y2 (20,20) cubizh []
Alg y2 R' U' R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U y2 (20,20) cubizh []
Alg y R' U Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U Rw U R' U' y' (20,20) cubizh []
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 []


Two Dedges (Unoriented)

Opposite

Alg F2 l E F2 E' l' r' E F2 E' r F2/Safe (16,12) Christopher Mowla []
Alg F2 l E' F2 E l' r' E' F2 E r F2/Safe (16,12) Christopher Mowla []
Alg (y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y') (18,12) author []
Alg r U2 l D2 l' U2 M U2 r D2 r' U2 l'/Safe (19,13) Kenneth Gustavsson []
Alg (y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y) (20,13) author []
Alg (y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y') (20,13) author []
Alg l U2 M l U2 M' l' U2 M' U2 Rw M' U2 M r' U2 Rw'/Safe (23,17) Kenneth Gustavsson []
Alg (F r U' R U' Lw U2 Rw U2) r2 (U2 Rw' U2 Lw' U R' U r' F') (24,19) Christopher Mowla []
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 []


Adjacent

Alg (R B) r2 U2 r2 Uw2 r2 u2 (B' R') (16,10) author []
Alg (R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R') (18,11) author []
Alg ((Lw r') U Rw2 U2 F2) r2 (F2 U2 Rw2 U' (Lw' r)) (18,11) author []
Alg R B U2 r2 U2 B2 l r U2 M' U2 r2 B R'/Safe (21,14) author []


Four Dedges (Oriented)

Circular 4-cycle of Dedges (O Perm)

CG03 r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2 (20,11) Clément Gallet []
PKF03 Uw2 r2 Uw2 r2 U2 l2 U M2 U' M' E2 M' D2 y2 (22,13) Per Kristen Fredlund []
Alg M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2 (23,14) author []
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 []
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 []
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 []
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 []
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 []
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 []
Alg U Rw2 U2 R U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw R' U' R U R' U' R2 U' Rw2 (31,22) cubizh []
Alg U Rw2 U' R2 U' R' U R U' Rw R' U2 Rw2 U2 Rw2 U2 Rw U R' U' R U2 Rw2 (31,22) cubizh []
Alg Rw' U Rw U R' Rw U' Rw' U R' U' R' U' R2 U Rw' U' R' Rw U R Rw U R' Rw' (24,23) cubizh []
Alg U Rw2 U2 Rw U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw' U' R' U R' U' R2 U' Rw2 (29,23) cubizh []
Alg U Rw2 U' R2 U' R' U R' U' Rw' U' Rw2 R U2 Rw2 R' U2 Rw2 R U' Rw U2 Rw2 (29,23) cubizh []
Alg U Rw2 R2 U' R' U R' U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R' U R U Rw2 (30,23) cubizh []
Alg U Rw2 R2 U' R' U R' U2 Rw U2 Rw2 U2 Rw2 U2 Rw U R' U' R' U R U Rw2 (30,23) cubizh []
Alg U Rw2 U R U R' U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 R' U R' U' Rw2 R2 (30,23) cubizh []
Alg U Rw2 U R U R' U' R' U Rw U2 Rw2 U2 Rw2 U2 Rw U2 R' U R' U' Rw2 R2 (30,23) cubizh []
Alg R2 U Rw U' Rw2 U' R2 U Rw2 U Rw' U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2 (30,23) cubizh []
Alg R2 U Rw' U' Rw2 U' R2 U Rw2 U Rw U Rw2 U Rw2 U R2 U' Rw2 R2 U' Rw2 R2 (30,23) cubizh []
Alg R2 U R U R' U' R' U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U R' (31,23) cubizh []
Alg R2 U R U R' U' R' U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U R' (31,23) cubizh []
Alg U Rw2 U2 R U' R' U Rw' U2 Rw2 U2 Rw2 U2 Rw' R' U' R U R' U' R2 U' Rw2 (32,33) cubizh []
Alg U Rw2 U' R2 U' R' U R U' Rw' R' U2 Rw2 U2 Rw2 U2 Rw' U R' U' R U2 Rw2 (32,33) cubizh []
Alg R2 U R U R2 U' Rw2 R2 U2 Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2 R U' R' U2 R'/safe (33,23) cubizh []
Alg R2 U R U R2 U' Rw2 R2 U2 Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2 R U' R' U2 R'/safe (33,23) cubizh []


Zigzag 4-cycle of Dedges (W Perm/8 Perm)

PKF04 (r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2) (22,13) Per Kristen Fredlund []
CG04 R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2 (26,14) Clément Gallet []
Alg Uw2 F2 U R2 F2 R2 U R2 F2 Uw2 R2 F2 Uw2 R2 (26,14) Clément Gallet []
SP04 R' U R' U' R' U' R' U R U' Uw2 r2 Uw2 r2 U2 Rw2 (21,16) Stefan Pochmann []
Alg R2 U R' U' R2 U R U Rw2 U2 R' Rw U2 R' Rw2 U2 Rw2 U2 Rw U2 Rw2/safe (30,20) cubizh []
Alg R2 U R' U' R2 U R U R' Rw2 U2 R' Rw U2 Rw2 U2 Rw2 U2 Rw U2 Rw2/safe (30,20) cubizh []
Alg R2 U R' U' R2 U R U R' Rw2 U2 R' Rw' U2 Rw2 U2 Rw2 U2 Rw' U2 Rw2/safe (31,21) cubizh []
Alg y R2 U' R' U' R U2 Rw U R Rw' U' Rw' U' Rw U Rw U' Rw' U' R Rw' U R Rw y' (24,22) cubizh []
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 []


Two Corner Swaps

Adjacent

PKF10 y' B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2 y (25,16) Per Kristen Fredlund []
Alg R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2 (25,16) author []
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 []
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 []
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 []
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 []
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 []


Opposite/Diagonal

CG14 Rw2 f2 U2 Fw2 D Rw2 U2 Fw2 U' Fw2 L2 U2 B2 Lw2 U (27,15) Clément Gallet []
MF14 Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U (27,15) Michael Fung []
Alg Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U (27,16) Christopher Mowla []
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 []
Alg y' r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2 y (30,17) Christopher Mowla []
Alg y' r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2 y (31,17) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []


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

Adjacent

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 []
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 []
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 []
Alg y' (Rw' R2 U' R' U R' Rw U' R U2' R' U' R' Rw U R Rw' U' Rw' F Rw2 U' Rw' U') (Rw U Rw' F') y (27,25) Robert Yau []
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 []
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 []
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 []
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 []
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 []
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 []


Opposite/Diagonal

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 []
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 []


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.

Alg y Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U y' (13,10) author []
Alg Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U' (13,12) Christopher Mowla []
Alg Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F' (15,14) author []
Alg Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U (15,15) Christopher Mowla []



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

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 []
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 []
Alg Rw' E Uw2 Fw Uw Rw' r' Fw' r Fw Rw Uw' Fw' Uw r Uw E' Rw (19,18) Christopher Mowla []
Alg Lw' S Bw2 Dw r Dw' Bw Dw r' Dw' r' Bw' r Bw r Bw S' Lw (19,18) Christopher Mowla []
Alg Lw' F' b' Rw' Bw' Rw u Rw' Bw Rw u2 Bw' u Bw u b F Lw (19,18) Christopher Mowla []
Alg Rw2 B r' U R' U r U' R U' r B U2 r U2 r' B2 Rw2 (23,18) Christopher Mowla []
Alg z r f2 3u U y' 2R' u2 y' l2 u' 2R' u l2 u' 2R 3u' 2u' U' x' u2 r' z/SiGN (23,18) Christopher Mowla []
Alg r2 U2 r2 U2 r U2 r U2 r' U2 B2 U' r' U B2 U' r U' (27,18) Christopher Mowla []
Alg r2 U2 r2 U2 r U2 r U2 r' U2 B2 U r' U' B2 U r U (27,18) Christopher Mowla []
Alg Rw' E Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw E' Rw (19,19) Christopher Mowla []
Alg Rw' E Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw r Rw Fw' Uw Lw E' Rw (19,19) Christopher Mowla []
Alg Rw' D' u' Uw' Rw f Rw' Uw Rw f' Rw' f' Uw' f Uw f u D Rw (19,19) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
Alg Rw U2 Rw2 U L' U r U' L U2 L' U r' U' L U Rw' U2 r U2 Rw' U2 Rw' (29,23) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []
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 []


One Dedge Flip + PLL Parity (Double Parity)

Alg x r F2 Lw' F r' F' U2 F r F' U2 Lw x' E2 l' U2 l y2 (21,16) Christopher Mowla []
Alg Rw2 B2 l F2 r' F2 U2 r' U2 r U2 M' r U2 B2 Rw2 (26,16) author []
Alg(v1) Rw2 U B2 U' r' U B2 U' Rw r U B2 U r' U' B2 U' Rw (23,18) Christopher Mowla []
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 []
Alg(v1) r2 U' B2 U r' U' B2 U r2 U' B2 U' r' U B2 U r (23,18) Christopher Mowla []
Alg(v2) 2R2 3d' R2 3d 2R' 3d' R2 3d 2R2 3d' R2 3d' 2L' 3d R2 3d 2R/SiGN (23,18) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []


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

Alg (y' r2 F Rw' F') r2 U2 r' U2 r' U2 r' U2 (F Rw F' r2 y) (23,16) Christopher Mowla []
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 []
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 []
Alg R B y2 r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l B' R' (25,18) Kenneth Gustavsson []
Alg R B' r2 B2 r B2 r' B2 r B2 U2 r U2 r B2 r2 B' R' (27,18) author []
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 []
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 []
Alg r2 F' Rw' F' U2 F r F l D2 r' D2 F2 l' U2 F R F r2 (26,19) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []


Three Flips

OLL Parity (Only)

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 []
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 []
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 []
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 []
Alg y M U l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r' U' M' y' (27,21) Christopher Mowla []
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 []
Alg y M U r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2 U' M' y' (27,21) Christopher Mowla []
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 []
Alg y M U l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r U' M' y' (27,21) Christopher Mowla []
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 []
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 []
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 []
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 []

Other Cases

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 []
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 []


OLL Parity + PLL Parity (Double Parity)

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 []
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 []
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 []


Pure Flips/OLL Parity Algorithms which Don't Preserve the Last Layer (WCA Notation)

  • If all inner slice turns of the algorithms in this section are converted to wide turns, the algorithms will simply affect more pieces in the last layer.
  • The maximum number of wide turns are used in each algorithm to do pure flips to allow the easiest execution possible, but no extra outer face turns are included as to make any algorithm longer (in STM or SQTM) than what it is without any inserted face turns at all.
  • Of course, all wide turns may be converted into inner slice turns to achieve the same pure flip result.


OLL Parity (Only)

and


15 STM Solutions

  • The following 26 (25,15) solutions can be used to generate all possible (25,15) solutions if we do the following to any of the (25,15) algorithms listed:
    • Take the mirror.
    • Take the inverse.
    • Take the mirror and the inverse.
    • Rotate the cube so that the single flipped dedge is in the desired location on the cube.
    • For (25,15) solutions which end with "B2", conjugate these solutions with B2 and then apply all of the adjustments above to the resulting algorithms.
  • These 26 solutions have been carefully sorted into 4 groups. An algorithm in its group can be transformed into any other algorithm in its group, and thus there are technically only 4 distinct (25,15) paths.


Group 1 (non-symmetrical algorithms)

Alg.1(v1) r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2 (25,15) Frédérick_Badie []
Alg.1(v2) r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2 (25,15) Frédérick_Badie []
Alg.1(v3) r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2 (25,15) Frédérick_Badie []
Alg.1(v4) r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2 (25,15) Frédérick_Badie []
Alg.1(v5) r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2 (25,15) Frédérick_Badie []


Group 2 (non-symmetrical algorithms)

Alg.2(v1) r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2 (25,15) author []
Alg.2(v2) r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2 (25,15) author []
Alg.2(v3) r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2 (25,15) author []
Alg.2(v4) r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2 (25,15) author []
Alg.2(v5) r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2 (25,15) author []


Group 3 (symmetrical algorithms)

Old Standard Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2 (25,15) author []
Alg.3(v2) Rw2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 Rw2 (25,15) author []
Alg.3(v3) Rw2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 Rw2 (25,15) author []
Alg.3(v4) Rw2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 Rw2 (25,15) author []
Alg.3(v5) Rw2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 Rw2 (25,15) author []
Alg.3(v6) Rw2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 Rw2 (25,15) author []
Alg.3(v7) Rw2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 Rw2 (25,15) author []
Alg.3(v8) Rw2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 Rw2 (25,15) author []


Group 4 (symmetrical algorithms)

Alg.4(v1) Rw2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 Rw2 (25,15) author []
Alg.4(v2) Rw2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 Rw2 (25,15) author []
Alg.4(v3) Rw2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 Rw2 (25,15) author []
Alg.4(v4) Rw2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 Rw2 (25,15) author []
Alg.4(v5) Rw2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 Rw2 (25,15) author []
Alg.4(v6) Rw2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 Rw2 (25,15) author []
Alg.4(v7) Rw2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 Rw2 (25,15) author []
Alg.4(v8) Rw2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 Rw2 (25,15) author []


23 Single Slice Quarter Turn Solutions

  • The 53 23 single slice quarter turn solutions listed below contain at least some quarter face turns as opposed to the (25,15) solutions above.
  • Additional unique 23 single slice quarter turn pure one dedge flip solutions can be created from all these by doing one of the following, but note that no additional inner slice turns may be used in the resulting algorithms more than what is already used in these solutions.
    • If the algorithm contains face quarter turns with inner l and r slices in between them, invert all face quarter turns in the algorithm.
    • If the algorithm contains face quarter turns with u, d, f, or b slices in between them,
      • Invert all face quarter turns in the algorithm
      • Convert u inner slice turns to d inner slice turns (and vice versa) OR convert f inner slice turns to b inner slice turns (and vice versa). Do not invert these turns, just substitute.
  • Like the (25,15) solutions, these solutions have been grouped next to their transformations. To save space, we label each group's algorithm as Alg(v1),Alg(v2),Alg(v3), and so forth.
  • These are most likely not all of the possible 23 single slice quarter turn solutions. Perhaps in the future, we will have efficient optimal solvers in the single slice quarter turn metric for which we can use to extract all possible solutions.
    • Since there is currently one 23 single slice quarter turn algorithm listed in the previous category, and since we can create an additional pure dedge flip algorithm from each of the following 53 solutions, we effectively show 107 unique 23 single slice quarter turn solutions on this page.
  • Lastly, it's worthy to note that using the classic setup through depth 18 of single slice half turns, the following 21 slice quarter turn algorithm was the only 21 slice quarter turn 3x3x3 algorithm which was closest to being a single dedge flip algorithm. Perhaps if the classic setup is used up to depth 21, some 21 slice quarter turn solutions may be found, but, as of yet, 23 is the current upperbound.
Alg r' F l' F2 r F r' F2 D F' D l D' F D' l F2 r (21,18) Christopher Mowla []


cmowlaparity x' Rw2 U2 Lw' U2 r U2 Lw F2 U r U' F2 U r' U Rw2 x (23,16) Christopher Mowla []
cmowlaparity(v2) x' Rw2 U2 Rw' F2 r F2 Rw F2 U r U' F2 U r' U Rw2 x (23,16) Christopher Mowla []
Alg(v1) x Rw2 U2 Rw U2 l' U2 Rw' F2 U' l' U F2 U' l U' Rw2 x' (23,16) Christopher Mowla []
Alg(v2) x Rw2 U2 Lw F2 l' F2 Lw' F2 U' l' U F2 U' l U' Rw2 x' (23,16) Christopher Mowla []
Alg r' U' r' U B2 U' r U' r' U2 r' B2 l U2 l' U2 r2 (23,17) Christopher Mowla []
Alg(v1) Rw' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 B' Rw (22,17) Christopher Mowla []
Alg(v2) Rw' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 B' Rw (22,17) Christopher Mowla []
Alg(v1) r B l B' D2 B l' B l B2 r F2 l' F2 l D2 r2 (23,17) Christopher Mowla []
Alg(v2) r B l B' D2 B l' B l B2 l D2 l' D2 r D2 r2 (23,17) Christopher Mowla []
Alg(v1) Rw D B2 D' l D B2 U2 Rw D2 l D2 Rw' D' l' U2 Rw' (23,17) Christopher Mowla []
Alg(v2) Rw D B2 D' l D B2 U2 Lw B2 l B2 Lw' D' l' U2 Rw' (23,17) Christopher Mowla []
Alg(v1) Rw' F2 D2 B l B' D2 B l' B' Rw' B2 l B2 Rw F2 Rw (23,17) Christopher Mowla []
Alg(v2) Rw' F2 D2 B l B' D2 B l' B' Lw' D2 l D2 Lw F2 Rw (23,17) Christopher Mowla []
Alg r2 D2 r D2 l' D l D' F2 D l' D l D2 l F2 r (23,17) Christopher Mowla []
Alg(v1) Rw' B' U2 B r' B' U2 F2 Lw' B2 r' B2 Lw B r F2 Rw (23,17) Christopher Mowla []
Alg(v2) Rw' B' U2 B r' B' U2 F2 Rw' U2 r' U2 Rw B r F2 Rw (23,17) Christopher Mowla []
Alg(v1) l' r' D' r D' B2 D r' D' B2 l' D2 l' F2 l F2 l2 (23,17) Christopher Mowla []
Alg(v2) l r U' r U' F2 U r' U' F2 l' U2 l' B2 l B2 r2 (23,17) Christopher Mowla []
Alg(v1) Rw U2 F2 D' r' D F2 D' r D Lw D2 r' D2 Lw' U2 Rw' (23,17) Christopher Mowla []
Alg(v2) Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw' (23,17) Christopher Mowla []
Alg(v1) r2 B' r B' U2 B r' B' U2 l' B2 Lw' D2 l D2 Lw r (23,17) Christopher Mowla []
Alg(v2) l2 F' r F' D2 F r' F' D2 l' F2 l' U2 l U2 l' r' (23,17) Christopher Mowla []
Alg(v1) r2 U2 l' U2 l F' r' F U2 F' r F' r' F2 r' U2 r' (23,17) Christopher Mowla []
Alg(v2) r2 U2 r' F2 l D' r' D F2 D' r D' r' D2 l' U2 r' (23,17) Christopher Mowla []
Alg r2 B2 D2 r D b' D F2 D' b D r' B2 l r F2 r (23,17) Christopher Mowla []
Alg r2 F2 U2 l' U' f U' B2 U f' U' r' B2 r l F2 r (23,17) Christopher Mowla []
Alg r2 D f D' B2 D f' D r D2 F2 r' B2 l r F2 r (23,17) Christopher Mowla []
Alg r2 U' b' U F2 U' b U' l' U2 B2 r' B2 r l F2 r (23,17) Christopher Mowla []
Alg(v1) r2 D2 r D b' D F2 D' b D r' B2 l B2 r F2 r (23,17) Christopher Mowla []
Alg(v2) r2 D2 r D b' D F2 D' b D l' D2 l D2 l F2 r (23,17) Christopher Mowla []
Alg(v1) r2 F2 r' B2 l D f D' B2 D f' D r D2 r F2 r (23,17) Christopher Mowla []
Alg(v2) r2 F2 l' D2 l F u F' D2 F u' F r F2 l F2 r (23,17) Christopher Mowla []
Alg(v3) r2 B2 r U2 r' B' d' B U2 B' d B' r' U2 r' U2 r' (23,17) Christopher Mowla []
Alg Lw' B' r' B D2 B' r B' r' B2 r' D2 l B2 l' B2 r Lw (23,18) Christopher Mowla []
Alg(v1) r Lw F2 l' F2 l D' r' D F2 D' r D' r' D2 r' F2 Lw' (23,18) Christopher Mowla []
Alg(v2) Rw l F2 l' F2 r F' r' F U2 F' r F' r' F2 r' U2 Rw' (23,18) Christopher Mowla []
Alg(v3) r Lw F2 r' D2 l B' r' B D2 B' r B' r' B2 l' F2 Lw' (23,18) Christopher Mowla []
Alg(v1) Rw' U' r' U B2 U' r U' r' U2 l' D2 r D2 r' B2 Rw l (23,18) Christopher Mowla []
Alg(v2) Rw' U' r' U B2 U' r U' r' U2 r' B2 r B2 l' B2 Rw l (23,18) Christopher Mowla []
Alg(v1) Rw' F2 D b' D l D2 l' D' b D Rw' B2 l B2 Rw F2 Rw (23,18) Christopher Mowla []
Alg(v2) Rw' F2 D b' D l D2 l' D' b D Lw' D2 l D2 Lw F2 Rw (23,18) Christopher Mowla []
Alg r2 B' D2 r D b' D F2 D' b D r' B2 l B' r F2 r (23,18) Christopher Mowla []
Alg r2 B D2 r D b' D F2 D' b D r' B2 l B r F2 r (23,18) Christopher Mowla []
Alg r' Lw' B' d' B U2 B' d B' l' B2 D2 r' D2 r l U2 Lw (23,18) Christopher Mowla []
Alg Rw l D2 F2 l' F' d F' U2 F d' F' l D2 r' l' U2 Rw' (23,18) Christopher Mowla []
Alg Rw l F' u' F D2 F' u F' l' F2 U2 l D2 r' l' U2 Rw' (23,18) Christopher Mowla []
Alg(v1) Rw l F2 l' F' d F' U2 F d' F' Lw D2 r' D2 Lw' U2 Rw' (23,18) Christopher Mowla []
Alg(v2) Rw l F2 l' F' d F' U2 F d' F' Rw F2 r' F2 Rw' U2 Rw' (23,18) Christopher Mowla []
Alg r' Lw' U2 B2 l' B' u B' D2 B u' B' r' D2 r l U2 Lw (23,18) Christopher Mowla []
Alg(v1) Rw l U2 r F2 r' U' b' U F2 U' b U' l' U2 r' U2 Rw' (23,18) Christopher Mowla []
Alg(v2) r Lw U2 r F2 r' U' b' U F2 U' b U' r' F2 r' F2 Lw' (23,18) Christopher Mowla []
Alg(v1) Rw U2 F' d F' r' F2 r F d' F' Lw D2 r' D2 Lw' U2 Rw' (23,18) Christopher Mowla []
Alg(v2) Rw U2 F' d F' r' F2 r F d' F' Rw F2 r' F2 Rw' U2 Rw' (23,18) Christopher Mowla []


Algorithms of this category which are not optimal (in either single slice metric)

  • The following list of algorithms are all unique solutions generated with the classic setup which use only 2 different face turns which are at most 27 single slice quarter turns and 18 single slice half turns.
    • There is only one algorithm which just uses the face turn, U2.
  • Like the (25,15) solutions, all solutions ending in B2 may be conjugated with B2 to create a handful more "unique" algorithms.
    • All other algorithms can be modified by inverses, mirrors, cube rotations, or a combination of any of these to create every possible algorithm which uses 2 faces which are generated from the classic setup.
  • Since this is a large set of algorithms,
    • None of these algorithms have any wide turns in them (despite that some algorithms can have some).
    • Even though it is very likely that algorithms related by transformations are listed next to each other, no official sorting by transformations was done.
  • Since these algorithms use either U and F faces or U and B faces, all algorithms which affect one or the other have been grouped together for convenience of personal preference.


Alg r' U2 r U2 l F2 l' r' F2 r' U2 r' U2 F2 r2 F2 (25,16) author []
Alg r' U2 r U2 l' U2 l r U2 r U2 r' U2 F2 r2 F2 (25,16) author []
Alg r' U2 l F2 l' F2 l r F2 r F2 l' U2 F2 r2 F2 (25,16) author []


Alg r B2 r' U2 l B2 l2 B2 U2 r B2 l' B2 l' r' B2 (25,16) author []
Alg l' r' B2 r' B2 l U2 B2 r2 B2 r U2 l' B2 l B2 (25,16) author []


Alg r' U2 r U2 r U2 r2 F2 l r2 F2 l' U2 F2 r2 F2 (27,16) author []
Alg r' U2 l F2 r F2 l2 U2 l r2 U2 r' U2 F2 r2 F2 (27,16) author []


Alg r' U2 r' U2 r2 U2 r U2 r2 B2 r U2 r U2 r2 B2 (27,16) author []
Alg r' U2 l' B2 r2 B2 l U2 r2 B2 r U2 r U2 r2 B2 (27,16) author []


Alg r U2 r U2 r' U2 l F2 l' F2 r F2 r' F2 r' U2 r' (25,17) author []
Alg r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r' (25,17) author []
Alg r U2 l F2 l' U2 r U2 r' F2 r F2 r' F2 r' U2 r' (25,17) author []
Alg r U2 l F2 r' F2 r F2 l' F2 r F2 r' F2 r' U2 r' (25,17) author []
Alg r' F2 l' F2 r U2 r' F2 r F2 l' F2 l F2 l U2 l (25,17) author []
Alg r' F2 l' F2 r U2 l' U2 r U2 r' F2 l F2 l U2 l (25,17) author []
Alg l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l' r' (25,17) author []
Alg l r U2 r F2 r' F2 U2 r' U2 l F2 l' F2 U2 l' r' (25,17) author []


Alg r' U2 r' U2 l F2 r' U2 r' U2 r2 F2 r' U2 l' U2 r2 (27,17) author []
Alg r' U2 r U2 r' F2 l r F2 l' r2 U2 r' U2 F2 r2 F2 (27,17) author []
Alg r' U2 r U2 r U2 l' r' U2 l r2 U2 r' U2 F2 r2 F2 (27,17) author []
Alg r' U2 l F2 l' F2 r2 U2 l F2 r' F2 l' r F2 r2 F2 (27,17) author []
Alg r' U2 l F2 r F2 l' r' F2 l r2 F2 l' U2 F2 r2 F2 (27,17) author []
Alg r' U2 l F2 l2 r U2 l r U2 l F2 l' U2 F2 r2 F2 (27,17) author []
Alg r' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 r2 U2 l' r (27,17) author []
Alg r2 U2 r' U2 l F2 U2 r2 U2 r F2 l' U2 l U2 l' r (27,17) author []
Alg r2 U2 r' F2 r F2 l' U2 l F2 r' U2 r' U2 r2 F2 r (27,17) author []
Alg r2 U2 l' U2 l F2 r' F2 r F2 r' U2 r' U2 r2 F2 r (27,17) author []
Alg r2 U2 l' U2 r U2 r' U2 l F2 r' U2 r' U2 r2 F2 r (27,17) author []
Alg r2 F2 r F2 l2 r U2 F2 l' F2 l F2 r' F2 U2 l r (27,17) author []
Alg r2 F2 r' U2 l F2 l' U2 r U2 r' F2 r' U2 r2 F2 r (27,17) author []
Alg r2 F2 r' U2 l F2 r' F2 r F2 l' F2 r' U2 r2 F2 r (27,17) author []
Alg r2 F2 r' U2 r U2 r' U2 l F2 l' F2 r' U2 r2 F2 r (27,17) author []
Alg r2 F2 r' U2 r U2 r' U2 r U2 l' U2 r U2 l2 F2 l' (27,17) author []
Alg l r2 F2 r F2 r F2 l' r' F2 r' U2 r' U2 F2 r2 F2 (27,17) author []


Alg r B2 r' U2 r U2 l2 B2 l' B2 l B2 U2 l2 U2 l r' (27,17) author []
Alg r B2 l' B2 r B2 r2 U2 l' U2 r B2 U2 l2 U2 l r' (27,17) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 r' U2 l' r2 B2 l r B2 (27,17) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l2 U2 l' r (27,17) author []
Alg r2 U2 r B2 r U2 r2 B2 r B2 r U2 l' B2 l U2 r (27,17) author []
Alg r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 l U2 l' r (27,17) author []
Alg r2 U2 r' U2 r' B2 r2 U2 r' U2 l' r' B2 r B2 l B2 (27,17) author []
Alg r2 U2 r' U2 r' B2 l' r' B2 r' B2 r2 B2 r B2 l B2 (27,17) author []
Alg r2 U2 l' U2 r U2 r' U2 r U2 r' B2 r' B2 r2 U2 l (27,17) author []
Alg r2 U2 l' B2 r B2 l r' B2 r2 B2 r U2 l' B2 l B2 (27,17) author []
Alg r2 B2 U2 l' U2 r U2 r' U2 B2 l r2 U2 l U2 l' r' (27,17) author []
Alg r2 B2 U2 l' U2 r U2 r' U2 l r' U2 r' U2 r B2 r2 (27,17) author []
Alg r2 B2 r U2 l' B2 l r' B2 r' B2 r B2 r' U2 B2 r2 (27,17) author []
Alg r2 B2 r U2 r' B2 l' B2 l U2 l' B2 l U2 r2 U2 r' (27,17) author []
Alg r2 B2 r U2 r' U2 B2 r' B2 r B2 l' B2 l r' B2 r2 (27,17) author []
Alg r2 B2 r U2 r' U2 l r' U2 l' B2 r B2 r' U2 B2 r2 (27,17) author []
Alg r2 B2 r U2 r' U2 l r' U2 r' U2 r U2 l' U2 B2 r2 (27,17) author []
Alg r2 B2 l' r B2 l' B2 l U2 r' U2 B2 r' B2 l B2 r2 (27,17) author []


Alg r U r U' F2 U r' U' l F2 l' F2 U2 r' U2 r2 F2 r (25,18) author []
Alg r2 U2 l U2 r' U2 r F2 r F r' F U2 F' r F l' r2 (25,18) author []
Alg r2 F2 r F2 l2 r U2 r' F2 U' l' U F2 U' l U' l r (25,18) author []
Alg r' F2 l' F2 l F2 l' U' l' U F2 U' l U F2 l2 F2 r (25,18) author []


Alg r U2 r U2 r' U2 r B r B' U2 B r' B' U2 r2 U2 r' (25,18) author []
Alg r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' B2 l r2 (25,18) author []
Alg r2 B2 r U2 r' U2 B r' B' l U2 l' U2 l' B' l B' r2 (25,18) author []
Alg r2 B2 r U2 r' U2 B r' B' r B2 l' B2 r' B' l B' r2 (25,18) author []
Alg r2 B' r B' U2 B r' B' U2 l' B2 l r2 U2 l U2 l' r' (25,18) author []


Alg r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r' (27,18) author []


Alg r U2 r2 U2 r' U2 l F2 l' U2 l U2 r F2 r' U2 l' r' (27,18) author []
Alg r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 l r2 F2 l' (27,18) author []
Alg r U2 r U2 r' U2 r U2 r' F2 r F2 l' U2 l r2 U2 r' (27,18) author []
Alg r U2 l F2 r' F2 l' r2 U2 l' U2 l F2 r' F2 r' U2 r' (27,18) author []
Alg r U2 l F2 l' U2 r U2 l' U2 r U2 l r2 F2 r' U2 r' (27,18) author []
Alg r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 l' r' U2 l r' (27,18) author []
Alg r' U2 r U2 r' F2 r2 U2 r U2 r' U2 l' r U2 l r F2 (27,18) author []
Alg r' U2 r U2 r' F2 l r F2 r F2 r' F2 l' r F2 r2 F2 (27,18) author []
Alg r' U2 r U2 l' U2 l r U2 l F2 r' F2 l' r F2 r2 F2 (27,18) author []
Alg r' U2 l F2 r' U2 r2 U2 F2 l' U2 r U2 l r U2 l' r (27,18) author []
Alg r' U2 l F2 l' F2 r2 U2 l F2 l' U2 l' r U2 l r F2 (27,18) author []
Alg r' F2 r2 U2 r U2 r F2 r' F2 r F2 r' F2 l F2 l' r' (27,18) author []
Alg r' F2 l' F2 r U2 l' U2 r U2 l' U2 l U2 l2 r' U2 l (27,18) author []
Alg r' F2 l' F2 r U2 l' U2 l F2 l' F2 r U2 l2 r' U2 l (27,18) author []
Alg r' F2 l' F2 r U2 l' U2 l F2 l' F2 l F2 l2 r' F2 r (27,18) author []
Alg r' F2 l' F2 l F2 l' F2 r F2 l' F2 r U2 l2 r' U2 l (27,18) author []
Alg r' F2 l' F2 l F2 l' F2 r F2 l' F2 l F2 l2 r' F2 r (27,18) author []
Alg r' F2 l' F2 l F2 l' F2 l' r2 U2 r' F2 l F2 l U2 l (27,18) author []
Alg r' F2 l2 F2 r U2 r' F2 r U2 r' U2 l' F2 l U2 l r (27,18) author []
Alg r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r' U2 l' r' U2 l (27,18) author []
Alg r2 U2 r' F2 r F2 r' F2 r F2 r' U2 r F2 l r F2 l' (27,18) author []
Alg r2 F2 U2 l' U2 l F' r' F U2 F' r F r2 U2 r2 F2 r (27,18) author []
Alg r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l (27,18) author []
Alg r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r F2 l r F2 l' (27,18) author []
Alg r2 F2 l' r F2 l' U2 l U2 l' U2 F2 l' F2 l U2 l r (27,18) author []
Alg l r' U2 l' U2 l F2 r' U2 r2 U2 F2 r' F2 r F2 l' r' (27,18) author []


Alg r U2 r U2 l' B2 r B2 r' U2 r U2 r' U2 l r2 U2 r' (27,18) author []
Alg r U2 r U2 l' B2 r B2 l' B2 l U2 r' U2 r' B2 l r2 (27,18) author []
Alg r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' B2 l r2 (27,18) author []
Alg r U2 l2 B2 l' B2 l' U2 l U2 l' U2 r B2 r' B2 l' r' (27,18) author []
Alg r U2 l2 B2 l' B2 l' U2 r B2 l' B2 l B2 r' B2 l' r' (27,18) author []
Alg r U2 l2 B2 l' B2 l' U2 r B2 r' U2 l U2 l' B2 l' r' (27,18) author []
Alg r U2 l2 B2 l' U2 l' B2 l B2 r' U2 r B2 l' U2 l' r' (27,18) author []
Alg r U2 l2 B2 l' U2 r' U2 l U2 l' U2 r B2 l' U2 l' r' (27,18) author []
Alg r U2 l2 B2 l' U2 r' U2 r B2 l' B2 l B2 l' U2 l' r' (27,18) author []
Alg r U2 l2 B2 r' B2 l B2 r' B2 r B2 r' B2 r U2 l r (27,18) author []
Alg r B2 r' U2 r U2 l' r' U2 l' U2 r B2 U2 l2 U2 l r' (27,18) author []
Alg r B2 r' U2 l B2 l2 B2 U2 r B2 r' U2 l' r' U2 l' r (27,18) author []
Alg r B2 l B2 r' U2 l B2 l B2 l2 U2 l B2 r B2 l' r' (27,18) author []
Alg r B2 l' B2 r B2 l' r' B2 l' B2 l B2 U2 l2 U2 l r' (27,18) author []
Alg r B2 l' B2 r' U2 l r U2 l B2 l B2 U2 l2 U2 l r' (27,18) author []
Alg r' U2 r U2 r' B2 l r U2 l' r U2 r' U2 r U2 r2 B2 (27,18) author []
Alg r' U2 r U2 r' B2 r2 B2 l' r B2 r' B2 r B2 l r B2 (27,18) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 l' r' B2 l r (27,18) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 l' r (27,18) author []
Alg r' U2 r' U2 l' r' B2 r B2 l r B2 r U2 r U2 r2 B2 (27,18) author []
Alg r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l r (27,18) author []
Alg r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 l r' (27,18) author []
Alg l r' U2 l' U2 r U2 r' B2 r2 B2 U2 l' B2 r B2 l r (27,18) author []
Alg r2 U2 l' B2 l U2 l r' U2 l' r' B2 r U2 l' B2 l B2 (27,18) author []
Alg r2 B2 r U2 r' U2 B2 r' B2 r B2 r' U2 l r' U2 l' r' (27,18) author []


Alg Rw U2 Rw2 U L U r U' L' U2 L U r' U' L' U Rw' U2 r U2 Rw' U2 Rw' (29,23) Christopher Mowla []


OLL Parity + PLL Parity (Double Parity)

and

Alg r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l y2 (21,14) Kenneth Gustavsson []
Alg r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x (25,15) Frédérick Badie []
Alg x r F2 l' F' r' F U2 F' r F U2 l x' E2 l' U2 l y2 (21,16) Christopher Mowla []
Alg x' F2 U2 r2 U2 x U2 r U2 r' U2 x' r U2 Rw' U2 r' U2 Rw U2 r' x (29,18) author []


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

  • Algorithms in WCA notation are labeled.

OLL Parity (Only)

  • Note that, unlike the previous section, none of these are pure flips if wide turns are converted to inner slice turns.

1 Flip

  • With the exception of Kåre Krig's 2 gen algorithms, all algorithms listed in this section were derived from algorithms in the previous section by using 4x4x4 wide turn equivalencies such as Rw = (Lw x), Lw2 = (Rw2 x2), etc.
    • Specifically, these algorithms were derived from the classic setup's solutions which are at most 18 single slice half turns. They only involve 2 face turns and thus they are additional transformations which are "legal" in wide turns, but "illegal" transformations to keep these algorithms pure dedge flips.
      • Therefore we have more 15 STM solutions which preserve F3L in wide turns than we have for pure dedge flips, for example.
      • Most of these algorithms need to be adjusted to work on 5x5x5.
  • Lastly, it's interesting to note that the following algorithm (although it contains more than 2 types of face turns and thus is not a part of the chosen set of algorithms listed in this section) cannot even be used to solve OLL parity if all of its wide turns are converted into single slice turns.
Alg r2 B2 l' U' r U l U2 r' U2 B2 r' U2 F' r' F U2 r' (25,18) Christopher Mowla []


Alg r' U2 r U2 r U2 r2 F2 r' U2 r' U2 F2 r2 F2 (25,15) author []
Alg r' U2 r U2 r' F2 r2 U2 r U2 r' U2 F2 r2 F2 (25,15) author []
Alg r' U2 l F2 r' U2 r2 U2 F2 l' U2 l F2 r2 U2 x (25,15) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 l' B2 l U2 r2 B2 (25,15) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 r2 B2 (25,15) author []
Alg r' U2 r U2 l' U2 r2 B2 l U2 l' B2 U2 r2 U2 x' (25,15) author []
Alg r2 U2 r' U2 r U2 B2 r2 B2 r U2 r' U2 r B2 (25,15) author []
Alg x' r2 B2 l B2 r' U2 B2 l2 B2 l' U2 l U2 l' B2 (25,15) author []


Alg l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 l2 x' (25,16) author []
Alg l r U2 F2 l' F2 r F2 r' F2 U2 r' U2 l U2 r2 x (25,16) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 r' U2 r U2 l r U2 x (25,16) author []
Alg r' U2 r U2 r U2 l' r' U2 r' B2 r' B2 U2 r2 U2 x' (25,16) author []


Alg r' U2 r U2 l r2 U2 r2 U2 F2 l' U2 l F2 r2 U2 x (27,16) author []
Alg r' U2 r U2 l r2 U2 r2 U2 F2 l' U2 r U2 l2 F2 x2 (27,16) author []
Alg r' U2 r U2 l2 r B2 l2 U2 r U2 l' B2 U2 r2 U2 x' (27,16) author []
Alg r' U2 r U2 r' B2 r2 B2 U2 r' U2 r' B2 r2 U2 r2 (27,16) author []
Alg r' U2 r U2 r U2 l2 B2 l r2 B2 r' B2 U2 r2 U2 x' (27,16) author []
Alg r' U2 r' U2 r2 U2 r' B2 r2 U2 l' B2 l U2 r2 B2 (27,16) author []
Alg r' U2 r' U2 r2 U2 r' B2 r2 U2 r' U2 r U2 r2 B2 (27,16) author []
Alg r2 U2 B2 r B2 r B2 U2 r U2 r' U2 r' U2 r2 U2 B2 (27,16) author []
Alg r2 U2 r' U2 r' B2 r2 U2 r' U2 r2 U2 r U2 l U2 x (27,16) author []
Alg x' r2 B2 l2 r' U2 l' U2 B2 l2 B2 l' U2 l U2 l' B2 (27,16) author []


Alg r' U' r' U B2 U' r U' r' U2 r' x' U2 r U2 l' U2 r2 (23,17) Christopher Mowla []
Alg r2 U2 l' U2 r U' r' U B2 U' r U' r' U2 r' x' U2 r' (23,17) Christopher Mowla []
Alg l r U' r U' F2 U r' U' x U2 r' U2 r' U2 l U2 r2 x (23,17) Christopher Mowla []


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 []
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 []
Alg r U2 r U2 l' B2 l U2 l' U2 r U2 r' U2 r' x' U2 r' (25,17) author []
Alg r U2 r U2 r' U2 r U2 r' F2 r F2 r' F2 r' U2 r' (25,17) author []


Alg r' U2 r U2 r U2 l' r' U2 l2 r F2 l' U2 F2 r2 F2 (27,17) author []
Alg r' U2 r' U2 r2 U2 r U2 l r U2 r F2 r F2 r2 U2 x (27,17) author []
Alg r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 l' B2 l2 x (27,17) author []
Alg r' U2 r' U2 r U2 r' B2 r' B2 r2 U2 r' B2 r' U2 r2 (27,17) author []
Alg r2 U2 l' U2 r U2 l' B2 l U2 r' B2 r' B2 r2 U2 l (27,17) author []
Alg l r U2 l' r2 U2 r' U2 B2 r' B2 l U2 l' U2 B2 r2 (27,17) author []


Alg r U2 r U2 r' U2 l U r U' F2 U r' U' x U2 r2 U2 r' (25,18) Christopher Mowla []


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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []


3 Flip

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 []
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 []
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 []
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 []


OLL Parity + PLL Parity (Double Parity)

1 Flip

Alg_1(v1) r' U2 r' U2 l U2 r' U2 r U2 x U2 r2 U2 r' U2 r (25,16) author []
Alg_1(v2) l U2 l U2 r' U2 l U2 l' U2 x U2 l2 U2 l U2 l' (25,16) author []
Alg_2(v1) r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2 (25,16) author []
Alg_2(v2) l' U2 l U2 l' U2 l' U2 r U2 l' U2 l U2 x' U2 l2 (25,16) author []
Alg_3(v1) r2 U2 x' U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r (25,16) author []
Alg_3(v2) l2 U2 x' U2 l U2 l' U2 r U2 l' U2 l' U2 l U2 l' (25,16) author []
Alg_4(v1) r U2 r' U2 r2 U2 x U2 r U2 r' U2 l U2 r' U2 r' (25,16) author []
Alg_4(v2) l' U2 l U2 l2 U2 x U2 l' U2 l U2 r' U2 l U2 l (25,16) author []
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 []
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 []
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 []
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 []
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 []
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 []


3 Flip

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 []


  • You can make a 3 flip from a one flip, for example, by conjugating a 1 flip with B' R'. For example,
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 []

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)

OLL Parity (Only)

Alg r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r' (21,15) Christopher Mowla & Bruce Norskog []
Alg l U2 F' U2 F U2 l U2 l U2 l F' U2 F l (21,15) Christopher Mowla & Bruce Norskog []
Alg r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r' (21,17) Christopher Mowla & Bruce Norskog []
Alg l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l' (21,17) Christopher Mowla & Bruce Norskog []
Alg r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2 (21,17) Christopher Mowla []
Alg r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2 (21,17) Christopher Mowla []
Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2 (22,18) Kåre Krig []
Alg Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw (22,18) Kåre Krig []
Alg Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw (22,18) Kåre Krig []
Alg Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw (24,18) Kåre Krig []
Alg Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2 (24,19) Kåre Krig []
Alg Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2 (24,19) Kåre Krig []
Alg Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw (24,19) Kåre Krig []
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 []


FR F3L Slot Destroyers

OLL Parity (Only)

Alg l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F (22,17) Christopher Mowla []
Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F (22,17) Christopher Mowla []
Alg Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw' (24,18) Kåre Krig []
Alg Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r' (24,18) Kåre Krig []
Alg Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw (24,19) Kåre Krig []


OLL Parity + PLL Parity (Double Parity)

Alg Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw (21,18) Kåre Krig []
Alg Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2 (24,18) Kåre Krig []
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 []


Petrus (They Destroy 2 Adjacent Faces)

OLL Parity (Only)

Alg_1 r B' U2 B r B2 l B2 r B D2 B' r/SiGN (17,13) Bruce Norskog []
Alg_1(v2) x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'/SiGN (17,13) Bruce Norskog []
Alg_1(v3) x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'/SiGN (17,13) Bruce Norskog []
Alg_1(v4) x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x/SiGN (17,13) Bruce Norskog []
Alg Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw' (20,16) Christopher Mowla []
Alg Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw' (20,16) Christopher Mowla []
Alg Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x' (21,16) Christopher Mowla []
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 []
Alg Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw (21,17) Kåre Krig []
Alg Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw (21,17) Kåre Krig []
Alg Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw' (21,17) Bruce Norskog & Christopher Mowla []
Alg Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F (22,17) Christopher Mowla []
Alg Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw (23,17) Kåre Krig []
Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw' (25,17) Kåre Krig & Christopher Mowla []
Alg Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw' (25,17) Kåre Krig & Christopher Mowla []
Alg Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw (25,17) Kåre Krig []
Alg Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw' (21,18) Kåre Krig []
Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R' U' R U2 R' U Rw' (22,18) Kåre Krig []
Alg Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw (23,18) Kåre Krig []
Alg Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw (23,18) Kåre Krig []
Alg Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw (23,18) Kåre Krig []
Alg Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw' (24,18) Kåre Krig []
Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw' (24,18) Kåre Krig []
Alg Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw' (24,18) Kåre Krig []
Alg Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw (22,19) Kåre Krig []
Alg Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw (22,19) Kåre Krig []
Alg Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw (22,19) Kåre Krig []
Alg Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw (23,19) Kåre Krig []
Alg Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw (23,19) Kåre Krig []


OLL Parity + PLL Parity (Double Parity)

Alg_1(v1) l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'/SiGN (20,14) Bruce Norskog []
Alg_1(v2) l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'/SiGN (20,14) Bruce Norskog []
Alg_2(v1) r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'/SiGN (20,14) Bruce Norskog []
Alg_2(v2) r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'/SiGN (20,14) Bruce Norskog []
Alg r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw (21,17) Christopher Mowla []
Alg Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw' (24,19) Stefan Pochmann []


More than 1 F3L Slot Destroyed (Not Petrus)

OLL Parity (Only)
Alg r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r'/SiGN (21,15) Bruce Norskog & Christopher Mowla []
Alg Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw (22,16) Christopher Mowla []
Alg Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r (22,16) Christopher Mowla []
Alg Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z' (20,17) Christopher Mowla []
Alg Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x' (22,18) Christopher Mowla []
Alg Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R (23,19) Christopher Mowla []


Affect M Layer Only

OLL Parity (Only)

Alg r B2 l' D2 l' B2 r2 B2 U2 l' D2 l U2 l2 B2 (25,15) author []
Alg r2 D2 r' U2 r D2 B2 l2 B2 r U2 r B2 l' B2 (25,15) author []
Alg l r F2 l B u' B D2 B' u B r' D2 B2 l2 F2 r' (23,17) Christopher Mowla []
Alg l r F2 l B' d' B' D2 B d B' r' D2 B2 l2 F2 r' (23,17) Christopher Mowla []
Alg r' D2 l' r' B2 D2 l' B u B' D2 B u' B l D2 r2 (23,17) Christopher Mowla []
Alg r' D2 l' r' B2 D2 l' B' d B D2 B' d' B' l D2 r2 (23,17) Christopher Mowla []
Alg l' r' U2 l' D' f D' B2 D f' D' r B2 D2 l2 U2 r (23,17) Christopher Mowla []
Alg l' r' U2 l' D b D B2 D' b' D r B2 D2 l2 U2 r (23,17) Christopher Mowla []
Alg r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2 (24,17) Christopher Mowla []
Alg r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2 (24,17) Christopher Mowla []
Alg r F2 r2 F2 U2 D' l D F2 D' l' D r F2 r' U2 r2 (24,17) Christopher Mowla []
Alg r F2 r2 F2 U2 D l D' F2 D l' D' r F2 r' U2 r2 (24,17) Christopher Mowla []
Alg r' D2 l2 D2 F2 l' D b D' F2 D b' D M l D2 r2 (24,17) Christopher Mowla []
Alg r' D2 l2 D2 F2 l' D' f D F2 D' f' D' M l D2 r2 (24,17) Christopher Mowla []
Alg r2 U2 M' r U2 r' B2 U2 r2 U2 M r' B2 r' B2 r B2 (27,17) author []
Alg r2 F2 r U2 r U2 F2 r2 U2 F2 r' U2 r U2 F2 r U2 (29,17) author []
Alg r2 U2 F2 r U2 F2 r U2 r2 U2 F2 r U2 r F2 r' U2 (29,17) author []
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 []
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 []


OLL Parity + PLL Parity (Double Parity)

Alg r U2 r' U2 r' D2 r D2 r' B2 r B2 r' (19,13) Christopher Mowla []
Alg r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l' (20,14) Christopher Mowla []
reParity(v2) r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2 (23,15) reThinking the Cube []
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 []


Complete 3x3x3 Scrambles

OLL Parity (Only)

Alg Rw B U2 B' r B2 l B2 r B' D2 B Rw (17,13) Bruce Norskog []
Alg r U F2 U' l F2 2R U2 r U B2 U' r/SiGN (17,13) Bruce Norskog []
Alg r U' F2 U l F2 2R U2 r U' B2 U r/SiGN (17,13) Bruce Norskog []
Alg Uw M R D R' Bw f M d' M' Fw b M' F Uw (15,15) Bruce Norskog []
Alg Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw' (20,16) Christopher Mowla []
Alg Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw' (20,16) Christopher Mowla []
Alg r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r/SiGN (21,16) Christopher Mowla []
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 []


OLL Parity + PLL Parity (Double Parity)

Alg_1 r F2 U2 l F U' R U' r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog []
Alg_2 r F2 U2 l F' U L' U r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog []
Alg_3 r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog []
Alg_4 r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2/SiGN (19,13) Bruce Norskog []
reParity r U2 l' U2 x' (r' U2 l U2)2 l' (19,13) reThinking the Cube []
Alg Rw U' b M r' D' b D l' b2 Lw E' B' Rw (15,14) Bruce Norskog []
Alg Uw M F R' B u d l' u d F R' B M Uw (15,15) Bruce Norskog []
Alg Uw M F' L B' u d l' u d F' L B' M Uw (15,15) Bruce Norskog []
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 []


  • 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

Alg_1(v1) r U2 r U2 x U2 r U2 l' x' U2 l U2 r2 (19,12) author []
Alg_1(v2) l' B2 r' B2 D2 r' D2 r D2 l' D2 l2 (19,12) author []
Alg r U2 r U2 M' U2 r U2 r' U2 l U2 r2 (20,13) author []
Alg Rw' U2 r' U2 (Rw' l) U2 r' U2 r U2 l' U2 Rw2 (20,13) author []
Alg z Rw' U l' Uw' Rw Uw l' Fw' l' Fw l2 Uw' Rw' u Rw z' (16,15) Christopher Mowla []
Alg l F2 r F2 l D f' D r D2 r' D' f D l2 (19,15) Christopher Mowla []
Alg b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b' (17,16) Christopher Mowla []
Alg Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F' (23,16) Christopher Mowla []
Alg l' B2 l D2 r' D2 l' B2 l' D2 r' D2 l2 D2 r D2 (25,16) Christopher Mowla []
Alg l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D' (21,17) Christopher Mowla []
Alg r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D' (21,17) Christopher Mowla []
Alg r' U2 l D2 l' U2 l D2 l' U2 r' U2 r' U2 r' U2 r' (25,17) Christopher Mowla []
Alg Dw' Fw l' Fw' Uw Fw l' Uw' u' R u l' u' R' Uw u l2 Fw' y' (19,18) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []


Opposite/diagonal 2-Swap

Alg l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2 (21,14) Kenneth Gustavsson []
Alg l2 B2 U2 l U2 l2 B2 l U2 l2 U2 B2 l B2 (25,14) Nicholas Ho []
Alg r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2 (25,14) Nicholas Ho []
Alg Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' (16,15) Christopher Mowla []
Alg Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw' (16,15) Christopher Mowla []
Alg Uw Lw' Bw' r' Bw Lw2 Bw' Rw Fw' r' Fw R' Bw Lw' Uw' (16,15) Christopher Mowla []
Alg Fw' L2 Uw b' Uw' Lw2 Uw L' Uw b' Uw' Lw Uw' l2 Fw (18,15) Christopher Mowla []
Alg Fw' Uw B2 Rw' u Rw Bw2 Lw2 d Lw d' Lw b2 Uw' Fw (19,15) Christopher Mowla []
Alg Uw Rw' F2 Rw' f Rw Bw2 Lw2 u Lw u' Rw u2 Rw Uw' y2 (19,15) Christopher Mowla []
Alg Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x' (25,15) Christopher Mowla []
Alg Fw' L U' f Uw2 Lw2 Dw r Dw' Lw2 Uw f' Uw U L' Fw (19,16) Christopher Mowla []
Alg l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r (25,16) author []
Alg l' F2 D2 r' D2 F' l2 U2 l2 F' l F l2 U2 l2 F' (25,16) Christopher Mowla []
Alg Lw' U2 l U2 l U2 r' U2 l U2 l' U2 M' U2 l2 U2 Lw (26,17) author []
Alg Uw Rw Fw' L Fw d Fw' L' Fw Rw2 Fw2 Lw u Lw' Fw2 Rw b' Uw' (21,18) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []


In Adjacent Dedges

Case 1 (Close Adjacent Unoriented)

Alg l2' U Lw U2 r' U2 Rw' U2 x U' r' U x' U2 x U' M' l' (20,15) Christopher Mowla []
Alg x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x (23,15) reThinking the Cube []
Alg r U2 r U2 F' L F' r F L' F l' U2 l U2 r2 (21,16) Christopher Mowla []
Alg x' l2 F U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F' l2 x (24,16) Christopher Mowla []
Alg z F' Rw2 b' Uw Lw' Uw' b Uw b Lw b' Lw' b' Lw Uw' Rw2 F z' (19,17) Christopher Mowla []
Alg z F' Lw2 Uw Bw' l Bw Uw' Bw' Lw Uw l Uw' Lw' l' Bw Lw2 F z' (19,17) Christopher Mowla []
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 []
Alg Lw' b Uw2 Lw Uw f' Uw' Lw' Uw f' Lw f' Lw' f2 Uw b' Lw (19,17) Christopher Mowla []
Alg r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2 (23,17) Christopher Mowla []
Alg l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2 (25,17) Christopher Mowla []
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 []
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 []
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 []
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 []


Case 2 (Far Adjacent Unoriented)

Alg l2 U' Lw U2 r' U2 Rw' U2 F r' F' U2 F M' l' x (20,15) Christopher Mowla []
Alg x Rw2 F' U2 l U2 r' U2 r U2 F2 r F2 l' F Rw2 x' (23,15) Christopher Mowla []
Alg r U2 r U2 F R' F r F' R F' l' U2 l U2 r2 (21,16) Christopher Mowla []
Alg x Rw2 F' U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F Rw2 x' (24,16) Christopher Mowla []
Alg Rw r z l Fw' Uw Fw l' Fw' l' Uw' l Uw l Uw' Fw z' Rw' r' (17,17) Christopher Mowla []
Alg Rw r y Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Uw' Rw' r' (17,17) Christopher Mowla []
Alg Lw r Uw' Fw l' Fw' Uw Fw Lw' Uw' l' Uw Lw l Fw' Lw' r' (17,17) Christopher Mowla []
Alg Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw (21,17) Christopher Mowla []
Alg r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2 (23,17) Christopher Mowla []
Alg Lw2 U' M U2 l U2 r' U2 r U2 M' U2 r U2 l' U Lw2 (25,17) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []
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 []
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 []


Case 3 (Oriented Case)

Alg y' Fw2 l Uw' Bw Uw l' Uw' l' Bw' l Bw l Bw' Uw Fw2 y (17,15) Christopher Mowla []
Alg Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2 (17,15) Christopher Mowla []
Alg y' z' Fw2 Rw' Dw l' Dw' Rw Dw Lw' Bw' l' Bw Lw l Dw' Fw2 z y (17,15) Christopher Mowla []
Alg Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2 (17,15) Christopher Mowla []
Alg y' z' Fw' l' Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 l Fw z y (19,15) Christopher Mowla []
Alg Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw' (16,16) Christopher Mowla []
Alg y' Bw' R Dw r' Dw' Rw' Bw Rw' R' Dw r' Dw' Rw2 Fw' u Fw y (17,16) Christopher Mowla []
Alg y' Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw' y (19,16) Christopher Mowla []
Alg r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw' (19,16) Christopher Mowla []
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 []
Alg y' Bw' Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r Bw y (19,16) Christopher Mowla []
Alg y' l' r' U Rw U2 l' U2 Lw' U2 x' U' l' U F2 U' M' l' y (20,16) Christopher Mowla []
Alg z Uw' Rw Uw2 l' Uw r' Uw' l Uw2 R' Uw Bw2 Uw' r' Uw Bw2 z' (20,16) Christopher Mowla []
Alg x l' U L U l' U' L' U' F2 l' F2 r U2 r' U2 l2 x' (21,16) Christopher Mowla []
Alg L' B' l' U2 l' U2 x U2 l' U2 x' r U2 r' U2 l2 B L (23,16) author []
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 []
Alg x l' U L U l' U' L' U' M' U2 l' U2 l U2 r' U2 l2 x' (22,17) Christopher Mowla []
Alg x l U2 l U2 M U L U l U' L' U' l' U2 r U2 l2 x' (22,17) Christopher Mowla []
Alg Rw U2 l U2 (L M) U L' U l U' L U' l' U2 r U2 Lw2 x' (22,17) Christopher Mowla []
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 []
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 []
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 []
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 []
Alg r Uw' Lw Uw r' Uw' Fw' Uw' B Rw2 B' l B Rw2 B' Uw Fw Lw' Uw (21,19) Christopher Mowla []
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 []
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 []
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 []
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 []
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 []
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 []


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

Alg Rw2 U2 r' E2 r E2 r' U2 Rw2 (15,9) Tom Rokicki & Ed Trice []
Alg (f2 u' r2 Uw2 S') r (S Uw2 r2 u f2) (17,11) Christopher Mowla []
Alg (f2 u r2 Uw2 S') r (S Uw2 r2 u' f2) (17,11) Christopher Mowla []
Alg r2 U2 r S2 r S2 r' U2 l2 f2 M2 f2 (21,12) author []
Alg r2 U2 r S2 r S2 r' U2 l2 b2 M2 b2 (21,12) author []
Alg r S' L2 S r U2 r U2 r S' L2 S r (17,13) Christopher Mowla []
Alg r S R2 S' r U2 r U2 r S R2 S' r (17,13) Christopher Mowla []
Alg (Rw2 Uw U S Lw2 u2) r (u2 Lw2 S' U' Uw' Rw2) (19,13) Christopher Mowla []
Alg (Rw2 Uw' U' S Lw2 u2) r (u2 Lw2 S' U Uw Rw2) (19,13) Christopher Mowla []
Alg Rw2 S r' U2 r' U2 r' U2 r' U2 r' S' Rw2 (19,13) Christopher Mowla []
Alg Rw2 S' r' U2 r' U2 r' U2 r' U2 r' S Rw2 (19,13) Christopher Mowla []
Alg_(v1) r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r' (21,13) author []
Alg_(v2) l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l' (21,13) author []


Bowtie/Hourglass

  • 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.


Alg r U2 r U2 F2 r F2 l' U2 M r' Uw2 r2 u2 (22,14) author []
Alg r U2 r U2 M' U2 r U2 r' U2 M r' Uw2 r2 u2 (23,15) author []
Alg r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2 (25,15) author []
Alg r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2 (25,16) author []
Alg (B' R Uw' u' r' f2 Rw2 E) f' (E' Rw2 f2 r u Uw R' B) (21,17) Christopher Mowla []
Alg (B' R Uw' u' r f2 Rw2 E) f' (E' Rw2 f2 r' u Uw R' B) (21,17) Christopher Mowla []
Alg r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r' (26,17) author []


In Adjacent Dedges

Checkboard

Alg F2 Uw' F2 Rw2 Uw2 R2 z' S u F' B' Uw2 Rw2 Uw' F2 (22,14) Tom Rokicki []
Alg (F U' F' Rw2 U2) r' E2 r E2 r' (U2 Rw2 F U F') (21,15) Tom Rokicki & Ed Trice []
Alg (R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2) (21,15) Christopher Mowla []
Alg (R2 Uw' u' r f2 Rw2 E) f (E' Rw2 f2 r' u Uw R2) (21,15) Christopher Mowla []
Alg (Rw' F2 M2 F) U2 l U2 l2 U2 l U2 l (F' M2 F2 Rw) (25,16) Christopher Mowla []
Alg (Lw' U2 M2 U) M U2 l U2 l2 U2 l U2 r (U' M2 U2 Lw) (26,17) Christopher Mowla []
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 []


Bowtie/Hourglass

Alg R B Rw2 U2 r' E2 r E2 r' U2 Rw2 B' R' (19,13) Tom Rokicki & Ed Trice []
Alg (R Fw f r u2 Rw2 S) u' (S' Rw2 u2 r' Fw' f' R') (19,15) Christopher Mowla []
Alg (R Fw f r' u2 Rw2 S) u' (S' Rw2 u2 r Fw' f' R') (19,15) Christopher Mowla []
Alg F' Lw U D Lw2 Bw2 Rw' R' U' D B2 Lw2 Fw2 D2 Lw' F (21,15) Tom Rokicki []
Alg (Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw) (25,16) Christopher Mowla []
Alg R B r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r B' R' (25,17) author []
Alg (r U2 M2 U') M' U2 l' U2 l2 U2 l' U2 r' (U M2 U2 r') (26,17) Christopher Mowla []
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 []


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).


Arranged by Rank (Worst Last Layer Cases Are First)
Last Layer Case Minimum SQTM Minimum STM Optimal Average Rank
Adjacent Double Parity 23 16 19.5 1
One Dedge Flip 19 15 18.5 2
Bowtie/Hourglass 21 14 18 3
Adjacent Checkerboard 21 14 18 3
Adjacent 2-Cycle Case 1 (Close "Unoriented" Case) 19 15 17.5 4
Double Parity 21 14 17.5 4
Adjacent 2-Cycle Case 2 (Far Adjacent "Unoriented" Case) 17 15 17 5
Adjacent Bowtie/Hourglass 19 13 16 6
Adjacent 2-Cycle Case 3 (“Oriented" Case) 16 15 16 6
Opposite/diagonal 2-swap 16 14 15.5 7
Adjacent 2-swap 16 12 15.5 7
Checkerboard Pattern 15 9 12 8

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

Alg Rw2 U r' U' B2 U r U r' U2 B2 Rw2 (17,12) Christopher Mowla []
Alg Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2 (17,12) Christopher Mowla []
Alg Rw2 (Dw u') l U' R2 U l' U y r U2 F2 Rw2 (17,12) Christopher Mowla []
Alg Lw2 (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw2 (17,13) Christopher Mowla []
Alg Rw2 U' r' U B2 U' r U B2 D2 l D2 Rw2 (19,13) Christopher Mowla []
Alg Rw2 (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw2 (19,13) Christopher Mowla []
Alg Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2 (21,13) author []
Alg Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2 (21,13) author []
Alg l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2 (21,13) author []
Alg r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r (15,14) Christopher Mowla []
Alg r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r (21,14) Lucas Garron []
Alg r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r (21,14) Nicholas Ho []
Alg x r R' U' Rw U' r U Rw' r' U R U' r U r' x' (15,15) author []


One Dedge Flip + PLL Parity (Double Parity)

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


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

Alg (r2 U' Rw U' R' U') r' (U R U Rw' U r2) (15,13) Christopher Mowla []
Alg (r2 U F2 U' r' F2) r (F2 r U F2 U' r2) (19,13) Christopher Mowla []
Alg Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw (16,14) Christopher Mowla []
Alg (x Uw F U r' U R' U) r (U' R U' r U' F' Uw' x') (15,15) Christopher Mowla []
Alg x' r2 U' Rw U' l' U2 l' U2 l' U2 l2 U' Rw' U r2 x (21,15) Christopher Mowla []


Three Flips

OLL Parity (Only)

Alg (r2 F2 U) r U2 r' U2 r U2 r' U2 r (U' F2 r2) (23,15) Christopher Mowla []
Alg (r2 U2 F' M' U) r U2 r' U2 r U2 r' U2 r (U' M F U2 r2) (27,19) Christopher Mowla []


OLL Parity + PLL Parity (Double Parity)

Alg (r' U' F' R' F R2 U') r' (U R2 F' R F U r) (r U2 r' U2) (23,18) Christopher Mowla []


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

Adjacent 2-Swap

Alg l U' l' U' F2 U l U' F2 U2 (13,10) Christopher Mowla []
Alg l U l' U F2 U' l U F2 U2 (13,10) Christopher Mowla []
Alg z2 y' U2 R2 U l U' R2 U l' U y r z2 (13,10) Christopher Mowla []
Alg l F2 r' U2 l U2 l' U2 r U2 F2 (17,11) author []
Alg l' U Lw' U L U' l' U L' U' Lw l U' (13,13) author []


Opposite/Diagonal 2-Swap

  • Some of these are nearly the same as the one dedge flip algorithms.
Alg Lw' U' l U B2 U' l' U' l U2 B2 Lw (15,12) Christopher Mowla []
Alg Lw' U l U' B2 U l' U l U2 B2 Lw (15,12) Christopher Mowla []
Alg Lw' (Dw' u) r' U L2 U' r U' y' l' U2 F2 Lw (17,12) Christopher Mowla []
Alg x' U Rw' U r' U' Rw r U' R' U r' U' R x (13,13) Marc Waterman []
Alg x' R U Rw' U r' U' Rw r U' R' U r' U' x (13,13) Marc Waterman []
Alg x' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' x (13,13) Christopher Mowla []
Alg Lw' (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw (15,13) Christopher Mowla []
Alg Lw' U l U' B2 U l' U' B2 D2 r' D2 Lw (17,13) Christopher Mowla []
Alg Lw' (Dw' u) r' U L2 U' r U D2 y' r' D2 F2 Lw (17,13) Christopher Mowla []
Alg (x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x) (19,13) author []
Alg Lw' U2 l' U2 r U2 r' U2 l F2 l' F2 Lw (19,13) author []
Alg Lw' U2 l' U2 r U2 r' U2 l B2 r' B2 Lw (21,13) author []
Alg M' l' U2 l' U2 l U2 r' U2 l U2 l' U2 l (20,14) Nicholas Ho []


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

Adjacent 2-Swap

Alg y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw (13,12) Christopher Mowla []
Alg U' Rw' U r' U' Rw r U' R' U r' U' R U2 (15,14) Francois Courtes []


Opposite/Diagonal 2-Swap

  • These are the same as the one dedge flips but without first and last moves.
Alg U r' U' B2 U r U r' U2 B2 (13,10) Christopher Mowla []
Alg U' r' U B2 U' r U' r' U2 B2 (13,10) Christopher Mowla []
Alg (Dw u') l U' R2 U l' D l U' D' R2 y (13,11) Christopher Mowla []
Alg U' r' U B2 U' r U B2 D2 l D2 (15,11) Christopher Mowla []
Alg (Dw u') l U' R2 U l' U' D2 y l D2 F2 (15,11) Christopher Mowla []
Alg x' U2 l U2 r' U2 r U2 l' F2 r F2 x (17,11) author []
Alg U2 r U2 l' U2 l U2 r' F2 r F2 (17,11) author []
Alg U2 r U2 l' U2 l U2 r' B2 l B2 (17,11) author []


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

Checkboard

Alg Rw2 U2 r U2 Rw2 (9,5) Marc Waterman []


Bowtie/Hourglass

Alg (y L' U B' Rw2 U2) r' (U2 Rw2 B U' L y') (15,11) author []
Alg (y L F' U Rw2 F2) r (F2 Rw2 U' F L' y') (15,11) author []
Alg r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x (19,12) Nicholas Ho []
Alg r2 U2 r U2 x' D2 r' U2 r D2 r' U2 r' x (19,12) Kenneth Gustavsson []


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)

Alg Rw2 U r' U' B2 U r U r' B2 Rw2 (15,11) Christopher Mowla []
Alg Rw2 U' r' U B2 U' r U' r' B2 Rw2 (15,11) Christopher Mowla []
Alg Rw2 U f U' B2 U f' U l B2 Rw2 (15,11) Christopher Mowla []
Alg r' U' R U' r U2 r U2 r U' R' U' r' (15,13) Christopher Mowla []
Alg r' U' R U r' U2 r' U2 r' U R' U' r' (15,13) Christopher Mowla []
Alg r' U' R U r' F2 U2 r U2 F2 r' U R' U' r' (19,15) Christopher Mowla []


OLL Parity + PLL Parity (Double Parity)

Alg Rw U R B R' l Fw2 r' Fw2 U' Rw2 x (14,11) Bruce Norskog []
Alg Rw U R B l Fw2 r' Fw2 R' U' Rw2 x (14,11) Bruce Norskog []
Alg Rw2 U r' U' B2 U r U r B2 Rw2 (15,11) Christopher Mowla []
Alg Rw2 U' r' U B2 U' r U' r B2 Rw2 (15,11) Christopher Mowla []
Alg Rw2 U f U' B2 U f' U l' B2 Rw2 (15,11) Christopher Mowla []
Alg Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2 (21,15) Christopher Mowla []
Alg Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw' (21,15) Kåre Krig & Christopher Mowla []


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


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.
Alg r' U' B2 U r U r' (8,7) Christopher Mowla []
Alg r' U B2 U' r U' r' (8,7) Christopher Mowla []
Alg r' U L2 U' r D' r' (8,7) Christopher Mowla []
Alg r' U' R2 U r D r' (8,7) Christopher Mowla []


External Links

OLL Parity Algorithms

OLL Parity Algorithms which don't preserve F3L

PLL Parity Algorithms

SuperCube Parity Algorithms

Miscellaneous

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