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Use Speffz for wing and center orbits on all cubes. #379

@lgarron

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@lgarron

Filing this to keep track across projects.

  1. CORNERS, EDGES, and CENTERS should match the Reid 3×3×3 definition when they exist (only corners exist on odd cubes).
  2. Wings and centers should use Speffz layout.
  3. The default pattern should have identical pieces for centers on the same side.

I believe @rokicki has a sense for how to implement this.

To save on size, for N×N×N I would prefer to serialize definitions with:

  • Uv
  • Fv
  • F
  • 2F
  • [N-1]F

Then derive:

Derived moves Example
y, z "y": Uv"
x "x": [y: z]"
Lv, Rv, Bv, Dv "Lv": [y': Fv]
Fw "Fw": 2F F
3Fw "3Fw": 3F Fw
4Fw, … [N-1]Fw "4Fw": 4F 3Fw
U, 2U, … [N-1]U "U": "[x': F]"
Uw, 3Uw, … [N-1]Uw "Uw": "[x': Fw]"
(same as for *U and *Uw for the other 4 faces)

In particular, note that the F face is the center of the Speffz net — i.e. the only face that can be moved to any other face with a single rotation move while preserving the ordering of pieces on the face. This makes it nicer to inspect and debug the conjugations for derived moves.

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