Speedsolving.com Wiki - User contributions [en]

Rubik's Domino Algorithms

2026-06-20T18:10:11Z

Manfredi: Removed an incomplete part i thought i would finish

'''Rubik's Domino 1-Look Last Layer''' refers to the [[Last Layer]] of the [[Rubik's Domino]]. This cuboid is functionally a 3x3 where the only moves allowed are〈U, D, R2, L2, F2, B2〉and the equator line is ignored.
In this 3x3x2 cuboid, [[OLL]] is always skipped after compleating the first layer: it is impossible to not have the two 3x3s faces always oriented correctly.
[[File:Domino_reduction_pairty.png|thumb|right|"(R2 U2)3" is an example of a swap of four edges, effectivelly creating a swap of 2 visible edges and 2 invisible edges on the Rubik's Domino.]]
The reason why you can get pairity on the Domino Cube is because swapping 4 edges is possible on a 3x3, therefore you can swap 2 pieces on the hidden equator line of the Domino Cube to swap just two pieces.

=3x3 Top Layer: Last Layer Algorithms=

<table cellspacing='5' cellpadding='5'>
<tr>
<td valign='top'>
==Permutations of edges only (No Parity)==
<tr>
<td valign='top'>
===H Permutation===
[[File:PLL H.png]]
{{Alg|M2 U M2 U2 M2 U M2}}

</td>

<td valign='top'>
===Ua Permutation===
[[File:PLL U(a).png]]
{{Alg|y2 F2 U R2 F2 R2'U2 R2 F2 R2 U F2}}
{{Alg|R2 U F2 L2 B2 D' B2 L2 F2 U2 R2}}

</td>
<td valign='top'>
===Ub Permutation===
[[File:PLL U(b).png]]
{{Alg|y2 F2 U' R2 F2 R2 U2 R2 F2 R2 U' F2}}
{{Alg|R2 U2 F2 L2 B2 D B2 L2 F2 U' R2}}

</td>
<td valign='top'>
===Z Permutation===
[[File:PLL Z.png]]
{{Alg|M2 U' M2 F2 M2 F2 U M2}}
{{Alg|y F2 M2 F2 M2 U M2 U M2}}
</td>

<tr>
<td valign='top'>
==Permutations of corners only (No Parity)==
<tr>
<td valign='top'>

===Aa Permutation===
[[File:PLL A(a).png]]
{{Alg|y2 R2 U R2 U' F2 U R2 U' F2 R2}}
{{Alg|R2 U F2 U' F2 R2 U' R2 U F2}}

</td>
<td valign='top'>
===Ab Permutation===
[[File:PLL A(b).png]]
{{Alg|y2 R2 F2 U R2 U' F2 U R2 U' R2}}
{{Alg|F2 U' R2 U R2 F2 U F2 U' R2}}

</td>
<td valign='top'>
===E Permutation===
[[File:PLL E.png]]
{{Alg|R2 U2 R2 U' R2 U2 y' R2 U' R2 U R2 y U2 R2 U' R2}}
{{Alg|y R2 U' R2 U B2 U' R2 F2 U B2 U' F2 U R2}}
{{Alg|F2 U R2 U' L2 U R2 F2 U' L2 U F2 U' F2}}
</td>

<tr>
<td valign='top'>
==Permutations of Edges and Corners (No Parity)==
<tr>
<td valign='top'>

===F Permutation===
[[File:PLL F.png]]
{{Alg|y R2 U R2 F2 U2 F2 U R2 U' R2 U' R2 U2 F2}}
{{Alg|R2 F2 U' F2 D F2 L2 D L2 D' L2 U L2 F2 R2}}
</td>
<td valign='top'>

===Ga Permutation===
[[File:PLL G(a).png]]
{{Alg|y2 F2 r2 R2 U F2 U' R2 U R2 U' r2 F2}}
{{Alg|y' F2 U2 F2 U F2 U' F2 U' R2 U2 F2 U F2 U R2}}
{{Alg|y2 F2 R2 L2 U R2 U' R2 U F2 U' L2 F2}}
</td>
<td valign='top'>

===Gb Permutation===
[[File:PLL G(b).png]]
{{Alg|y2 F2 r2 U R2 U' R2 U F2 U' R2 r2 F2 U}}
{{Alg|y2 F2 L2 U F2 U' R2 U R2 U' M2 B2}}
</td>
<td valign='top'>

===Gc Permutation===
[[File:PLL G(c).png]]
{{Alg|y2 F2 R2 r2 U' F2 U r2 U' F2 U R2 F2}}
{{Alg|R2 U2 R2 U' R2 U R2 U F2 U2 R2 U' R2 U' F2}}
{{Alg|y2 F2 R2 L2 U' L2 U L2 D' L2 D R2 F2}}
</tr>
<td valign='top'>

===Gd Permutation===
[[File:PLL G(d).png]]
{{Alg|y2 F2 R2 U' F2 U r2 U' F2 U R2 r2 F2}}
{{Alg|y' U2 F2 U R2 U2 F2 R2 U' R2 U' R2 U F2 U F2}}
{{Alg|y2 F2 R2 D' L2 D L2 U' L2 U L2 R2 F2}}
</td>
<td valign='top'>

===Ja Permutation===
[[File:PLL J(a).png]]
{{Alg|y2 R2 U' R2 U y' R2 U' R2 U R2 B2}}
{{Alg|y2 R2 U' R2 U F2 U' F2 U F2 R2}}
{{Alg|y D2 R2 F2 D' L2 U L2 D' L2 U L2}}
</td>
<td valign='top'>

===Jb Permutation===
[[File:PLL J(b).png]]
{{Alg|y2 F2 R2 U R2 U' R2 y' U R2 U' R2}}
{{Alg|y2 F2 R2 U R2 U' R2 U F2 U' F2}}
{{Alg|y' D2 L2 F2 D R2 U' R2 D R2 U' R2}}
</td>
<td valign='top'>

===Na Permutation===
[[File:PLL N(a).png]]
{{Alg|F2 R2 U2' R2 U' R2 y' R2 U2' R2 U R2 U2' f2 x2}}
{{Alg|R2 U2 F2 U' F2 U2 F2 R2 U R2 U2 R2 F2}}
</tr>
<td valign='top'>

===Nb Permutation===
[[File:PLL N(b).png]]
{{Alg|F2 U2 R2 U R2 U2' R2 y' R2 U' R2 U2 R2 B2}}
{{Alg|F2 U2' R2 U R2 U2' R2 F2 U' F2 U2' F2 R2}}
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U' R2 U2 F2}}
</td>
<td valign='top'>

===Ra Permutation===
[[File:PLL R(a).png]]
{{Alg|y2 R2 U' R2 U R2 U2 R2 y U R2 U R2 U' R2 U' F2}}
{{Alg|y F2 U2 R2 U' L2 U R2 F2 U F2 U2 L2 U' F2}}
</td>
<td valign='top'>

===Rb Permutation===
[[File:PLL R(b).png]]
{{Alg|y2 R2 U R2 U' R2 U2' R2 U' y' R2 U' R2 U R2 U B2}}
{{Alg|y F2 R2 F2 U F2 R2 U R2 U' R2 U F2 U' R2 F2}}
{{Alg|y F2 U2 L2 U R2 U' L2 F2 U' F2 U2 R2 U F2}}
</td>
<td valign='top'>

===T Permutation===
[[File:PLL T.png]]
{{Alg|R2 U' R2 U R2 y R2 U R2 U' R2}}
{{Alg|R2 D' F2 U F2 R2 U R2 U' R2}}
</tr>
<td valign='top'>

===V Permutation===
[[File:PLL V.png]]
{{Alg|R2 U' R2 U2 F2 U R2 U R2 y' R2 U2 R2 U f2 x2}}
{{Alg|R2 D R2 D2 F2 U' F2 D R2 F2 U2 F2 U R2 U'}}
</td>
<td valign='top'>

===Y Permutation===
[[File:PLL Y.png]]
{{Alg|y2 R2 U' R2 U2 y R2 U R2 U R2 U2 R2 y' R2 U R2}}
{{Alg|y R2 U R2 U2 F2 U' F2 U' F2 U2 F2 R2 U' R2}}
</td>

<tr>
<td valign='top'>
==All Corners Solved (Parity)==
<tr>
<td valign='top'>

===I Permutation===
[[File:ParityPLL1.png]]
{{Alg|R2 U2 R2 U2 R2}}
</td>
<td valign='top'>

===Adjacent Edges Permutation===
[[File:ParityPLLtwo.png]]
{{Alg|R2 U R2 U' R2 U2 R2 U2 R2 U' R2 U' R2}}
</td>
<td valign='top'>

===Oa Permutation===
[[File:ParityPLL5.png]]
{{Alg|M2 U' M2 U' M2 F2 M2 y' U2 R2 U2 R2}}
</td>
<td valign='top'>

===Ob Permutation===
[[File:ParityPLL4.png]]
{{Alg|R2 U2 R2 U2 y M2 F2 M2 U M2 U M2}}
</tr>
<td valign='top'>

===W Permutation===
[[File:ParityPLL3.png]]
{{Alg|r2 U M2 U R2 U' M2 U' r2}}
</td>

<tr>
<td valign='top'>
==Adjacent Corner Swap (Parity)==
<tr>
<td valign='top'>

===Adjacent Corners Permutation===
[[File:ADJC_parity_pll.png]]
{{Alg|y R2 U2 R2 U2 R2 U R2 U R2 U' R2 y' R2 U' R2 U R2}}

</td>
<td valign='top'>
===Pa Permutation===
[[File:Pa parity pll.png]]
{{Alg|y' F2 U R2 U R2 U2 F2 U' R2 U' R2 U' R2}}

</td>
<td valign='top'>
===Pb Permutation===
[[File:Pb parity pll.png]]
{{Alg|y R2 U R2 U R2 U F2 U2 R2 U' R2 U' F2}}

</td>
<td valign='top'>
===Ka Permutation===
[[File:Ka Pll Parity.png]]
{{Alg|R2 U R2 U F2 U' R2 U R2 U F2 U R2}}

</tr>
<td valign='top'>
===Kb Permutation===
[[File:Kb pll parity.png]]
{{Alg|R2 U R2 U' F2 U R2 U R2 U2 F2 R2}}

</td>
<td valign='top'>
===Ba Permutation===
[[File:Ba pll parity.png]]
{{Alg|R2 U' R2 U R2 U2 y R2 U2 R2 U' R2 U' R2}}

</td>
<td valign='top'>
===Bb Permutation===
[[File:Bb parity pll.png]]
{{Alg|R2 U R2 U' R2 U2 y' R2 U2 R2 U R2 U R2}}
{{Alg|R2 U R2 U F2 U2 R2 F2 U F2 U F2}}

</td>
<td valign='top'>
===Da Permutation===
[[File:Da pll parity.png]]
{{Alg|R2 U' R2 U' R2 U2' R2 y U2 R2 U R2 U' R2}}
{{Alg|R2 U' R2 U F2 U' F2 U' R2 U2 F2 R2}}

</tr>
<td valign='top'>
===Db Permutation===
[[File:DD pll parity.png]]
{{Alg|R2 U R2 U R2 U2 R2 y' U2 R2 U' R2 U R2}}
{{Alg|R2 U R2 U R2 F2 U2 R2 U F2 U F2 U2}}

</td>
<td valign='top'>
===Ca Permutation===
[[File:Ca parity pll.png]]
{{Alg|y' R2 r2 F2 U r2 U R2 U2 F2 r2 U r2 U R2}}
{{Alg|y' R2 F2 U' R2 F2 U R2 U2 R2 U' R2 F2 U R2}}

</td>
<td valign='top'>
===Cb Permutation===
[[File:Cb parity pll.png]]
{{Alg|R2 U' r2 U' r2 F2 U2 R2 U' r2 U' F2 r2 R2}}
{{Alg|R2 U' F2 R2 U R2 U2 R2 U' F2 R2 U F2 R2}}

</td>
<td valign='top'>
===M Permutation===
[[File:M pll parity.png]]
{{Alg|R2 U' R2 U R2 y R2 U R2 U R2 U2 R2 U}}
</td>

<tr>
<td valign='top'>
==Diagonal Corners Swap (Parity)==
<tr>
<td valign='top'>

===Diagonal Corners Permutation===
[[File:ParityPLL6.png]]
{{Alg|y F2 R2 U2 R2 U' R2 y' R2 U2 R2 U R2 B2 U2 B2}}
{{Alg|y F2 R2 U2 R2 U' R2 F2 U2 F2 U F2 R2 U2 R2}}

</td>
<td valign='top'>

===Q Permutation===
[[File:ParityPLL8.png]]
{{Alg|R2 U' F2 U2 R2 U F2 U' R2 U2 F2 U R2}}

</td>
<td valign='top'>

===X Permutation===
[[File:ParityPLL7.png]]
{{Alg|F2 R2 U R2 U2 F2 U' R2 U F2 U2 R2 U' R2 F2}}
{{Alg|F2 r2 U F2 U2 r2 U' F2 U r2 U2 F2 U' r2 F2}}
{{Alg|F2 U' R2 r2 U' F2 r2 U' r2 U2 F2 U' r2 U2 F2}}
{{Alg|F2 U' R2 r2 U' F2 r2 U F2 U2 r2 U r2 U2 F2}}
{{Alg|F2 U2 R2 U' r2 U F2 R2 F2 U' r2 U R2 U2 F2}}
</td>
<td valign='top'>

===Sa Permutation===
[[File:Sb_PLL_Parity.png]]
{{Alg|R2 U' F2 U R2 U' F2 U' R2 U R2 U' R2}}

</tr>
<td valign='top'>

===Sb Permutation===
[[File:Sa_PLL_Parity.png]]
{{Alg|y R2 U' R2 U2 F2 U R2 U R2 U2 F2 U' R2}}

</tr>
<td valign='top'>
=External Links=
* [https://docs.google.com/spreadsheets/d/1uwCNW2EdiuEKNUjoW9VboVuwQACywqULWZUlY2RX3B4/edit?gid=1389888337#gid=1389888337 akanearcane's 2x3x3 Rubik's Domino Algorithm Sheet]

Rubik's Domino Algorithms

2026-05-25T20:35:35Z

Manfredi:

'''Rubik's Domino 1-Look Last Layer''' refers to the [[Last Layer]] of the [[Rubik's Domino]]. This cuboid is functionally a 3x3 where the only moves allowed are〈U, D, R2, L2, F2, B2〉and the equator line is ignored.
In this 3x3x2 cuboid, [[OLL]] is always skipped after compleating the first layer: it is impossible to not have the two 3x3s faces always oriented correctly.
[[File:Domino_reduction_pairty.png|thumb|right|"(R2 U2)3" is an example of a swap of four edges, effectivelly creating a swap of 2 visible edges and 2 invisible edges on the Rubik's Domino.]]
The reason why you can get pairity on the Domino Cube is because swapping 4 edges is possible on a 3x3, therefore you can swap 2 pieces on the hidden equator line of the Domino Cube to swap just two pieces.

=3x3 Top Layer: Last Layer Algorithms=

<table cellspacing='5' cellpadding='5'>
<tr>
<td valign='top'>
==Permutations of edges only (No Parity)==
<tr>
<td valign='top'>
===H Permutation===
[[File:PLL H.png]]
{{Alg|M2 U M2 U2 M2 U M2}}

</td>

<td valign='top'>
===Ua Permutation===
[[File:PLL U(a).png]]
{{Alg|y2 F2 U R2 F2 R2'U2 R2 F2 R2 U F2}}
{{Alg|R2 U F2 L2 B2 D' B2 L2 F2 U2 R2}}

</td>
<td valign='top'>
===Ub Permutation===
[[File:PLL U(b).png]]
{{Alg|y2 F2 U' R2 F2 R2 U2 R2 F2 R2 U' F2}}
{{Alg|R2 U2 F2 L2 B2 D B2 L2 F2 U' R2}}

</td>
<td valign='top'>
===Z Permutation===
[[File:PLL Z.png]]
{{Alg|M2 U' M2 F2 M2 F2 U M2}}
{{Alg|y F2 M2 F2 M2 U M2 U M2}}
</td>

<tr>
<td valign='top'>
==Permutations of corners only (No Parity)==
<tr>
<td valign='top'>

===Aa Permutation===
[[File:PLL A(a).png]]
{{Alg|y2 R2 U R2 U' F2 U R2 U' F2 R2}}
{{Alg|R2 U F2 U' F2 R2 U' R2 U F2}}

</td>
<td valign='top'>
===Ab Permutation===
[[File:PLL A(b).png]]
{{Alg|y2 R2 F2 U R2 U' F2 U R2 U' R2}}
{{Alg|F2 U' R2 U R2 F2 U F2 U' R2}}

</td>
<td valign='top'>
===E Permutation===
[[File:PLL E.png]]
{{Alg|R2 U2 R2 U' R2 U2 y' R2 U' R2 U R2 y U2 R2 U' R2}}
{{Alg|y R2 U' R2 U B2 U' R2 F2 U B2 U' F2 U R2}}
{{Alg|F2 U R2 U' L2 U R2 F2 U' L2 U F2 U' F2}}
</td>

<tr>
<td valign='top'>
==Permutations of Edges and Corners (No Parity)==
<tr>
<td valign='top'>

===F Permutation===
[[File:PLL F.png]]
{{Alg|y R2 U R2 F2 U2 F2 U R2 U' R2 U' R2 U2 F2}}
{{Alg|R2 F2 U' F2 D F2 L2 D L2 D' L2 U L2 F2 R2}}
</td>
<td valign='top'>

===Ga Permutation===
[[File:PLL G(a).png]]
{{Alg|y2 F2 r2 R2 U F2 U' R2 U R2 U' r2 F2}}
{{Alg|y' F2 U2 F2 U F2 U' F2 U' R2 U2 F2 U F2 U R2}}
{{Alg|y2 F2 R2 L2 U R2 U' R2 U F2 U' L2 F2}}
</td>
<td valign='top'>

===Gb Permutation===
[[File:PLL G(b).png]]
{{Alg|y2 F2 r2 U R2 U' R2 U F2 U' R2 r2 F2 U}}
{{Alg|y2 F2 L2 U F2 U' R2 U R2 U' M2 B2}}
</td>
<td valign='top'>

===Gc Permutation===
[[File:PLL G(c).png]]
{{Alg|y2 F2 R2 r2 U' F2 U r2 U' F2 U R2 F2}}
{{Alg|R2 U2 R2 U' R2 U R2 U F2 U2 R2 U' R2 U' F2}}
{{Alg|y2 F2 R2 L2 U' L2 U L2 D' L2 D R2 F2}}
</tr>
<td valign='top'>

===Gd Permutation===
[[File:PLL G(d).png]]
{{Alg|y2 F2 R2 U' F2 U r2 U' F2 U R2 r2 F2}}
{{Alg|y' U2 F2 U R2 U2 F2 R2 U' R2 U' R2 U F2 U F2}}
{{Alg|y2 F2 R2 D' L2 D L2 U' L2 U L2 R2 F2}}
</td>
<td valign='top'>

===Ja Permutation===
[[File:PLL J(a).png]]
{{Alg|y2 R2 U' R2 U y' R2 U' R2 U R2 B2}}
{{Alg|y2 R2 U' R2 U F2 U' F2 U F2 R2}}
{{Alg|y D2 R2 F2 D' L2 U L2 D' L2 U L2}}
</td>
<td valign='top'>

===Jb Permutation===
[[File:PLL J(b).png]]
{{Alg|y2 F2 R2 U R2 U' R2 y' U R2 U' R2}}
{{Alg|y2 F2 R2 U R2 U' R2 U F2 U' F2}}
{{Alg|y' D2 L2 F2 D R2 U' R2 D R2 U' R2}}
</td>
<td valign='top'>

===Na Permutation===
[[File:PLL N(a).png]]
{{Alg|F2 R2 U2' R2 U' R2 y' R2 U2' R2 U R2 U2' f2 x2}}
{{Alg|R2 U2 F2 U' F2 U2 F2 R2 U R2 U2 R2 F2}}
</tr>
<td valign='top'>

===Nb Permutation===
[[File:PLL N(b).png]]
{{Alg|F2 U2 R2 U R2 U2' R2 y' R2 U' R2 U2 R2 B2}}
{{Alg|F2 U2' R2 U R2 U2' R2 F2 U' F2 U2' F2 R2}}
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U' R2 U2 F2}}
</td>
<td valign='top'>

===Ra Permutation===
[[File:PLL R(a).png]]
{{Alg|y2 R2 U' R2 U R2 U2 R2 y U R2 U R2 U' R2 U' F2}}
{{Alg|y F2 U2 R2 U' L2 U R2 F2 U F2 U2 L2 U' F2}}
</td>
<td valign='top'>

===Rb Permutation===
[[File:PLL R(b).png]]
{{Alg|y2 R2 U R2 U' R2 U2' R2 U' y' R2 U' R2 U R2 U B2}}
{{Alg|y F2 R2 F2 U F2 R2 U R2 U' R2 U F2 U' R2 F2}}
{{Alg|y F2 U2 L2 U R2 U' L2 F2 U' F2 U2 R2 U F2}}
</td>
<td valign='top'>

===T Permutation===
[[File:PLL T.png]]
{{Alg|R2 U' R2 U R2 y R2 U R2 U' R2}}
{{Alg|R2 D' F2 U F2 R2 U R2 U' R2}}
</tr>
<td valign='top'>

===V Permutation===
[[File:PLL V.png]]
{{Alg|R2 U' R2 U2 F2 U R2 U R2 y' R2 U2 R2 U f2 x2}}
{{Alg|R2 D R2 D2 F2 U' F2 D R2 F2 U2 F2 U R2 U'}}
</td>
<td valign='top'>

===Y Permutation===
[[File:PLL Y.png]]
{{Alg|y2 R2 U' R2 U2 y R2 U R2 U R2 U2 R2 y' R2 U R2}}
{{Alg|y R2 U R2 U2 F2 U' F2 U' F2 U2 F2 R2 U' R2}}
</td>

<tr>
<td valign='top'>
==All Corners Solved (Parity)==
<tr>
<td valign='top'>

===I Permutation===
[[File:ParityPLL1.png]]
{{Alg|R2 U2 R2 U2 R2}}
</td>
<td valign='top'>

===Adjacent Edges Permutation===
[[File:ParityPLLtwo.png]]
{{Alg|R2 U R2 U' R2 U2 R2 U2 R2 U' R2 U' R2}}
</td>
<td valign='top'>

===Oa Permutation===
[[File:ParityPLL5.png]]
{{Alg|M2 U' M2 U' M2 F2 M2 y' U2 R2 U2 R2}}
</td>
<td valign='top'>

===Ob Permutation===
[[File:ParityPLL4.png]]
{{Alg|R2 U2 R2 U2 y M2 F2 M2 U M2 U M2}}
</tr>
<td valign='top'>

===W Permutation===
[[File:ParityPLL3.png]]
{{Alg|r2 U M2 U R2 U' M2 U' r2}}
</td>

<tr>
<td valign='top'>
==Adjacent Corner Swap (Parity)==
<tr>
<td valign='top'>

===Adjacent Corners Permutation===
[[File:ADJC_parity_pll.png]]
{{Alg|y R2 U2 R2 U2 R2 U R2 U R2 U' R2 y' R2 U' R2 U R2}}

</td>
<td valign='top'>
===Pa Permutation===
[[File:Pa parity pll.png]]
{{Alg|y' F2 U R2 U R2 U2 F2 U' R2 U' R2 U' R2}}

</td>
<td valign='top'>
===Pb Permutation===
[[File:Pb parity pll.png]]
{{Alg|y R2 U R2 U R2 U F2 U2 R2 U' R2 U' F2}}

</td>
<td valign='top'>
===Ka Permutation===
[[File:Ka Pll Parity.png]]
{{Alg|R2 U R2 U F2 U' R2 U R2 U F2 U R2}}

</tr>
<td valign='top'>
===Kb Permutation===
[[File:Kb pll parity.png]]
{{Alg|R2 U R2 U' F2 U R2 U R2 U2 F2 R2}}

</td>
<td valign='top'>
===Ba Permutation===
[[File:Ba pll parity.png]]
{{Alg|R2 U' R2 U R2 U2 y R2 U2 R2 U' R2 U' R2}}

</td>
<td valign='top'>
===Bb Permutation===
[[File:Bb parity pll.png]]
{{Alg|R2 U R2 U' R2 U2 y' R2 U2 R2 U R2 U R2}}
{{Alg|R2 U R2 U F2 U2 R2 F2 U F2 U F2}}

</td>
<td valign='top'>
===Da Permutation===
[[File:Da pll parity.png]]
{{Alg|R2 U' R2 U' R2 U2' R2 y U2 R2 U R2 U' R2}}
{{Alg|R2 U' R2 U F2 U' F2 U' R2 U2 F2 R2}}

</tr>
<td valign='top'>
===Db Permutation===
[[File:DD pll parity.png]]
{{Alg|R2 U R2 U R2 U2 R2 y' U2 R2 U' R2 U R2}}
{{Alg|R2 U R2 U R2 F2 U2 R2 U F2 U F2 U2}}

</td>
<td valign='top'>
===Ca Permutation===
[[File:Ca parity pll.png]]
{{Alg|y' R2 r2 F2 U r2 U R2 U2 F2 r2 U r2 U R2}}
{{Alg|y' R2 F2 U' R2 F2 U R2 U2 R2 U' R2 F2 U R2}}

</td>
<td valign='top'>
===Cb Permutation===
[[File:Cb parity pll.png]]
{{Alg|R2 U' r2 U' r2 F2 U2 R2 U' r2 U' F2 r2 R2}}
{{Alg|R2 U' F2 R2 U R2 U2 R2 U' F2 R2 U F2 R2}}

</td>
<td valign='top'>
===M Permutation===
[[File:M pll parity.png]]
{{Alg|R2 U' R2 U R2 y R2 U R2 U R2 U2 R2 U}}
</td>

<tr>
<td valign='top'>
==Diagonal Corners Swap (Parity)==
<tr>
<td valign='top'>

===Diagonal Corners Permutation===
[[File:ParityPLL6.png]]
{{Alg|y F2 R2 U2 R2 U' R2 y' R2 U2 R2 U R2 B2 U2 B2}}
{{Alg|y F2 R2 U2 R2 U' R2 F2 U2 F2 U F2 R2 U2 R2}}

</td>
<td valign='top'>

===Q Permutation===
[[File:ParityPLL8.png]]
{{Alg|R2 U' F2 U2 R2 U F2 U' R2 U2 F2 U R2}}

</td>
<td valign='top'>

===X Permutation===
[[File:ParityPLL7.png]]
{{Alg|F2 R2 U R2 U2 F2 U' R2 U F2 U2 R2 U' R2 F2}}
{{Alg|F2 r2 U F2 U2 r2 U' F2 U r2 U2 F2 U' r2 F2}}
{{Alg|F2 U' R2 r2 U' F2 r2 U' r2 U2 F2 U' r2 U2 F2}}
{{Alg|F2 U' R2 r2 U' F2 r2 U F2 U2 r2 U r2 U2 F2}}
{{Alg|F2 U2 R2 U' r2 U F2 R2 F2 U' r2 U R2 U2 F2}}
</td>
<td valign='top'>

===Sa Permutation===
[[File:Sb_PLL_Parity.png]]
{{Alg|R2 U' F2 U R2 U' F2 U' R2 U R2 U' R2}}

</tr>
<td valign='top'>

===Sb Permutation===
[[File:Sa_PLL_Parity.png]]
{{Alg|y R2 U' R2 U2 F2 U R2 U R2 U2 F2 U' R2}}

=2x3 Top Layer: Last Layer Algorithms=

<table cellspacing='5' cellpadding='5'>
<tr>
<td valign='top'>
==Permutation of Last Layer==
<tr>
<td valign='top'>
===I Permutation===
[[File:233 1.png]]
{{Alg|R2 U2 F2 R2 F2 U2 R2 F2}}
</td>
<td valign='top'>

===Diagonal Corners Permutation===
[[File:223 2.png]]
{{Alg|R2 U2 R' F2 U2 R2 F2 U2 R U2 F2 R2 F2 R' F2}}
{{Alg|R2 U2 R' U2 B2 R2 B2 R B2 U2 R2 U2 R B2}}

<tr>
<td valign='top'>
==T Shapes==
<tr>
<td valign='top'>
===T Shape 1===
[[File:233 3.png]]
{{Alg|x' R U2 R D2 R' U2 R D2 R2}}
</td>
<td valign='top'>

</tr>
<td valign='top'>
=External Links=
* [https://docs.google.com/spreadsheets/d/1uwCNW2EdiuEKNUjoW9VboVuwQACywqULWZUlY2RX3B4/edit?gid=1389888337#gid=1389888337 akanearcane's 2x3x3 Rubik's Domino Algorithm Sheet]

File:233 3.png

2026-05-25T20:31:54Z

Manfredi:

File:223 2.png

2026-05-25T20:23:09Z

Manfredi:

File:233 1.png

2026-05-25T20:19:01Z

Manfredi:

Rubik's Domino Algorithms

2026-05-24T14:19:07Z

Manfredi:

'''Rubik's Domino 1-Look Last Layer''' refers to the [[Last Layer]] of the [[Rubik's Domino]]. This cuboid is functionally a 3x3 where the only moves allowed are〈U, D, R2, L2, F2, B2〉and the equator line is ignored.
In this 3x3x2 cuboid, [[OLL]] is always skipped after compleating the first layer: it is impossible to not have the two 3x3s faces always oriented correctly.
[[File:Domino_reduction_pairty.png|thumb|right|"(R2 U2)3" is an example of a swap of four edges, effectivelly creating a swap of 2 visible edges and 2 invisible edges on the Rubik's Domino.]]
The reason why you can get pairity on the Domino Cube is because swapping 4 edges is possible on a 3x3, therefore you can swap 2 pieces on the hidden equator line of the Domino Cube to swap just two pieces.

=3x3 Top Layer: Last Layer Algorithms=

<table cellspacing='5' cellpadding='5'>
<tr>
<td valign='top'>
==Permutations of edges only (No Parity)==
<tr>
<td valign='top'>
===H Permutation===
[[File:PLL H.png]]
{{Alg|M2 U M2 U2 M2 U M2}}

</td>

<td valign='top'>
===Ua Permutation===
[[File:PLL U(a).png]]
{{Alg|y2 F2 U R2 F2 R2'U2 R2 F2 R2 U F2}}
{{Alg|R2 U F2 L2 B2 D' B2 L2 F2 U2 R2}}

</td>
<td valign='top'>
===Ub Permutation===
[[File:PLL U(b).png]]
{{Alg|y2 F2 U' R2 F2 R2 U2 R2 F2 R2 U' F2}}
{{Alg|R2 U2 F2 L2 B2 D B2 L2 F2 U' R2}}

</td>
<td valign='top'>
===Z Permutation===
[[File:PLL Z.png]]
{{Alg|M2 U' M2 F2 M2 F2 U M2}}
{{Alg|y F2 M2 F2 M2 U M2 U M2}}
</td>

<tr>
<td valign='top'>
==Permutations of corners only (No Parity)==
<tr>
<td valign='top'>

===Aa Permutation===
[[File:PLL A(a).png]]
{{Alg|y2 R2 U R2 U' F2 U R2 U' F2 R2}}
{{Alg|R2 U F2 U' F2 R2 U' R2 U F2}}

</td>
<td valign='top'>
===Ab Permutation===
[[File:PLL A(b).png]]
{{Alg|y2 R2 F2 U R2 U' F2 U R2 U' R2}}
{{Alg|F2 U' R2 U R2 F2 U F2 U' R2}}

</td>
<td valign='top'>
===E Permutation===
[[File:PLL E.png]]
{{Alg|R2 U2 R2 U' R2 U2 y' R2 U' R2 U R2 y U2 R2 U' R2}}
{{Alg|y R2 U' R2 U B2 U' R2 F2 U B2 U' F2 U R2}}
{{Alg|F2 U R2 U' L2 U R2 F2 U' L2 U F2 U' F2}}
</td>

<tr>
<td valign='top'>
==Permutations of Edges and Corners (No Parity)==
<tr>
<td valign='top'>

===F Permutation===
[[File:PLL F.png]]
{{Alg|y R2 U R2 F2 U2 F2 U R2 U' R2 U' R2 U2 F2}}
{{Alg|R2 F2 U' F2 D F2 L2 D L2 D' L2 U L2 F2 R2}}
</td>
<td valign='top'>

===Ga Permutation===
[[File:PLL G(a).png]]
{{Alg|y2 F2 r2 R2 U F2 U' R2 U R2 U' r2 F2}}
{{Alg|y' F2 U2 F2 U F2 U' F2 U' R2 U2 F2 U F2 U R2}}
{{Alg|y2 F2 R2 L2 U R2 U' R2 U F2 U' L2 F2}}
</td>
<td valign='top'>

===Gb Permutation===
[[File:PLL G(b).png]]
{{Alg|y2 F2 r2 U R2 U' R2 U F2 U' R2 r2 F2 U}}
{{Alg|y2 F2 L2 U F2 U' R2 U R2 U' M2 B2}}
</td>
<td valign='top'>

===Gc Permutation===
[[File:PLL G(c).png]]
{{Alg|y2 F2 R2 r2 U' F2 U r2 U' F2 U R2 F2}}
{{Alg|R2 U2 R2 U' R2 U R2 U F2 U2 R2 U' R2 U' F2}}
{{Alg|y2 F2 R2 L2 U' L2 U L2 D' L2 D R2 F2}}
</tr>
<td valign='top'>

===Gd Permutation===
[[File:PLL G(d).png]]
{{Alg|y2 F2 R2 U' F2 U r2 U' F2 U R2 r2 F2}}
{{Alg|y' U2 F2 U R2 U2 F2 R2 U' R2 U' R2 U F2 U F2}}
{{Alg|y2 F2 R2 D' L2 D L2 U' L2 U L2 R2 F2}}
</td>
<td valign='top'>

===Ja Permutation===
[[File:PLL J(a).png]]
{{Alg|y2 R2 U' R2 U y' R2 U' R2 U R2 B2}}
{{Alg|y2 R2 U' R2 U F2 U' F2 U F2 R2}}
{{Alg|y D2 R2 F2 D' L2 U L2 D' L2 U L2}}
</td>
<td valign='top'>

===Jb Permutation===
[[File:PLL J(b).png]]
{{Alg|y2 F2 R2 U R2 U' R2 y' U R2 U' R2}}
{{Alg|y2 F2 R2 U R2 U' R2 U F2 U' F2}}
{{Alg|y' D2 L2 F2 D R2 U' R2 D R2 U' R2}}
</td>
<td valign='top'>

===Na Permutation===
[[File:PLL N(a).png]]
{{Alg|F2 R2 U2' R2 U' R2 y' R2 U2' R2 U R2 U2' f2 x2}}
{{Alg|R2 U2 F2 U' F2 U2 F2 R2 U R2 U2 R2 F2}}
</tr>
<td valign='top'>

===Nb Permutation===
[[File:PLL N(b).png]]
{{Alg|F2 U2 R2 U R2 U2' R2 y' R2 U' R2 U2 R2 B2}}
{{Alg|F2 U2' R2 U R2 U2' R2 F2 U' F2 U2' F2 R2}}
{{Alg|R2 F2 U2 F2 U F2 R2 U2 R2 U' R2 U2 F2}}
</td>
<td valign='top'>

===Ra Permutation===
[[File:PLL R(a).png]]
{{Alg|y2 R2 U' R2 U R2 U2 R2 y U R2 U R2 U' R2 U' F2}}
{{Alg|y F2 U2 R2 U' L2 U R2 F2 U F2 U2 L2 U' F2}}
</td>
<td valign='top'>

===Rb Permutation===
[[File:PLL R(b).png]]
{{Alg|y2 R2 U R2 U' R2 U2' R2 U' y' R2 U' R2 U R2 U B2}}
{{Alg|y F2 R2 F2 U F2 R2 U R2 U' R2 U F2 U' R2 F2}}
{{Alg|y F2 U2 L2 U R2 U' L2 F2 U' F2 U2 R2 U F2}}
</td>
<td valign='top'>

===T Permutation===
[[File:PLL T.png]]
{{Alg|R2 U' R2 U R2 y R2 U R2 U' R2}}
{{Alg|R2 D' F2 U F2 R2 U R2 U' R2}}
</tr>
<td valign='top'>

===V Permutation===
[[File:PLL V.png]]
{{Alg|R2 U' R2 U2 F2 U R2 U R2 y' R2 U2 R2 U f2 x2}}
{{Alg|R2 D R2 D2 F2 U' F2 D R2 F2 U2 F2 U R2 U'}}
</td>
<td valign='top'>

===Y Permutation===
[[File:PLL Y.png]]
{{Alg|y2 R2 U' R2 U2 y R2 U R2 U R2 U2 R2 y' R2 U R2}}
{{Alg|y R2 U R2 U2 F2 U' F2 U' F2 U2 F2 R2 U' R2}}
</td>

<tr>
<td valign='top'>
==All Corners Solved (Parity)==
<tr>
<td valign='top'>

===I Permutation===
[[File:ParityPLL1.png]]
{{Alg|R2 U2 R2 U2 R2}}
</td>
<td valign='top'>

===Adjacent Edges Permutation===
[[File:ParityPLLtwo.png]]
{{Alg|R2 U R2 U' R2 U2 R2 U2 R2 U' R2 U' R2}}
</td>
<td valign='top'>

===Oa Permutation===
[[File:ParityPLL5.png]]
{{Alg|M2 U' M2 U' M2 F2 M2 y' U2 R2 U2 R2}}
</td>
<td valign='top'>

===Ob Permutation===
[[File:ParityPLL4.png]]
{{Alg|R2 U2 R2 U2 y M2 F2 M2 U M2 U M2}}
</tr>
<td valign='top'>

===W Permutation===
[[File:ParityPLL3.png]]
{{Alg|r2 U M2 U R2 U' M2 U' r2}}
</td>

<tr>
<td valign='top'>
==Adjacent Corner Swap (Parity)==
<tr>
<td valign='top'>

===Adjacent Corners Permutation===
[[File:ADJC_parity_pll.png]]
{{Alg|y R2 U2 R2 U2 R2 U R2 U R2 U' R2 y' R2 U' R2 U R2}}

</td>
<td valign='top'>
===Pa Permutation===
[[File:Pa parity pll.png]]
{{Alg|y' F2 U R2 U R2 U2 F2 U' R2 U' R2 U' R2}}

</td>
<td valign='top'>
===Pb Permutation===
[[File:Pb parity pll.png]]
{{Alg|y R2 U R2 U R2 U F2 U2 R2 U' R2 U' F2}}

</td>
<td valign='top'>
===Ka Permutation===
[[File:Ka Pll Parity.png]]
{{Alg|y R2 U R2 U R2 U F2 U2 R2 U' R2 U' F2}}

</tr>
<td valign='top'>
===Kb Permutation===
[[File:Kb pll parity.png]]

</td>
<td valign='top'>
===Ba Permutation===
[[File:Ba pll parity.png]]

</td>
<td valign='top'>
===Bb Permutation===
[[File:Bb parity pll.png]]

</td>
<td valign='top'>
===Da Permutation===
[[File:Da pll parity.png]]

</tr>
<td valign='top'>
===Db Permutation===
[[File:DD pll parity.png]]

</td>
<td valign='top'>
===Ca Permutation===
[[File:Ca parity pll.png]]

</td>
<td valign='top'>
===Cb Permutation===
[[File:Cb parity pll.png]]

</td>
<td valign='top'>
===M Permutation===
[[File:M pll parity.png]]

This article is not finished

Parity PLL

2026-05-23T16:58:49Z

Manfredi: /* Diagonal Corners Swap Cases */

Normal [[PLL]] (Permutation of the Last Layer) contains only even [[permutation]]s. However, in certain puzzles (for instance, the [[Square-1]],the [[4x4x4]] and some [[cuboid]]s) this restriction is absent because of the existence of [[parity]]. This means that on these puzzles we can get a PLL that is not one of the normal 21 found on the [[3x3x3]] - that is, we can get a '''Parity PLL'''.

The following page gives a list of all the parity PLLs, along with some tentative names. Unlike normal PLL, there is no official/traditional naming scheme, probably because few people have bothered to learn algorithms for each of these cases. These cases can simply be solved by doing a parity algorithm and then solving the normal PLL case, but it may be faster to have a one-look alg for them, depending on the puzzle.

=All Parity PLL Cases=
==All Corners Solved Cases==

{| cellspacing='7' cellpadding='7'
|- valign='top'
| '''I Permutation'''
[[File:ParityPLL1.png]]

Other Names: Pure-E Permutation, Opposite Parity

| '''Adjacent Edges Permutation'''
[[File:ParityPLLtwo.png]]

Other Names: // Permutation, Double Slash Permutation, Adjacent-E Permutation, Adjacent Parity

| '''W Permutation'''
[[File:ParityPLL3.png]]

Other Names: B Permutation

|- valign='top'
| '''Oa Permutation'''
[[File:ParityPLL5.png]]

Other Names: O- Permutation, CcwO Permutation

| '''Ob Permutation'''
[[File:ParityPLL4.png]]

Other Names: O+ Permutation, CwO Permutation
|}
==Adjacent Corner Swap Cases==

{| cellspacing='7' cellpadding='7'
|- valign='top'
| '''Adjacent Corners Permutation'''
[[File:ADJC_parity_pll.png]]

Other Names: Pj Permutation

| '''Pa Permutation'''
[[File:Pa parity pll.png]]

Other Names: Ka Permutation

| '''Pb Permutation'''
[[File:Pb parity pll.png]]

Other Names: Kb Permutation

|- valign='top'
| '''Ka Permutation'''
[[File:Ka Pll Parity.png]]

| '''Kb Permutation'''
[[File:Kb pll parity.png]]

| '''Ba Permutation'''
[[File:Ba pll parity.png]]

Other Names: RGc Permutation

|- valign='top'
| '''Bb Permutation'''
[[File:Bb parity pll.png]]

Other Names: RGa Permutation

| '''Da Permutation'''
[[File:Da pll parity.png]]

Other Names: RGb Permutation

| '''Db Permutation'''
[[File:DD pll parity.png]]

Other Names: RGd Permutation

|- valign='top'
| '''Ca Permutation'''
[[File:Ca parity pll.png]]

| '''Cb Permutation'''
[[File:Cb parity pll.png]]

| '''M Permutation'''
[[File:M pll parity.png]]
|}
==Diagonal Corners Swap Cases==

{| cellspacing='7' cellpadding='7'
|- valign='top'
| '''Diagonal Corners Permutation'''
[[File:ParityPLL6.png]]

Other Names: Slash Permutation, \ Permutation

| '''Q Permutation'''
[[File:ParityPLL8.png]]

Other Names: θ Permutation, Theta Permutation

| '''X Permutation'''
[[File:ParityPLL7.png]]

Other Names: Ξ Permutation, Xi Permutation

|- valign='top'
| '''Sb Permutation'''
[[File:Sa PLL Parity.png]]

| '''Sa Permutation'''
[[File:Sb PLL Parity.png]]
|}

=How Parity Algorithms Affect Cases=
In speedsolving, you can either learn specific algorithms for each Parity PLL or you can learn what regular PLL you are gonna get after doing the regular opposite swap parity algorithm to reduce reaction time.

Generally, an opposite swap of edges is the fastest parity algorithms in a puzzle, therefore you should learn based on your preferences on what side you should perform the parity algorithm.

Note that in the following table, the orientation on which side you will get the PLL is correct, but the colors are not.
{| class="wikitable"
! Parity PLL
! PLL after vertical opposite edge swap
! PLL after horizontal opposite edge swap
|-
| [[File:ParityPLL1.png]]
I Permutation
| Solves the layer
| [[File:PLL H.png]]
H Permutation
|-
| [[File:ParityPLLtwo.png]]
Adjacent Edges Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL U(b).png|150px]]
</div>
Ub Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL U(a).png|150px]]
</div>
Ua Permutation
|-
| [[File:ParityPLL3.png]]
W Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL U(b).png|150px]]
</div>
Ub Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:PLL U(a).png|150px]]
</div>
Ua Permutation
|-
| [[File:ParityPLL5.png]]
Oa Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL Z.png]]
</div>
Z Permutation
| [[File:PLL Z.png]]
Z Permutation
|-
| [[File:ParityPLL4.png]]
Ob Permutation
| [[File:PLL Z.png]]
Z Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL Z.png]]
</div>
Z Permutation
|-
| [[File:ADJC parity pll.png]]
Adjacent Corners Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:F.gif]]
</div>
F Permutation
| [[File:T.gif]]
T Permutation
|-
| [[File:Pa parity pll.png]]
Pa Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:J1.gif]]
</div>
Ja Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G3.gif]]
</div>
Ga Permutation
|-
| [[File:Pb parity pll.png]]
Pb Permutation
| [[File:J.gif]]
Jb Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G1.gif]]
</div>
Gc Permutation
|-
| [[File:Ka Pll Parity.png]]
Ka Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL A(b).png]]
</div>
Ab Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL A(a).png]]
</div>
Aa Permutation
|-
| [[File:Kb pll parity.png]]
Kb Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL A(a).png]]
</div>
Aa Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL A(b).png]]
</div>
Ab Permutation
|-
| [[File:Ba pll parity.png]]
Ba Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G1.gif]]
</div>
Gc Permutation
| [[File:J.gif]]
Jb Permutation
|-
| [[File:Bb parity pll.png]]
Bb Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G3.gif]]
</div>
Ga Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:J1.gif]]
</div>
Ja Permutation
|-
| [[File:Da pll parity.png]]
Da Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:G.gif]]
</div>
Gd Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:R1.gif]]
</div>
Ra Permutation
|-
| [[File:DD pll parity.png]]
Db Permutation
| [[File:G2.gif]]
Gb Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:R.gif]]
</div>
Rb Permutation
|-
| [[File:Ca parity pll.png]]
Ca Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:R.gif]]
</div>
Rb Permutation
| [[File:G2.gif]]
Gb Permutation
|-
| [[File:Cb parity pll.png]]
Cb Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:R1.gif]]
</div>
Ra Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:G.gif]]
</div>
Gd Permutation
|-
| [[File:M pll parity.png]]
M Permutation
| [[File:T.gif]]
T Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:F.gif]]
</div>
F Permutation
|-
| [[File:ParityPLL6.png]]
Diagonal Corners Permutation
| [[File:N1.gif]]
I Permutation
| [[File:N.gif]]
I Permutation
|-
| [[File:ParityPLL8.png]]
Q Permutation
| [[File:PLL_E.png]]
E Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL_E.png]]
</div>
E Permutation
|-
| [[File:ParityPLL7.png]]
X Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL_E.png]]
</div>
E Permutation
| [[File:PLL_E.png]]
E Permutation
|-
| [[File:Sa PLL Parity.png]]
Sa Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:Y.gif]]
</div>
Y Permutation
| [[File:V.gif]]
V Permutation
|-
| [[File:Sb PLL Parity.png]]
Sb Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:Y.gif]]
</div>
Y Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:V.gif]]
</div>
V Permutation
|}

[[Category:Algorithms]]
[[Category:Puzzle theory]]

Parity PLL

2026-05-23T16:26:49Z

Manfredi:

Normal [[PLL]] (Permutation of the Last Layer) contains only even [[permutation]]s. However, in certain puzzles (for instance, the [[Square-1]],the [[4x4x4]] and some [[cuboid]]s) this restriction is absent because of the existence of [[parity]]. This means that on these puzzles we can get a PLL that is not one of the normal 21 found on the [[3x3x3]] - that is, we can get a '''Parity PLL'''.

The following page gives a list of all the parity PLLs, along with some tentative names. Unlike normal PLL, there is no official/traditional naming scheme, probably because few people have bothered to learn algorithms for each of these cases. These cases can simply be solved by doing a parity algorithm and then solving the normal PLL case, but it may be faster to have a one-look alg for them, depending on the puzzle.

=All Parity PLL Cases=
==All Corners Solved Cases==

{| cellspacing='7' cellpadding='7'
|- valign='top'
| '''I Permutation'''
[[File:ParityPLL1.png]]

Other Names: Pure-E Permutation, Opposite Parity

| '''Adjacent Edges Permutation'''
[[File:ParityPLLtwo.png]]

Other Names: // Permutation, Double Slash Permutation, Adjacent-E Permutation, Adjacent Parity

| '''W Permutation'''
[[File:ParityPLL3.png]]

Other Names: B Permutation

|- valign='top'
| '''Oa Permutation'''
[[File:ParityPLL5.png]]

Other Names: O- Permutation, CcwO Permutation

| '''Ob Permutation'''
[[File:ParityPLL4.png]]

Other Names: O+ Permutation, CwO Permutation
|}
==Adjacent Corner Swap Cases==

{| cellspacing='7' cellpadding='7'
|- valign='top'
| '''Adjacent Corners Permutation'''
[[File:ADJC_parity_pll.png]]

Other Names: Pj Permutation

| '''Pa Permutation'''
[[File:Pa parity pll.png]]

Other Names: Ka Permutation

| '''Pb Permutation'''
[[File:Pb parity pll.png]]

Other Names: Kb Permutation

|- valign='top'
| '''Ka Permutation'''
[[File:Ka Pll Parity.png]]

| '''Kb Permutation'''
[[File:Kb pll parity.png]]

| '''Ba Permutation'''
[[File:Ba pll parity.png]]

Other Names: RGc Permutation

|- valign='top'
| '''Bb Permutation'''
[[File:Bb parity pll.png]]

Other Names: RGa Permutation

| '''Da Permutation'''
[[File:Da pll parity.png]]

Other Names: RGb Permutation

| '''Db Permutation'''
[[File:DD pll parity.png]]

Other Names: RGd Permutation

|- valign='top'
| '''Ca Permutation'''
[[File:Ca parity pll.png]]

| '''Cb Permutation'''
[[File:Cb parity pll.png]]

| '''M Permutation'''
[[File:M pll parity.png]]
|}
==Diagonal Corners Swap Cases==

{| cellspacing='7' cellpadding='7'
|- valign='top'
| '''Diagonal Corners Permutation'''
[[File:ParityPLL6.png]]

Other Names: Slash Permutation, \ Permutation

| '''Q Permutation'''
[[File:ParityPLL8.png]]

Other Names: θ Permutation, Theta Permutation

| '''X Permutation'''
[[File:ParityPLL7.png]]

Other Names: Ξ Permutation, Xi Permutation

|- valign='top'
| '''Sa Permutation'''
[[File:Sa PLL Parity.png]]

| '''Sb Permutation'''
[[File:Sb PLL Parity.png]]
|}

=How Parity Algorithms Affect Cases=
In speedsolving, you can either learn specific algorithms for each Parity PLL or you can learn what regular PLL you are gonna get after doing the regular opposite swap parity algorithm to reduce reaction time.

Generally, an opposite swap of edges is the fastest parity algorithms in a puzzle, therefore you should learn based on your preferences on what side you should perform the parity algorithm.

Note that in the following table, the orientation on which side you will get the PLL is correct, but the colors are not.
{| class="wikitable"
! Parity PLL
! PLL after vertical opposite edge swap
! PLL after horizontal opposite edge swap
|-
| [[File:ParityPLL1.png]]
I Permutation
| Solves the layer
| [[File:PLL H.png]]
H Permutation
|-
| [[File:ParityPLLtwo.png]]
Adjacent Edges Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL U(b).png|150px]]
</div>
Ub Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL U(a).png|150px]]
</div>
Ua Permutation
|-
| [[File:ParityPLL3.png]]
W Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL U(b).png|150px]]
</div>
Ub Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:PLL U(a).png|150px]]
</div>
Ua Permutation
|-
| [[File:ParityPLL5.png]]
Oa Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL Z.png]]
</div>
Z Permutation
| [[File:PLL Z.png]]
Z Permutation
|-
| [[File:ParityPLL4.png]]
Ob Permutation
| [[File:PLL Z.png]]
Z Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL Z.png]]
</div>
Z Permutation
|-
| [[File:ADJC parity pll.png]]
Adjacent Corners Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:F.gif]]
</div>
F Permutation
| [[File:T.gif]]
T Permutation
|-
| [[File:Pa parity pll.png]]
Pa Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:J1.gif]]
</div>
Ja Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G3.gif]]
</div>
Ga Permutation
|-
| [[File:Pb parity pll.png]]
Pb Permutation
| [[File:J.gif]]
Jb Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G1.gif]]
</div>
Gc Permutation
|-
| [[File:Ka Pll Parity.png]]
Ka Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL A(b).png]]
</div>
Ab Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL A(a).png]]
</div>
Aa Permutation
|-
| [[File:Kb pll parity.png]]
Kb Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:PLL A(a).png]]
</div>
Aa Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL A(b).png]]
</div>
Ab Permutation
|-
| [[File:Ba pll parity.png]]
Ba Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G1.gif]]
</div>
Gc Permutation
| [[File:J.gif]]
Jb Permutation
|-
| [[File:Bb parity pll.png]]
Bb Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:G3.gif]]
</div>
Ga Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:J1.gif]]
</div>
Ja Permutation
|-
| [[File:Da pll parity.png]]
Da Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:G.gif]]
</div>
Gd Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:R1.gif]]
</div>
Ra Permutation
|-
| [[File:DD pll parity.png]]
Db Permutation
| [[File:G2.gif]]
Gb Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:R.gif]]
</div>
Rb Permutation
|-
| [[File:Ca parity pll.png]]
Ca Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:R.gif]]
</div>
Rb Permutation
| [[File:G2.gif]]
Gb Permutation
|-
| [[File:Cb parity pll.png]]
Cb Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:R1.gif]]
</div>
Ra Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:G.gif]]
</div>
Gd Permutation
|-
| [[File:M pll parity.png]]
M Permutation
| [[File:T.gif]]
T Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:F.gif]]
</div>
F Permutation
|-
| [[File:ParityPLL6.png]]
Diagonal Corners Permutation
| [[File:N1.gif]]
I Permutation
| [[File:N.gif]]
I Permutation
|-
| [[File:ParityPLL8.png]]
Q Permutation
| [[File:PLL_E.png]]
E Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL_E.png]]
</div>
E Permutation
|-
| [[File:ParityPLL7.png]]
X Permutation
| <div style="transform: rotate(90deg); display: inline-block; overflow: visible;">
[[File:PLL_E.png]]
</div>
E Permutation
| [[File:PLL_E.png]]
E Permutation
|-
| [[File:Sa PLL Parity.png]]
Sa Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:Y.gif]]
</div>
Y Permutation
| [[File:V.gif]]
V Permutation
|-
| [[File:Sb PLL Parity.png]]
Sb Permutation
| <div style="transform: rotate(180deg); display: inline-block; overflow: visible;">
[[File:Y.gif]]
</div>
Y Permutation
| <div style="transform: rotate(270deg); display: inline-block; overflow: visible;">
[[File:V.gif]]
</div>
V Permutation
|}

[[Category:Algorithms]]
[[Category:Puzzle theory]]

File:Pb parity pll.png

2026-05-22T20:52:36Z

Manfredi:

File:Pa parity pll.png

2026-05-22T20:51:01Z

Manfredi:

File:M pll parity.png

2026-05-22T20:48:55Z

Manfredi:

File:Kb pll parity.png

2026-05-22T20:46:23Z

Manfredi:

File:Ka Pll Parity.png

2026-05-22T20:43:36Z

Manfredi:

File:DD pll parity.png

2026-05-22T20:40:32Z

Manfredi:

File:Da pll parity.png

2026-05-22T20:36:27Z

Manfredi:

File:Cb parity pll.png

2026-05-22T20:33:08Z

Manfredi:

File:Ca parity pll.png

2026-05-22T20:29:08Z

Manfredi:

File:Bb parity pll.png

2026-05-22T20:23:17Z

Manfredi:

File:Ba pll parity.png

2026-05-22T20:20:03Z

Manfredi:

File:ADJC parity pll.png

2026-05-22T20:15:39Z

Manfredi:

File:Sb PLL Parity.png

2026-05-22T20:12:23Z

Manfredi: