4x4x4 parity algorithms
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Revision as of 05:48, 26 December 2012 by Cmowla (talk | contribs) (→More than 1 F3L Slot Destroyed (Not Petrus))
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:
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Alg | (r U2)4 r/(13,9) |
For those who are familiar with commutators and conjugates, this quick parity fix can be represented as [r: [U2, r] [r2 U2: r] ]. In fact, we can do the same 4-cycle of wing edges with just one conjugate [r2 d' r2 Uw2 S': r'].
The phrase "there is more than one way to solve any given problem" holds true with tackling 4x4x4 parity situations. In fact, there are different categories of parity algorithms, and algorithms can consist of different move patterns (the move set of one algorithm might be entirely different than the algorithm above and/or below it).
This page not only contains commonly practiced speedsolving algorithms, but it also contains algorithms which illustrate the veracity of the 4x4x4 cube parity algorithm domain.
NOTES
- Algorithms with a lower btm (block half turn) move count are listed first in each category.
- Most of these algorithms affect centers on the 4x4x4 supercube: not all algorithms affect the supercube centers in the same manner.
- All algorithms can be applied to the 6x6x6 if instead of turning the outer 2 layers, you turn the outer 3 layers. For slice moves, instead of turning 1 slice layer, you turn 2 slices.
Contents
- 1 PLL Parity (WCA Notation)
- 2 OLL Parity
- 3 Additional Last Layer 4-Cycle Cases in Two Dedges
- 4 Additional Last Layer 2-Cycle Cases
- 5 Summary of 2-Cycle and 4-Cycle ELL Case Movecounts
- 6 OLL Parity Algorithms Which Don't Preserve F3L (WCA Notation)
- 7 Algorithms Which Don't Preserve the Centers (WCA Notation)
- 8 Parity Algorithms Which Don't Preserve F3L or the Colors of the Centers (WCA Notation)
- 9 External Links
PLL Parity (WCA Notation)
Dedges
- Algorithms marked as "Safe" are supercube safe.
Two Dedges (Oriented)
Opposite
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Alg | r2 U2 r2 Uw2 r2 u2/(12,6) |
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Alg | r2 U2 r2 Uw2 r2 Uw2/(12,6) |
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Alg | (Rw2 R2') U2 (Rw2 R2') Uw2 (Rw2 R2') Uw2/(12,6) |
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Alg | Uw2 Rw2 U2 (Rw2 R2') U2 Rw2 Uw2/(14,7) |
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Alg | Uw2 Rw2 U2 r2 U2 Rw2 Uw2/(14,7) |
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Alg | Rw2 B2 U2 r2 U2 B2 Rw2/(14,7) |
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Alg | r2 U2 B2 l r U2 M' U2 r2 B2 U2/Safe(19,11) |
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Alg | r2 U2 r U2 r2 U2 r2 U2 r U2 r2 U2/Safe(22,12) |
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Alg | r' F U' R F' U l r U' F R' U F' l'/Safe(14,14) |
Adjacent
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Alg | (R2 D' x) r2 U2 r2 Uw2 r2 u2 (x' D R2)/(18,10) |
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Alg | (R2 D' x) Rw2 F2 U2 r2 U2 F2 Rw2 (x' D R2)/(20,11) |
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Alg | (F2 U Rw2 U2 F2) r2 (F2 U2 Rw2 U' F2)/(20,11) |
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Alg | y' R' F l E F2 E' l' r' E F2 E' r F' R y/Safe(16,14) |
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Alg | y' R' F l E' F2 E l' r' E' F2 E r F' R y/Safe(16,14) |
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Alg | (Rw' U R U Lw' U2 Rw' U2) r2 (U2 Rw U2 Lw U' R' U' Rw)/(22,17) |
Two Dedges (Unoriented)
Opposite
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Alg | F2 l E F2 E' l' r' E F2 E' r F2/Safe(16,12) |
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Alg | F2 l E' F2 E l' r' E' F2 E r F2/Safe(16,12) |
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Alg | (y R' U F') r2 U2 r2 Uw2 r2 u2 (F U' R y')/(18,12) |
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Alg | r U2 l D2 l' U2 M U2 r D2 r' U2 l'/Safe(19,13) |
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Alg | (y' R' F U' Rw2 U2 F2) r2 (F2 U2 Rw2 U F' R y)/(20,13) |
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Alg | (y R' U F' Rw2 F2 U2) r2 (U2 F2 Rw2 F U' R y')/(20,13) |
Adjacent
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Alg | (R B) r2 U2 r2 Uw2 r2 u2 (B' R')/(16,10) |
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Alg | (R B Rw2 F2 U2) r2 (U2 F2 Rw2 B' R')/(18,11) |
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Alg | ((Lw r') U Rw2 U2 F2) r2 (F2 U2 Rw2 U' (Lw' r))/(18,11) |
Four Dedges (Oriented)
Circular 4-cycle of Dedges
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Alg | r2 Uw2 r2 b2 U' r2 b2 U b2 Uw2 r2/(20,11) |
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Alg | M2 U' r2 U2 F2 r2 F2 U2 l r U2 M' U' M2/(23,14) |
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Alg | l r (U y') L R u' L' R' (U' y) M2 (U' y) L' R' u' L R (U y') l r/Safe(20,19) |
Zigzag 4-cycle of Dedges
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Alg | (r2 U2 r2 Uw2 r2 u2) (F2 U M' U2 M U F2)/(22,13) |
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Alg | R2 Uw2 B2 R2 Uw2 B2 R2 U R2 B2 R2 U B2 Uw2/(26,14) |
Two Corner Swaps
Adjacent
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Alg | R U' R B2 L' D L B2 R2 U r2 F2 r2 Fw2 r2 f2/(25,16) |
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Alg | B2 L U L' B2 R D' r2 F2 r2 Fw2 r2 f2 R D R2/(25,16) |
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Alg | z r2 U2 R' U2 R' U2 R x U2 Rw2 U2 B2 L U2 L' U2 Rw2 U2 z' y'/(29,17) |
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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) |
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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) |
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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) |
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Alg | z' x Rw2 R' U2 Rw U2 Rw2 U2 Rw2 U2 L Rw U2 R' U2 R U2 L' R U2 R U2 Rw2 x' z/(35,22) |
Opposite/Diagonal
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Alg | Rw2 f2 U2 Fw2 U' Rw2 U2 Fw2 U Fw2 R2 U2 F2 Rw2 U/(27,15) |
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Alg | Rw2 F2 U2 y Rw2 U' Rw2 U D Lw2' U' Lw2' y' r2 U2 F2 Rw2 U/(27,16) |
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reParity | z (R2' Uw2' R2 U R2') y (R2 U2 R2' U' R2) y' (R2' Uw2' R2 (Dw' u) R2) Uw2 U2 y' z' /(29,16) |
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Alg | r2 F2 R' F2 U2 R2 U2 R' F2 R2 U2 Rw' r' U2 F2 Rw2 U2/(30,17) |
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Alg | r2 B2 R' U2 Rw2 U2 B2 R' B2 r2 U2 Rw2 B2 U2 R' U2 Rw2/(31,17) |
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Alg | r2 U2 r2 Uw2 r2 Uw2 L' U R' U2 L U' L' R U R' U2 L U' R U/(29,21) |
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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) |
Two Corner Swaps (Only 2 X-center Piece Exchange on the Supercube)
Adjacent
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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) |
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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) |
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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) |
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Alg | 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'/(28,26) |
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Alg | 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'/(28,26) |
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Alg | 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 y2/(29,26) |
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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) |
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Alg | 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/(29,27) |
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Alg | 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/(29,28) |
Opposite/Diagonal
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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) |
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Alg | F Rw' F Rw2 U' Rw' U' Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' F'/(30,28) |
Two X-Center Piece Swap Algorithms
- These algorithms, and other algorithms like them, are used to make two corner swap algorithms which only swap two X-center pieces on the 4x4x4 supercube.
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Alg | Rw U' Lw Uw2 Rw' U Rw Uw2 x Rw2 U/(13,10) |
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Alg | Fw' U' Rw Fw Rw' U' Rw Fw' Rw' U2 Fw U'/(13,12) |
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Alg | Rw U Rw' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'/(15,14) |
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Alg | Rw' U' Lw U Lw' U' Rw U Lw U' Lw' Rw' U Rw U/(15,15) |
- Algorithms for almost all PLL Parity cases can be found here http://www.math.leidenuniv.nl/~mfung/speedcubing/algs/4x4x4/
OLL Parity
- Algorithms in WCA notation are labeled.
Impure Dedge Flips (SiGN Notation)
OLL Parity (Only)
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cmowlaparity | x' r2 U2 l' U2 r U2 r U2 x' U r U' F2 U r' U r2 x/(23,16) |
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Alg | r U2 x U2 F' r' F U2 F' r F r U2 r' U2 x' r' U2 r'/(23,17) |
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lucasparity | r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'/(25,17) |
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lucasparity | r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 x' r' U2 r'/(25,17) |
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Alg | r U2 r2 U2 x' U r U' F2 U r' U' l' U2 r U2 r' U2 r'/(25,18) |
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Alg | r2 B2 3d' r' 3d r U2 r' 3d' r U' y' r' U2 r' U2 r B2 r2/(25,18) |
OLL Parity + PLL Parity (Double Parity)
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Alg_1(v1) | r' U2 r' U2 l U2 r' U2 r U2 x U2 r2 U2 r' U2 r/(25,16) |
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Alg_1(v2) | l U2 l U2 r' U2 l U2 l' U2 x U2 l2 U2 l U2 l'/(25,16) |
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Alg_2(v1) | r U2 r' U2 r U2 r U2 l' U2 r U2 r' U2 x' U2 r2/(25,16) |
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Alg_2(v2) | l' U2 l U2 l' U2 l' U2 r U2 l' U2 l U2 x' U2 l2/(25,16) |
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Alg_3(v1) | r2 U2 x' U2 r' U2 r U2 l' U2 r U2 r U2 r' U2 r/(25,16) |
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Alg_3(v2) | l2 U2 x' U2 l U2 l' U2 r U2 l' U2 l' U2 l U2 l'/(25,16) |
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Alg_4(v1) | r U2 r' U2 r2 U2 x U2 r U2 r' U2 l U2 r' U2 r'/(25,16) |
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Alg_4(v2) | l' U2 l U2 l2 U2 x U2 l' U2 l U2 r' U2 l U2 l/(25,16) |
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Alg_5(v1) | Rw U2 Rw U2 Rw U R Rw U2 R2 U Rw U Rw2 R U Rw U' Rw/(23,19)(WCA) |
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Alg_5(v2) | Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' Rw2 R' U' Rw' U Rw'/(23,19)(WCA) |
Impure Dedge Flips with Wide Turns/Pure Flips with Inner Layer Turns (SiGN Notation)
- 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)
- Note that all 26 possible (25,15) solutions (excluding mirrors and inverses) of this category are listed.
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Frédérick_Badie(v1) | r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2/(25,15) |
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Frédérick_Badie(v2) | r' U2 r U2 l' U2 l2 F2 r F2 l' U2 F2 r2 F2/(25,15) |
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Frédérick_Badie(v3) | r B2 r' U2 r U2 r2 F2 r' D2 l D2 B2 r2 F2/(25,15) |
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Frédérick_Badie(v4) | r B2 r' U2 r U2 l2 B2 r' U2 l U2 F2 l2 F2/(25,15) |
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Frédérick_Badie(v5) | r B2 l' B2 l U2 r2 F2 l' F2 r U2 F2 l2 F2/(25,15) |
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Alg.2(v1) | r B2 r' U2 l B2 l2 B2 U2 l U2 l' U2 l2 B2/(25,15) |
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Alg.2(v2) | r B2 r' U2 r D2 r2 U2 F2 l F2 r' D2 r2 B2/(25,15) |
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Alg.2(v3) | r B2 r' U2 r D2 l2 D2 B2 l B2 r' U2 l2 B2/(25,15) |
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Alg.2(v4) | r B2 l' B2 l D2 l2 D2 B2 r D2 l' D2 r2 B2/(25,15) |
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Alg.2(v5) | r' U2 r U2 l' D2 r2 D2 B2 l' D2 r D2 l2 B2/(25,15) |
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Alg.3(v1) | r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2/(25,15) |
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Alg.3(v2) | r2 B2 U2 l U2 l' B2 r B2 U2 r U2 r' B2 r2/(25,15) |
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Alg.3(v3) | r2 F2 D2 r' D2 r F2 l' F2 D2 l' D2 l F2 r2/(25,15) |
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Alg.3(v4) | r2 F2 D2 r' D2 l D2 l' D2 B2 l' B2 r F2 r2/(25,15) |
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Alg.3(v5) | r2 B2 U2 r B2 r' B2 l U2 F2 r F2 l' B2 r2/(25,15) |
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Alg.3(v6) | r2 F2 D2 l' F2 l F2 r' D2 B2 l' B2 r F2 r2/(25,15) |
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Alg.3(v7) | r2 B2 U2 r B2 l' D2 r D2 B2 l U2 r' B2 r2/(25,15) |
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Alg.3(v8) | r2 F2 D2 l' F2 r U2 l' U2 F2 r' D2 l F2 r2/(25,15) |
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Alg.4(v1) | r2 B2 U2 l' U2 r U2 r' U2 B2 r' B2 l B2 r2/(25,15) |
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Alg.4(v2) | r2 B2 U2 l' U2 l F2 r' F2 U2 r' U2 r B2 r2/(25,15) |
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Alg.4(v3) | r2 F2 D2 r D2 r' B2 l B2 D2 l D2 l' F2 r2/(25,15) |
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Alg.4(v4) | r2 F2 D2 r D2 l' D2 l D2 F2 l F2 r' F2 r2/(25,15) |
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Alg.4(v5) | r2 B2 U2 r' F2 r F2 l' U2 B2 r' B2 l B2 r2/(25,15) |
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Alg.4(v6) | r2 B2 U2 r' F2 l D2 r' D2 F2 l' U2 r B2 r2/(25,15) |
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Alg.4(v7) | r2 F2 D2 l B2 r' U2 l U2 B2 r D2 l' F2 r2/(25,15) |
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Alg.4(v8) | r2 F2 D2 l B2 l' B2 r D2 F2 l F2 r' F2 r2/(25,15) |
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cmowlaparity | x' r2 U2 l' U2 r U2 l F2 U r U' F2 U r' U r2 x/(23,16) |
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Alg | r U2 F2 D' r' D F2 D' r D r F2 r' F2 r' U2 r'/(23,17) |
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lucasparity | r U2 r U2 r' U2 r U2 l' U2 l F2 r' F2 r' U2 r'/(25,17) |
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Alg | r2 U2 l' U2 r U2 r' U2 r U2 r' x' U2 r' U2 r2 F2 l x/(27,17) |
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Alg | r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 l r2 U2 r'/(27,18) |
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Alg | r2 F2 r' U2 r U2 r' U2 r U2 r' F2 r' U2 l' r' U2 l/(27,18) |
OLL Parity + PLL Parity (Double Parity)
- If the following group of algorithms is executed using WCA notation (where lowercase = inner layer turns), pure one dedge flips + PLL Parity will result.
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Alg | r2 B2 r' U2 r' U2 x' U2 r' U2 r U2 r' U2 r2 U2 x/(25,15) |
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Alg | r U2 r' U2 r U2 r U2 r' x U2 r U2 r' U2 x' U2 r2 U2/(27,17) |
Pure Flips (WCA Notation)
- Algorithms in SiGN Notation are labeled.
- Algorithms marked as "Safe" are supercube safe.
One Dedge Flip
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cmowlaparity | x' Rw2 U2 Lw' U2 r U2 Rw U2 x' U r U' F2 U r' U Rw2 x/(23,16) |
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Alg | x' Rw2 U2 Lw' U2 r U2 Rw U2 x' U' r U F2 U' r' U' Rw2 x/(23,16) |
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Alg | Rw Uw2 x' U D r y Uw2 Rw2 Uw r Uw' Rw2 Dw r' u D' x Uw2 Rw'/(22,17) |
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Alg | Rw U2 F2 D' r' D F2 D' r D Rw F2 r' F2 Rw' U2 Rw'/(23,17) |
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Alg | Rw U2 F2 D r' D' F2 D r D' Rw F2 r' F2 Rw' U2 Rw'/(23,17) |
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lucasparity | Rw U2 Rw U2 r' U2 r U2 l' U2 l F2 r' F2 Rw' U2 Rw'/(25,17) |
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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) |  [1]
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Alg | Rw' E Uw2 Fw Uw Rw' r' Fw' r Fw Rw Uw' Fw' Uw r Uw E' Rw/(19,18) |
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Alg | Lw' S Bw2 Dw r Dw' Bw Dw r' Dw' r' Bw' r Bw r Bw S' Lw/(19,18) |
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Alg | Lw' F' b' Rw' Bw' Rw u Rw' Bw Rw u2 Bw' u Bw u b F Lw/(19,18) |
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Alg | Rw2 F' r U' R U' r' U R' U r' F' U2 r' U2 r F2 Rw2/(23,18) |
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Alg | z r f2 3u U y' 2R' u2 y' l2 u' 2R' u l2 u' 2R 3u' u' U' x' u2 r' z/(23,18)(SiGN) |
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Alg | Rw2 B2 U' b' U r U2 r' U' b U' Rw' U2 r' U2 Rw B2 Rw2/(25,18) |
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Alg | Rw U2 Rw2 U2 x' U r U' F2 U r' U' Lw' U2 r U2 Rw' U2 Rw'/(25,18) |
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Alg | Rw U2 Rw2 U2 x' U' r U F2 U' r' U Lw' U2 r U2 Rw' U2 Rw'/(25,18) |
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Alg | Rw U2 Rw U2 r' U2 Rw U2 l' U2 r U2 r' U2 (Rw' l) Rw' U2 Rw'/(27,18) |
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Alg | r2 U2 r2 U2 r U2 r U2 r' U2 B2 U' r' U B2 U' r U'/(27,18) |
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Alg | r2 U2 r2 U2 r U2 r U2 r' U2 B2 U r' U' B2 U r U/(27,18) |
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Alg | Rw' E Uw b' Uw r Uw r' Uw' b Uw r' Uw' r Uw r Uw E' Rw/(19,19) |
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Alg | Rw' E Uw' r' Uw Lw' Uw' Fw Rw' Fw' r' Fw r Rw Fw' Uw Lw E' Rw/(19,19) |
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Alg | Rw' D' u' Uw' Rw f Rw' Uw Rw f' Rw' f' Uw' f Uw f u D Rw/(19,19) |
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Alg | Rw' E R Uw' Fw' u' Fw Uw2 Bw' Uw Fw' u' Fw U' Bw Uw' R' E' Rw/(20,19) |
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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) |
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Alg | Rw' E r' f' Dw' f' Dw Fw Lw' f Fw Dw' f' Dw Fw' Lw F' r E' Rw/(20,20) |
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Alg | Uw Fw' D r' Dw b Dw b' Dw' r Dw b' Dw' b Dw b Dw2 D' Fw Uw'/(21,20) |
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Alg | Fw' U' l u2 Lw Bw' Lw' u Lw Uw Bw u' Bw' Uw' Bw Lw' u l' U Fw/(21,20) |
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Alg | Rw U L F' U l' Dw Uw Rw2 Dw' l' Dw Rw2 Dw' l Uw' U' F L' U' Rw'/(23,20) |
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Alg | Bw' R' u Rw' r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' Rw u' R Bw/(21,21) |
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Alg | Bw' R' u Rw' l' Dw Bw' Dw' l Dw Lw Bw l' Bw' Lw' Bw Dw' Rw u' R Bw/(21,21) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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) |
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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) |
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Alg | 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/(34,26) |
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Alg | 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/(34,26) |
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Alg | Rw U2 Rw U Rw U2 Rw U2 Rw' U2 Rw' U r' U' Rw U2 Rw U2 Rw' U2 Rw' U r2 U2 Rw' U2 Rw'/(37,27) |
One Dedge Flip + PLL Parity (Double Parity)
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Alg_1 | r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l y2/(21,14) |
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Alg_2(v1) | r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 B2/(25,15) |
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Alg_2(v2) | r2 F2 r U2 r U2 F2 r F2 r' F2 r F2 r2 F2/(25,15) |
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Alg_3 | Rw2 B2 U2 l r2 U2 r' U2 r U2 F2 r F2 l' B2 Rw2/(26,16) |
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Alg_4 | r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 U2 r' U2 r/(26,17) |
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Alg_5 | r' U2 r U2 r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2/(26,17) |
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Alg_6 | (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) |
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Alg_7 | (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) |
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Alg_8 | r' U' R' U' r' U R U r U2 r' U' R' U' r2 U R U r U2 r U2 r' U2/(29,24) |
One Dedge Flip + Adjacent PLL Parity (Adjacent Double Parity)
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Alg | (r2 F Rw' F') U2 r U2 r U2 r U2 r2 (F Rw F' r2)/(23,16) |
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Alg | (Rw' z' L' U r F) U2 r U2 r U2 r U2 r2 (F' r' U' L z Rw)/(23,18) |
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Alg | (x' r2 U' Rw U) M' U2 r' U2 r' U2 r' U2 l r (U' Rw' U r2 x)/(24,18) |
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Alg | R B r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l y2 B' R'/(25,18) |
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Alg | (R B r2 B2) r' U2 r' U2 B2 r' B2 r B2 r' (B2 r2 B R')/(27,18) |
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Alg | Rw U2 x U' Rw R U' r U2 r U2 r U2 r2 U' Rw' R' U x' U2 Rw'/(25,19) |
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Alg | Rw2 U x' U2 r U2 r' F2 l F2 U' L' U' l U L U l' x U' Rw2/(25,19) |
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Alg | r2 F' R' F' U2 l F2 D2 r D2 l' F' r' F' U2 F Rw F r2/(26,19) |
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Alg | M' U F2 r' B2 r B2 r F2 r' U' r' F R' F r F' R F' l/(24,20) |
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Alg | (Rw2 U x') U2 r U2 l' U2 l U2 M U' L' U' l U L U l' (x U' Rw2)/(26,20) |
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Alg | Rw2 F L F U2 l F2 D2 r D2 l' F r' F U2 F' r L' F' Rw2/(27,20) |
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Alg | (z' Rw' U' Rw' l' U L') U r U2 r U2 r U2 r2 U (L U' l Rw U Rw z)/(25,21) |
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Alg | (Rw2 F' L F r f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 r' F' L' F Rw2)/(29,21) |
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Alg | (x' Lw2 F' L2 F r f2 u' r2 Uw2 S') r (S Uw2 r2 u f2 r' F' L2 F Lw2 x)/(31,21) |
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Alg | x Uw F U r' U R' U r' U' R U' r' S' L2 S r' S' L2 S r' U' F' Uw' x'/(25,23) |
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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) |
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Alg | (Bw' R U b' R' Bw' Uw2 Rw' u2 l2 S') u (S l2 u2 Rw Uw2 Bw R b U' R' Bw)/(29,23) |
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Alg | (l2 z' F' Uw L Uw M Uw2 r' u2 Lw2 S') u (S Lw2 u2 r Uw2 M' Uw' L' Uw' F z l2)/(31,23) |
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Alg | Uw Fw' r Fw Uw' Fw' r Uw2 L' Uw' R' F' R F U' R U r U' R' U F' R' F R Uw L Uw2 r2 Fw/(33,30) |
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Alg | Uw Fw' r Fw Uw' Fw' r Uw2 L' Uw' R' U' F' R F R U r U' R' F' R' F U R Uw L Uw2 r2 Fw/(33,30) |
Three Flips
OLL Parity (Only)
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Alg | M U l' B2 r D2 r B2 l2 B2 U2 r D2 r' U2 r2 B2 U' M'/(29,19) |
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Alg | Rw U Rw U2 Rw U2 Rw U Rw' U2 r' U2 Rw' U Rw U2 Rw U2 Rw U Rw/(27,21) |
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Alg | Uw2 F2 Rw U R' U' Rw' U2 Rw U R U r U2 Rw F2 r' F2 Rw U2 Rw r F2 Uw2/(33,24) |
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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) |
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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) |
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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) |
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Alg | (Rw' U' F' R' F R2 U') r (U R2 F' R F U Rw) (D' U' F2 U D) (r' F2 r F2) (F2 r2 F2 r2 F2 r2 F2) (D' U' F2 U D) /(43,33) |
OLL Parity + PLL Parity (Double Parity)
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Alg | Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw R U2 x/(24,19) |
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Alg | M U r U2 r2 U2 r' U2 F2 r' F2 r2 U2 l F2 l' F2 r2 U' M'/(31,20) |
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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) |
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Alg | (r' U2 M l U) (r' U' F' R' F R2 U') r' (U R2 F' R F U r) r U2 r' U2 (U' M' l' U2 r)/(33,27) |
- For algorithms for OLL + OLL Parity and OLL Parity + F3L, see http://www.math.leidenuniv.nl/~mfung/speedcubing/algs/4x4x4/
Additional Last Layer 4-Cycle Cases in Two Dedges
- These are all of the other 4-cycles which can occur in two dedges besides double parity and adjacent double parity.
In Opposite Dedges
Checkerboard
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Alg_1 | (f2 u' r2 Uw2 S') r (S Uw2 r2 u f2)/(17,11) |
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Alg_2 | f2 M2 f2 l2 U2 r S2 r' S2 r' U2 r2/(21,12) |
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Alg_2 | r S' L2 S r U2 r U2 r S' L2 S r/(17,13) |
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Alg_2 | r S R2 S' r U2 r U2 r S R2 S' r/(17,13) |
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Alg_2 | r2 S r U2 r U2 r U2 r U2 r S' r2/(19,13) |
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Alg_2 | r2 S' r U2 r U2 r U2 r U2 r S r2/(19,13) |
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Alg_3(v1) | r U2 r2 U2 r' U2 r U2 r' U2 r2 U2 r/(21,13) |
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Alg_3(v2) | l' U2 l2 U2 l U2 l' U2 l U2 l2 U2 l'/(21,13) |
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Alg_3(v3) | r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'/(21,13) |
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Alg_3(v4) | l U2 l2 U2 l' U2 l U2 l' U2 l2 U2 l/(21,13) |
Bowtie/Hourglass
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Alg_1 | r2 U2 l' U2 l F2 U2 r2 U2 r F2 r' F2 r' F2/(25,15) |
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Alg_2(v1) | r' U2 r U2 l' U2 r U2 l F2 r' F2 r F2 r2 F2/(25,16) |
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Alg_2(v2) | l U2 l' U2 r U2 l' U2 r' F2 l F2 l' F2 l2 F2/(25,16) |
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Alg_3 | (B' R Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R' B)/(21,17) |
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Alg_4 | r U2 l' U2 r U2 r U2 r' U2 r U2 r2 U2 M U2 r'/(26,17) |
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Alg_5 | r U2 M' U2 r2 U2 r' U2 r U2 r' U2 r' U2 l U2 r'/(26,17) |
In Adjacent Dedges
Checkboard
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Alg | (R2 Uw' u' r' f2 Rw2 E) f (E' Rw2 f2 r u Uw R2)/(21,15) |
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Alg | (Rw' F2 M2 F) l' U2 l' U2 l2 U2 l' U2 (F' M2 F2 Rw)/(25,16) |
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Alg | (Rw U2 M2 U') M U2 r' U2 r2 U2 r' U2 l' (U M2 U2 Rw')/(26,17) |
Bowtie/Hourglass
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Alg | (L' Fw' f' l' u2 Lw2 S') u (S Lw2 u2 l f Fw L)/(19,15) |
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Alg | (Lw' U2 M2 U' x) r' U2 r' U2 r2 U2 r' U2 (x' U M2 U2 Lw)/(25,16) |
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Alg | R B r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r' B' R'/(25,17) |
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Alg | (l' U2 M2 U) M' U2 r U2 r2 U2 r U2 l (U' M2 U2 l)/(26,17) |
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Alg | Uw Fw' r Fw Uw' Fw' r Uw2 L' Uw' U' R U F' R' F r F' R F U' R' Uw U L Uw2 r2 Fw/(31,28) |
Additional Last Layer 2-Cycle Cases
- This section contains all of the 2-cycle cases besides the one dedge flip.
- Algorithms marked as "Safe" are supercube safe.
In Opposite Dedges
Adjacent 2-Swap
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Alg_1(v1) | r U2 r U2 x U2 r U2 l' x' U2 l U2 r2/(19,12) |
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Alg_1(v2) | l' U2 l' U2 x U2 l' U2 r x' U2 r' U2 l2/(19,12) |
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Alg_1(v3) | r2 D2 r' D2 l D2 l' D2 B2 l' B2 r'/(19,12) |
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Alg_2(v1) | r U2 r U2 M' U2 r U2 r' U2 l U2 r2/(20,13) |
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Alg_2(v2) | l' U2 l' U2 M' U2 l' U2 l U2 r' U2 l2/(20,13) |
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Alg | Rw' U2 r' U2 (Rw' l) U2 r' U2 r U2 l' U2 Rw2/(20,13) |
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Alg | z' Lw U' r Uw Lw' Uw' r Fw r Fw' r2 Uw Lw u' Lw' z/(16,15) |
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Alg | l2 D' f' D r D2 r' D' f D' l' F2 r' F2 l'/(19,15) |
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Alg | b u Bw' Rw' f' Rw Bw Rw' f2 Uw' f' Uw f' Rw u' b'/(17,16) |
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Alg | Rw U2 r U2 Rw U2 Rw2 F r F' Rw2 U2 Rw2 F r' F'/(23,16) |
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Alg | l' B2 l D2 r' D2 l' B2 l' D2 r' D2 l2 D2 r D2/(25,16) |
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Alg | l' B2 l D r' D' l' B2 l D l r F2 r' F2 l' D'/(21,17) |
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Alg | r' U2 r D r' D' r' U2 l' B2 r' B2 l r D r D'/(21,17) |
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Alg | r' U2 l D2 l' U2 l D2 l' U2 r' U2 r' U2 r' U2 r'/(25,17) |
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Alg | z' Lw' Uw f' Uw' Lw Uw f' Lw' l' B l f' l' B' Lw l f2 Uw' z/(19,18) |
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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) |
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Alg | r' U' r' U r U r' U' r' U' r D b2 r' b2 r U2 D' r U'/Safe(23,20) |
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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) |
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Alg | r' U' R U r' U R' U' r U R U2 R' U' r' U2 r' U2 r' U2 r'/(25,21) |
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Alg | x' r' Uw Lw Uw' r2 Fw2 Lw' Fw U' R U r' U' R' U Fw' Lw Fw2 r' Uw Lw' Uw' x/(25,22) |
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Alg | Rw U' R U Rw U2 Rw' U' R' U' r U R U Rw U2 Rw' U' R' U' r2 U2 Rw'/(27,23) |
Opposite/diagonal 2-Swap
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Alg_1(v1) | l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r z2/(21,14) |
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Alg_1(v2) | r S2 U2 r' U2 r U2 l' U2 l F2 r' B2 l' z2/(21,14) |
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Alg | r2 B2 U2 r' U2 r2 B2 r' U2 r2 U2 B2 r' B2/(25,14) |
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Alg | r2 B2 U2 r U2 r2 B2 r' U2 r2 U2 B2 r' B2/(25,14) |
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Alg | Uw Lw' Uw' l' Uw Lw2 Dw' Lw Uw' l' Uw L' Dw Lw' Uw'/(16,15) |
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Alg | Uw Lw' Uw' l' Uw Lw Fw' Lw2 Uw' l' Uw Lw' L' Fw Uw' /(16,15) |
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Alg | Uw Lw' Bw' r' Bw Lw2 Bw' Rw Fw' r' Fw R' Bw Lw' Uw'/(16,15) |
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Alg | Fw' L2 Uw b' Uw' Lw2 Uw L' Uw b' Uw' Lw Uw' l2 Fw/(18,15) |
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Alg | Fw Uw' B2 Lw u' Lw' Bw2 Rw2 d' Rw' d Rw' b2 Uw Fw'/(19,15) |
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Alg | Uw Rw' F2 Rw' f Rw Bw2 Lw2 u Lw u' Rw u2 Rw Uw' y2/(19,15) |
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Alg | Rw2 F2 U2 r U2 x U2 Rw2 U2 r' U2 l r U2 l' U2 x'/(25,15) |
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Alg | Fw' L U' f Uw2 Lw2 Dw r Dw' Lw2 Uw f' Uw U L' Fw/(19,16) |
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Alg_2(v1) | l' U2 l U2 l U2 r' U2 l U2 l' U2 F2 l2 F2 r/(25,16) |
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Alg_2(v2) | r U2 r' U2 r' U2 l U2 r' U2 r U2 F2 r2 F2 l'/(25,16) |
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Alg | r F2 D2 l D2 F r2 U2 r2 F r' F' r2 U2 r2 F/(25,16) |
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Alg | r U2 r' U2 r' U2 l U2 r' U2 r U2 M' U2 r2 U2 r'/(26,17) |
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Alg | Uw' Lw' Fw R' Fw' d' Fw R Fw' Lw2 Fw2 Rw' u' Rw Fw2 Lw' b Uw/(21,18) |
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Alg | x' l' Uw Rw' Uw' l Uw Fw Uw B' l2 B r' B' l2 B Uw' Fw' Rw Uw' x/(21,19) |
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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) |
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Alg | z' Fw' Uw r' Uw' Fw Uw r' Fw2 L Fw F R2 F' r' F R2 Fw' F' L' Fw2 r2 Uw' z/(27,22) |
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Alg | x r' U2 r U2 r' U2 r2 U r U' r' U2 r' U2 r2 U2 r' U' r' U' r' U2 x'/(31,22) |
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Alg | x r' U2 r U2 r' U2 r2 U' r U r' U2 r' U2 r2 U2 r' U r' U r' U2 x'/(31,22) |
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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) |
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Alg | Rw U2 r' U2 r' U' l r u2 l' r' U l r u2 x U2 l' U2 r U2 r' U2 Rw' x'/Safe(31,23) |
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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) |
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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) |
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Alg | Rw U Rw' U' Rw U2 Rw' U2 Rw' U' Rw U' Rw U' Rw2 U2 Rw2 U' Rw U2 Rw' U2 Rw U2 Rw U/(34,26) |
In Adjacent Dedges
Case 1 (Close Adjacent Unoriented)
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Alg | l2 U Lw U2 r' U2 Rw' U2 F' r' F U2 F' M' l' x/(20,15) |
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Alg | x' l2 F U2 l U2 r' U2 r U2 F2 r F2 l' F' l2 x/(23,15) |
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Alg | r U2 r U2 F' L F' r F L' F l' U2 l U2 r2/(21,16) |
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Alg | x' l2 F U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F' l2 x/(24,16) |
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Alg | z' F Lw2 b Uw' Rw Uw b' Uw' b' Rw' b Rw b Rw' Uw Lw2 F' z/(19,17) |
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Alg | z' F Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2 F' z/(19,17) |
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Alg | z' F Lw2 z Lw' Bw r' Bw' Lw Bw Rw' Dw' r' Dw Rw r Fw' Lw2 F' z/(19,17) |
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Alg | Rw b' Uw2 Rw' Uw' f Uw Rw Uw' f Rw' f Rw f2 Uw' b Rw'/(19,17) |
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Alg | r2 U2 l U2 r' U2 r U2 F' L F' r F L' F l' r2/(23,17) |
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Alg | l2 U M U2 l U2 r' U2 r U2 M' U2 r U2 l' U' l2/(25,17) |
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Alg | r' U' r' U' r U r U r' D' f2 r f2 r' D U2 r' U r U r2/Safe(25,21) |
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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) |
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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) |
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Alg | r F2 r' F2 U Lw' U2 r' U2 Lw B M U Rw2 F2 l2 F2 Rw2 U' M' B' U'/(31,22) |
Case 2 (Far Adjacent Unoriented)
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Alg | l2 U' Lw U2 r' U2 Rw' U2 F r' F' U2 F M' l' x/(20,15) |
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Alg | x Rw2 F' U2 l U2 r' U2 r U2 F2 r F2 l' F Rw2 x'/(23,15) |
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Alg | r U2 r U2 F R' F r F' R F' l' U2 l U2 r2/(21,16) |
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Alg | x Rw2 F' U2 l U2 r' U2 r U2 (l' Rw) U2 r U2 Rw' F Rw2 x'/(24,16) |
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Alg | Lw l b Uw' Rw Uw b' Uw' b' Rw' b Rw b Rw' Uw Lw' l'/(17,17) |
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Alg | Lw l z Lw' Bw r' Bw' Lw Bw Rw' Dw' r' Dw Rw r Fw' Lw' l'/(17,17) |
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Alg | Rw l Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' l' Rw'/(17,17) |
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Alg | Rw' l' x' U2 l U2 r' U2 r U2 x U R U r U' R' U' Rw/(21,17) |
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Alg | r2 U2 l U2 r' U2 r U2 F R' F r F' R F' l' r2/(23,17) |
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Alg | Lw2 U' M U2 l U2 r' U2 r U2 M' U2 r U2 l' U Lw2/(25,17) |
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Alg | z Dw' (M R') D Lw' Uw' r' Uw Lw Uw' Lw2' Bw' r' Bw Rw' R' u y' (M' R) Uw x2 z'/(19,18) |
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Alg | x U2 r' U2 r U2 l' U2 l F2 l' B D2 B' r' B D2 B' l F2 x'/(27,19) |
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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) |
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Alg | Rw' U R U r2 U' R' U' Rw' U2 Rw U R U r U' R' U' Rw' U2 Rw2/(25,21) |
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Alg | r' U r' U r U' r U' r' D b2 r b2 r' D' U2 r' U' r U' r2/Safe(25,21) |
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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) |
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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) |
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Alg | Rw2 R U2 Rw U r U' Rw' U2 Rw' U2 Rw U2 Rw U r2 U' Rw' U2 Rw' U2 Rw' R'/(30,23) |
Case 3 (Oriented Case)
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Alg | Lw2 b Uw' Rw Uw b' Uw' b' Rw' b Rw b Rw' Uw Lw2/(17,15) |
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Alg | Rw2 Uw' Bw r' Bw' Uw Bw Rw' Uw' r' Uw Rw r Bw' Rw2/(17,15) |
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Alg | Lw2 z Lw' Bw r' Bw' Lw Bw Rw' Dw' r' Dw Rw r Fw' Lw2/(17,15) |
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Alg | Rw2 f Uw' Bw Dw r' Dw' r' Bw' r Bw r Bw' Uw Rw2/(17,15) |
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Alg | z' Fw' l' Uw' Bw2 Uw' r Uw Bw2 Uw2 r Uw r' Uw2 l Fw z/(19,15) |
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Alg | Uw Rw' Uw' r' Uw Rw Bw' Rw' r' Uw' r' Uw R r' Bw Uw'/(16,16) |
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Alg | Bw L' Dw' l Dw Lw Bw' Lw L Dw' l Dw Lw2 Fw u' Fw'/(17,16) |
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Alg | Uw' Fw l' Fw' Uw Fw l' Uw2 R Uw l' Uw' R' Uw2 l2 Fw'/(19,16) |
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Alg | r' Uw Lw Uw' r2 Fw2 Lw' Fw r' Fw' Lw Fw2 r' Uw Lw' Uw'/(19,16) |
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Alg | z' Lw Uw' r Uw Lw' Uw' r Fw2 L' Fw' r Fw L Fw2 r2 Uw z/(19,16) |
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Alg | Bw' Uw2 r' Dw l' Dw' r Uw' Lw2 Uw' r' Uw Lw2 Uw' r Bw/(19,16) |
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Alg | l' r' U Rw U2 l' U2 Lw' U2 x' U' l' U F2 U' M' l'/(20,16) |
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Alg | z' Uw Lw' Uw2 r Uw' l Uw r' Uw2 L Uw' Bw2 Uw l Uw' Bw2 z/(20,16) |
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Alg | x l' U L U l' U' L' U' F2 l' F2 r U2 r' U2 l2 x'/(21,16) |
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Alg | R B r U2 r U2 x U2 r U2 l' x' U2 l U2 r2 B' R'/(23,16) |
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Alg | x l' U L U l' U' L' U' x U2 l' U2 l U2 r' U2 l r x2/(21,17) |
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Alg | x r U' R' U' r U R U M' U2 r U2 r' U2 l U2 r2 x'/(22,17) |
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Alg | x' f' Uw Rw' Fw' r' Fw Rw Uw' f r' Uw Rw' Fw' r' Fw Rw Uw' r2 x/(19,18) |
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Alg | r' U' F2 U r' U' F2 r' F' R' F' r' F R F r U r2/(21,18) |
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Alg | z' r' Uw Bw Uw' Bw L Bw r Bw' L' Bw' Uw Bw' Lw Uw' r Uw Lw' Uw' z/(19,19) |
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Alg | l' Uw Rw' Uw' l Uw Fw Uw B' Rw2 F r' F' Rw2 B Uw' Fw' Rw Uw'/(21,19) |
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Alg | x Rw U L U r2 U' L' U' Rw U2 Rw' U L U r' U' L' U' Rw U2 Rw2 x'/(25,21) |
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Alg | r' U' r U' r' D b2 r b2 r' D' U2 r' U' r U' r U r' U r2/Safe(25,21) |
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Alg | x r2 U2 Rw' U' r' U Rw U2 Rw U2 Rw' U2 Rw' U' r2 U Rw U2 Rw U2 Rw R2 x'/(30,22) |
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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) |
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Alg | 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'/(37,27) |
Summary of 2-Cycle and 4-Cycle ELL Case Movecounts
- Since there is disagreement among cubers about whether lowest q moves or lowest btm moves defines the "optimal algorithm", the table below categorizes all 2-cycle and 4-cycle ELL cases on the 4x4x4 by the average of q moves and btm.
- Algorithms optimal in btm need not be the algorithm with the lowest average of q and btm, and algorithms optimal in q turns need not be the algorithm with the lowest average of q and btm. Therefore the average for a given case might be from an algorithm optimal in q moves, optimal in btm moves or optimal in both.
- Of course this ranking is based off of required moves. It is not based off of the amount of time it takes to solve a case.
- These results will change in the future if shorter algorithms are found for any of these cases.
- The table shows that the "worst case" is Adjacent Double Parity, and that the "easiest case" is the Checkerboard Pattern (in two opposite edges).
| Last Layer Case | Minimum q Turns | Minimum btm | Optimal Average | Rank |
|---|---|---|---|---|
| Adjacent Double Parity | 23 | 16 | 19.5 | 1 |
| Bowtie/Hourglass | 21 | 15 | 19 | 2 |
| One Dedge Flip | 19 | 15 | 18.5 | 3 |
| Adjacent Checkerboard | 21 | 15 | 18 | 4 |
| Adjacent 2-Cycle Case 1 (Close "Unoriented" Case) | 19 | 15 | 18 | 4 |
| Double Parity | 21 | 14 | 17.5 | 5 |
| Adjacent Bowtie/Hourglass | 19 | 15 | 17 | 6 |
| Adjacent 2-Cycle Case 2 (Far Adjacent "Unoriented" Case) | 17 | 15 | 17 | 6 |
| Adjacent 2-Cycle Case 3 (“Oriented" Case) | 16 | 15 | 16 | 7 |
| Opposite/diagonal 2-swap | 16 | 14 | 15.5 | 8 |
| Adjacent 2-swap | 16 | 12 | 15.5 | 8 |
| Checkerboard Pattern | 17 | 11 | 14 | 9 |
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.
Complete 3x3x3 Scrambles
OLL Parity (Only)
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Alg | Rw B U2 B' r B2 l B2 r B' D2 B Rw/(17,13) |
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Alg | r U F2 U' l F2 2R U2 r U B2 U' r/(17,13)(SiGN) |
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Alg | r U' F2 U l F2 2R U2 r U' B2 U r/(17,13)(SiGN) |
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Alg | Uw M R D R' Fw f E' l' E Fw b E F Lw/(15,15) |
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Alg | Rw' S' L2 S Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'/(20,16) |
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Alg | Rw' S R2 S' Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'/(20,16) |
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Alg | r U2 r' U2 r D2 r D2 r' F L' F' U' r' D2 r/(21,16)(SiGN) |
OLL Parity + PLL Parity (Double Parity)
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Alg_1 | r F2 U2 l F U' R U' r2 B2 r' B2 r2/(19,13)(SiGN) |
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Alg_2 | r F2 U2 l F' U L' U r2 B2 r' B2 r2/(19,13)(SiGN) |
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Alg | r F2 U2 l F U' (L' R) U' r2 B2 r' B2 r2/(19,13)(SiGN) |
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Alg | r F2 U2 l F' U (L' R) U r2 B2 r' B2 r2/(19,13)(SiGN) |
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reParity | r U2 l' U2 x' (r' U2 l U2)2 l'/(19,13) |
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Alg | Uw R' b E' d' L' b L u' b2 Uw M' B' Uw/(15,14) |
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Alg | Uw S L B' R u d f' u d L B' R S Uw/(15,15) |
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Alg | Uw S L' F R' u d f' u d L' F R' S Uw/(15,15) |
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Alg | Rw' U2 r U2 Rw' x' U2 r' U' R' U' Rw' U2 Rw U R U' Rw x/(21,17) |
More than 1 F3L Slot Destroyed (Not Petrus)
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Alg | r' U2 F U2 F' U2 r' U2 r' U2 r' F U2 F' r'/(21,15)(SiGN) |
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Alg | Rw U D' R2 U' R2 D x' U2 Lw U2 Lw U2 Lw F' U2 F Lw/(22,16) |
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Alg | Rw F U2 F' Rw U2 Rw U2 Rw R U2 F U2 F' U2 r/(22,16) |
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Alg | Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' F U' B' U' S Dw' z'/(20,17) |
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Alg | Lw U' L' R U2 L U Lw U2 Lw U2 Lw U' R' U2 R U r x'/(22,18) |
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Alg | Lw U' L' R' U2 L U Lw U2 Lw U2 Lw U' R U2 R' U Lw R/(23,19) |
Petrus (They Destroy 2 Adjacent Faces)
OLL Parity (Only)
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Alg_1 | r B' U2 B r B2 l B2 r B D2 B' r/(17,13)(SiGN) |
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Alg_1(v2) | x' r' U F2 U' l' U2 r' U2 r' F' U2 F r'/(17,13)(SiGN) |
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Alg_1(v3) | x' r' U F2 U' l' U2 r' U2 l' U' B2 U r' x'/(17,13)(SiGN) |
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Alg_1(v4) | x' r' U F2 U' l' U2 r' 3d2 r' U' F2 U l' x/(17,13)(SiGN) |
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Alg | Rw' S' L2 S Rw' U2 Rw' U2 Rw' F U2 F' U' L' U Rw'/(20,16) |
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Alg | Rw' S R2 S' Rw' U2 Rw' U2 Rw' F' U2 F U R U' Rw'/(20,16) |
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Alg | Rw U2 Rw' U2 Rw D2 r D2 l' U L' U' B' l' U2 l x'/(21,16) |
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Alg | Rw' U R' U2 R U' Rw' U2 Rw' U2 Rw' U' R U2 R' U Rw'/(21,17) |
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Alg | Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw/(21,17) |
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Alg | Rw U' R' U2 R U Rw U2 Rw U2 r U R U2 R' U' Rw/(21,17) |
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Alg | Rw' U' L' U2 L U Rw' U2 Rw' U2 Rw' U L' U2 L U' Rw'/(21,17) |
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Alg | Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F Rw' U2 Rw F/(22,17) |
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Alg | Rw U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw/(23,17) |
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Alg | Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U Rw2 U2 Rw2 U R2 U' Rw'/(25,17) |
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Alg | Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 r2 U R2 U' Rw'/(25,17) |
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Alg | Rw U' R2 U2 R2 U r U2 r U2 r U R2 U2 R2 U' Rw/(25,17) |
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Alg | Rw' U R U2 R' U' r' U2 Rw' U2 Rw' F' U' R' U' R F Rw'/(21,18) |
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Alg | Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R' U' R U2 R' U Rw'/(22,18) |
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Alg | Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw/(23,18) |
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Alg | Rw U' R U2 R' U Rw U2 r U2 Rw R2 U R U2 R' U' Rw/(23,18) |
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Alg | Rw U' R U2 R' U Rw U2 Rw R2 U2 Rw U R' U2 R U' Rw/(23,18) |
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Alg | Rw U R U' Rw2 R U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2 U2 Rw'/(24,18) |
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Alg | Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' R2 U' R2 U2 R2 U Rw'/(24,18) |
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Alg | Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'/(24,18) |
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Alg | Rw U R' U Rw U2 r U2 r U' Rw' U R U R' U2 Rw U' Rw/(22,19) |
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Alg | Rw U R' U r U2 r U2 Rw U' Rw' U R U R' U2 Rw U' Rw/(22,19) |
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Alg | Rw U' Rw U2 R' U R U Rw' U' r U2 Rw U2 Rw U R' U Rw/(22,19) |
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Alg | Rw U' R' U2 R U Rw R U2 r U2 Rw R U R' U2 R U' Rw/(23,19) |
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Alg | Rw U' Rw U2 R' U R U Rw' U' Rw U2 r U2 Rw U R2 U Rw/(23,19) |
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Alg | Rw U' R' U2 R U' R' U2 r U2 Rw U2 r U R' U2 R U' Rw/(24,19) |
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Alg | Rw U' R U2 R' U' R' U2 r U2 Rw U2 r U R U2 R' U' Rw/(24,19) |
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Alg | Rw U' R' U2 R U r U2 Rw U2 Rw U R U2 R' U R' U2 Rw/(24,19) |
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Alg | Rw U R' U2 R' U2 R U Rw R U2 Rw U2 Rw U R U2 R' U' Rw/(25,20) |
OLL Parity + PLL Parity (Double Parity)
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Alg_1(v2) | l' U2 F2 l' U' F R' F l2 U2 r U2 l2 U' x'/(20,14)(SiGN) |
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Alg_1(v3) | l' U2 F2 l' U' F 3l' U l2 x' U2 r U2 l2 U' x'/(20,14)(SiGN) |
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Alg_2(v2) | r U2 F2 r U' F R' F r2 U2 l' U2 r2 U' x'/(20,14)(SiGN) |
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Alg_2(v3) | r U2 F2 r U' F 3l' U r2 x' U2 l' U2 r2 U' x'/(20,14)(SiGN) |
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Alg | r' U R U' r' U2 r U R' U r U2 r F2 Lw' U2 Lw/(21,17) |
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Alg | Rw' U Rw' U' Rw2 R' U' Rw' U' R U2 Rw' U' Rw' U2 Rw' U2 Rw'/(21,18) |
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Alg | Rw U2 Rw U2 Rw' U' R' Rw2 U2 r U' R' U' Rw U2 r2 U Rw2/(24,18) |
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Pochmann | Rw' U R U (Rw' U2)3 Rw2 U R' U' Rw2 U' R' U Rw'/(24,19) |
Affect M Layer Only
OLL Parity + PLL Parity (Double Parity)
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Alg | r U2 r' U2 r' D2 r D2 r' B2 r B2 r'/(19,13) |
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Alg | r U2 r' U2 M' l' U2 r U2 l' U2 r U2 l'/(20,14) |
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reParity(v2) | r U2 l' U2 l r2 U2 l U2 r' U2 l U2 l r2/(23,15) |
FR F3L Slot Destroyers
OLL Parity (Only)
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Alg | l U2 l' F U R U' Lw' D2 r D2 r U2 Rw' U2 Lw F/(22,17) |
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Alg | Rw U2 Lw' U2 l D2 l D2 Rw' U' L U F r' U2 r F/(22,17) |
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Alg | Rw U R' U' Rw2 R U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw'/(24,18) |
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Alg | Rw U R' U' Rw2 U2 Rw2 R U Rw U2 Rw' U2 Rw U' Rw2 U2 r'/(24,18) |
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Alg | Rw U2 R U R' U2 R U r U2 Rw U2 Rw U R U2 R' U' Rw/(24,19) |
OLL Parity + PLL Parity (Double Parity)
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Alg | Rw U2 Rw U2 Rw U Rw U2 R' U Rw U Rw2 R U Rw U' Rw/(21,18) |
Just Corners are Permuted (Most are also Just FR F3L Slot Destroyers)
OLL Parity (Only)
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Alg | r' U2 F' U2 F U2 r' U2 r' U2 r' F' U2 F r'/(21,15) |
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Alg | l U2 F' U2 F U2 l U2 l U2 l F' U2 F l/(21,15) |
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Alg | r' U R U2 R' U' r' U2 r' U2 r' U' R U2 R' U r'/(21,17) |
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Alg | l' U' R U2 R' U l' U2 l' U2 l' U R U2 R' U' l'/(21,17) |
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Alg | r2 S' r U' R U' r U2 r U2 r U' R' U' r S r2/(21,17) |
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Alg | r2 S r U' R U' r U2 r U2 r U' R' U' r S' r2/(21,17) |
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Alg | Rw U' R' U2 R U r U2 r U2 r U R' U2 R U' Rw R2/(22,18) |
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Alg | Rw U' R' U2 R U r U2 Rw R U2 r U R U2 R' U' Rw/(22,18) |
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Alg | Rw U' R U2 R' U r U2 Rw R U2 r U R' U2 R U' Rw/(22,18) |
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Alg | Rw R U' R2 U2 R2 U r U2 Rw U2 r U R U2 R' U' Rw/(24,18) |
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Alg | Rw U' R' U2 R U Rw R2 U2 r U2 Rw U R' U2 R U' Rw R2/(24,19) |
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Alg | Rw U' R' U2 R U Rw U2 r U2 Rw R2 U R' U2 R U' Rw R2/(24,19) |
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Alg | Rw U' R' U2 R U' R U2 r U2 Rw U2 r U R U2 R' U' Rw/(24,19) |
- To see more detailed information on how most of the optimal algorithms were found, see http://cubezzz.dyndns.org/drupal/?q=node/view/230
- To see Stefan Pochmann's explanation of his Petrus Parity Algorithm, see http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/13712
- To see a large list of (U,Rw,R) solutions that have been found, see http://www.speedsolving.com/forum/showthread.php?30127-New-4x4-parity-algs-using-R-Rw-U&p=806576&viewfull=1#post806576
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
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Alg | Rw2 U r' U' B2 U r U r' U2 B2 Rw2/(17,12) |
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Alg | Rw2 U' r' U B2 U' r U' r' U2 B2 Rw2/(17,12) |
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Alg | Rw2 (Dw u') l U' R2 U l' U y r U2 F2 Rw2/(17,12) |
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Alg | Lw2 (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw2/(17,13) |
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Alg | Rw2 U' r' U B2 U' r U B2 D2 l D2 Rw2/(19,13) |
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Alg | Rw2 (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw2/(19,13) |
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Alg | Rw2 U2 r U2 l' U2 l U2 r' F2 r F2 Rw2/(21,13) |
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Alg | Rw2 U2 r U2 l' U2 l U2 r' B2 l B2 Rw2/(21,13) |
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Alg | l U2 l' U2 Lw2 F2 r' F2 Rw2 U2 l' U2 r x2/(21,13) |
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Alg | r2 Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw' r/(15,14) |
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Alg | r2 U2 r' U2 r U2 l' U2 r U2 r' U2 l r/(21,14) |
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Alg | r2 U2 r U2 l' U2 l U2 l' U2 r U2 l r/(21,14) |
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Alg | x r R' U' Rw U' r U Rw' r' U R U' r U r' x'/(15,15) |
One Dedge Flip + PLL Parity (Double Parity)
- Most of these algorithms are exactly the same as the one dedge flip ones except that the extra quarter turn is inverted.
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Alg | Rw' F' u F' D2 F u' F' l D2 F2 Rw/(15,12) |
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Alg | Rw2 U r' U' B2 U r U r U2 B2 Rw2/(17,12) |
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Alg | Rw2 U' r' U B2 U' r U' r U2 B2 Rw2/(17,12) |
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Alg | Rw2 (Dw u') l U' R2 U l' U y r' U2 F2 Rw2/(17,12) |
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Alg | Lw2 (Dw' u) r' U L2 U' r D' r U D L2 y' Lw2/(17,13) |
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Alg | Rw2 U' r' U B2 U' r U B2 D2 l' D2 Rw2/(19,13) |
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Alg | Rw2 (Dw u') l U' R2 U l' U' D2 y l' D2 F2 Rw2/(19,13) |
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Alg | Rw2 U2 r U2 l' U2 l U2 r' F2 r' F2 Rw2/(21,13) |
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Alg | f' Uw2 Rw2 Uw' l' Uw Rw2 Uw' l u' U f U2 f'/(18,14) |
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Alg | Rw2 b2 D' f' D B2 D' f U' f U D Bw2 Rw2/(19,14) |
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Alg | l r U2 l U2 r' U2 r U2 r' U2 l' U2 l2/(21,14) |
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Alg | Fw Rw2 Fw' r' Fw Rw2 Bw' r Fw' r' Bw U2 r U2 r'/(19,15) |
One Dedge Flip + Adjacent PLL Parity (Adjacent Double Parity)
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Alg | (r2 U Rw' U R U) r' (U' R' U' Rw U' r2)/(15,13) |
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Alg | (r2 U F2 U' r' F2) r (F2 r U F2 U' r2)/(19,13) |
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Alg | Rw' U Rw U F2 U' r' U F2 r' U' R' U' Rw/(16,14) |
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Alg | x' r2 U' Rw U l2 U2 l U2 l U2 l U Rw' U r2 x/(21,15) |
3 Dedge Flips
OLL Parity (Only)
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Alg | (r2 F2 U) r U2 r' U2 r U2 r' U2 r (U' F2 r2)/(23,15) |
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Alg | (r2 U2 F' M' U) r U2 r' U2 r U2 r' U2 r (U' M F U2 r2)/(27,19) |
OLL Parity + PLL Parity (Double Parity)
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Alg | (r' U' F' R' F R2 U') r' (U R2 F' R F U r) (r U2 r' U2)/(23,18) |
2-Cycles In Two Adjacent Edges (in the M ring)
Adjacent 2-Swap
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Alg | r' U r U F2 U' r' U F2 U2/(13,10) |
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Alg | r' U' r U' F2 U r' U' F2 U2/(13,10) |
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Alg | y' U2 R2 U l U' R2 U l' U y r/(13,10) |
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Alg | F2 U2 l U2 r' U2 r U2 l' F2 r /(17,11) |
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Alg | r U' Rw U' R' U r U' R U r' Rw' U/(13,13) |
Opposite/Diagonal 2-Swap
- Some of these are nearly the same as the one dedge flip algorithms.
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Alg | Rw U r' U' B2 U r U r' U2 B2 Rw'/(15,12) |
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Alg | Rw U' r' U B2 U' r U' r' U2 B2 Rw'/(15,12) |
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Alg | Rw (Dw u') l U' R2 U l' U y r U2 F2 Rw'/(17,12) |
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Alg | x' U Rw' U r' U' Rw r U' R' U r' U' R x/(13,13) |
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Alg | x' R U Rw' U r' U' Rw r U' R' U r' U' x/(13,13) |
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Alg | r' Uw Bw' Uw' r Uw Rw Bw r' Bw' Rw' Bw Uw'/(13,13) |
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Alg | Lw' (Dw' u) r' U L2 U' r D' r' U D L2 y' Lw/(15,13) |
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Alg | Rw U' r' U B2 U' r U B2 D2 l D2 Rw'/(17,13) |
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Alg | Rw (Dw u') l U' R2 U l' U' D2 y l D2 F2 Rw'/(17,13) |
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Alg | (x') r' U2 r U2 l' U2 l U2 l' U2 r U2 l (x)/(19,13) |
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Alg | Rw U2 r U2 l' U2 l U2 r' F2 r F2 Rw'/(19,13) |
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Alg | Rw U2 r U2 l' U2 l U2 r' B2 l B2 Rw'/(21,13) |
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Alg | M' r U2 r U2 r' U2 l U2 r' U2 r U2 r'/(20,14) |
2-Cycles In Two Opposite Edges (in the M Ring)
Adjacent 2-Swap
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Alg | y Lw' Uw' r Fw r Fw' r2 Uw Lw Uw' r Dw/(13,12) |
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Alg | U' Rw' U r' U' Rw r U' R' U r' U' R U2/(15,14) |
Opposite/Diagonal 2-Swap
- These are the same as the one dedge flips but without first and last moves.
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Alg | U r' U' B2 U r U r' U2 B2/(13,10) |
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Alg | U' r' U B2 U' r U' r' U2 B2/(13,10) |
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Alg | (Dw' u) r' U L2 U' r D' r' U D L2 y'/(13,11) |
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Alg | U' r' U B2 U' r U B2 D2 l D2/(15,11) |
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Alg | (Dw u') l U' R2 U l' U' D2 y l D2 F2/(15,11) |
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Alg | U2 l U2 r' U2 r U2 l' F2 r F2/(17,11) |
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Alg | U2 r U2 l' U2 l U2 r' F2 r F2/(17,11) |
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Alg | U2 r U2 l' U2 l U2 r' B2 l B2/(17,11) |
4-Cycles in Adjacent Edges (in the M ring)
Checkboard
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Alg | Rw2 U2 r U2 Rw2/(9,5) |
Bowtie/Hourglass
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Alg | r U2 r' U2 x' U2 r U2 r2 U2 r' U2 r' x/(19,12) |
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Alg | x' r U2 r D2 r' U2 r D2 x U2 r' U2 r2/(19,12) |
Parity Algorithms Which Don't Preserve F3L or the Colors of the Centers (WCA Notation)
- These algorithms are least practical when it comes to use of parity algorithms, and therefore they are mentioned here for theoretical purposes only. They have fewer moves than any other OLL Parity algorithm forms.
OLL Parity (Only)
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Alg | Rw2 U r' U' B2 U r U r' B2 Rw2/(15,11) |
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Alg | Rw2 U' r' U B2 U' r U' r' B2 Rw2/(15,11) |
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Alg | Rw2 U f U' B2 U f' U l B2 Rw2/(15,11) |
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Alg | r' U' R U' r U2 r U2 r U' R' U' r'/(15,13) |
OLL Parity + PLL Parity (Double Parity)
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Alg | Uw L U B U' d Fw2 u' Fw2 L' Uw2 y/(14,11) |
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Alg | Uw L U B d Fw2 u' Fw2 U' L' Uw2 y/(14,11) |
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Alg | Rw2 U r' U' B2 U r U r B2 Rw2/(15,11) |
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Alg | Rw2 U' r' U B2 U' r U' r B2 Rw2/(15,11) |
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Alg | Rw2 U f U' B2 U f' U l' B2 Rw2/(15,11) |
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Alg | Rw U2 Rw U2 Rw U2 Rw2 U' R U Rw2 U R U' Rw2/(21,15) |
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Alg | Rw U2 Rw2 U' Rw' U2 Rw U2 Rw' U' Rw2 U' R2 U' Rw'/(21,15) |
Either OLL Parity (Only) or Double Parity
- The following list of algorithms can be considered either OLL Parity (Only) or Double Parity. Just exchange the last move Rw' with Lw', Rw with Lw, etc.
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Alg | Rw' U' R' U' Rw F' R' F' Rw'/(9,9) |
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Alg | Rw' U' R U' Rw F' R F' Rw'/(9,9) |
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Alg | Rw U' R U' r' D' R D' Rw/(9,9) |
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Alg | Rw' U R' U Rw U F2 U Rw'/(10,9) |
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Alg | Rw U' R U' Rw' D' R2 D' Lw/(10,9) |
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Alg | Rw' U' F2 U' r B' R B' Lw'/(10,9) |
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Alg | Rw U' L U' F2 Lw U' R U' Rw'/(11,10) |
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Alg | Rw U' L' U' F2 l U L U Rw'/(11,10) |
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Alg | Rw' U' L' U' Rw F2 U L U Rw/(11,10) |
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Alg | Rw' U' L' U' B2 Rw' B R B Rw/(11,10) |
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Alg | Rw' U R2 U Rw F2 U L' U Rw/(12,10) |
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Alg | Rw' U F' U l U2 F' U2 F Rw'/(12,10) |
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Alg | Rw U' R' U' Rw' D' L D L' D' Lw/(11,11) |
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Alg | Uw F R B' U f' E U M' U Fw/(11,11) |
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Alg | Rw U R' U R r' U2 B' L' B' Rw'/(12,11) |
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Alg | l' B' u B' D2 B u' B' l D2 l'/(13,11) |
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Alg | Rw F U' R U Rw' F U R F' U Rw/(12,12) |
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Alg | Rw' U F' L F Rw F R B' E y B Rw'/(12,12) |
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Alg | Uw S B D B' R f' R M E R Fw/(12,12) |
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Alg | Rw' U' F R' F' Rw F' U' F2 R U Rw'/(13,12) |
2-Cycles
- Although the following list of algorithms is not "OLL Parity", where dedge preservation is important, they are the briefest 2-cycle algorithms yet to be found. They do not preserve F3L or the centers.
- These are nothing more than 2-cycle algorithms which don't preserve centers with beginning and ending outer layer turns omitted.
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Alg | r' U' B2 U r U r'/(8,7) |
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Alg | r' U B2 U' r U' r'/(8,7) |
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Alg | r' U L2 U' r D' r'/(8,7) |
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Alg | r' U' R2 U r D r'/(8,7) |
External Links
OLL Parity Algorithms
- http://www.speedsolving.com/forum/showthread.php?11311-4x4x4-OP-DP-algorithms-%28more-finger-friendly%29
- http://www.speedsolving.com/forum/showthread.php?15614-Odd-parity-Algorithms-%28specifically-single-edge-quot-flip-quot-%29
- http://www.speedsolving.com/forum/showthread.php?2727-4x4-Orientation-parity
- http://www.speedsolving.com/forum/showthread.php?12487-4x4-Parity-Algorithms
- http://www.speedsolving.com/forum/showthread.php?30127-New-4x4-parity-algs-using-R-Rw-U
- http://www.twistypuzzles.com/forum/viewtopic.php?f=8&t=8829
- http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixOrientationParity
- http://www.stefan-pochmann.info/spocc/other_stuff/4x4_5x5_algs/?section=FixBothParities
- http://www.mementoslangues.fr/CubeDesign/4xCubes/DoubleMidgeFlip.pdf
- http://www.speedsolving.com/forum/showthread.php?11409-4x4-Optimal-Solver-v2
- http://apelgam.se/Rubik/4x4parity/
OLL Parity Algorithms which don't preserve F3L
- http://www.speedsolving.com/forum/showthread.php?37962-Fixing-4x4x4-orientation-parity-earlier-than-usual
- http://www.speedsolving.com/forum/showthread.php?26564-4x4x4-edge-parity-is-there-a-shorter-alg-that-doesn-t-preserve-corners
- http://www.speedsolving.com/forum/showthread.php?17839-WANTED-New-Dedge-Flip-Algorithm!
- http://twistypuzzles.com/forum/viewtopic.php?f=8&t=9502
PLL Parity Algorithms
- http://frederickbadie.free.fr/444PLLparity.html
- http://www.speedsolving.com/forum/showthread.php?21725-New-Two-Corner-Swap-Algorithm-Technique-for-Big-Even-Cubes-%28PLL-Parity%29
SuperCube Parity Algorithms
- http://www.speedsolving.com/forum/showthread.php?4659-4x4-algorithm
- http://www.speedsolving.com/forum/showthread.php?37308-Is-a-SuperCube-Safe-Single-Dedge-Flip-Algorithm-Possible-in-lt-U-Rw-gt
- http://www.speedsolving.com/forum/showthread.php?26622-God-s-algorithm-discovered-for-OLL-parity-edge-flip-%28theory%29
