[next] [prev] [up] Date: Thu, 19 Jan 95 00:08:00 -0500
[next] [prev] [up] From: Mark Longridge <mark.longridge@canrem.com >
~~~ ~~~ [up] Subject: Shift Invariance Recap
Shift Invariance the Final Chapter??
2 x Order 2           (the diagonal square element)
Subgroup <U2, D2, R2, L2>, order = 2
D2 F2 T2 F2 B2 T2 F2 T2

2 Swap                (the single square element)
Subgroup <U2, D, R2, L>, order = 2
D2 R2 D2 R2 D2 R2

2 H                   (the edge square element)
Subgroup <U, D, R2, L2>, order = 2
L2 R2 B2 L2 R2 F2

12 flip               (the central element)
Subgroup <U, D, F, B, L, R>, order = 2
R1 L1 D2 B3 L2 F2 R2 U3 D1 R3 D2 F3 B3 D3 F2 D3 R2 U3 F2 D3
Special Property: Effects all edges the same

6 Counterclockwise twist   (the odd element)
Subgroup <U, R>, order = 3
U2 R1 U1 R1 U1 R3 U1 R3 U1 R3 U2 R1 U1 R1 U1 R3 U1 R3 U1 R3
Special Property: Effects all corners the same

Martin's message about the SuperSkewb having a non-trivial centre
reminded me that the SuperCube should have 3 more positions which
are also shift invariant:

3x3x3 cube with 6 centre pieces rotated 90, 180 and 270 degrees,
with orders 4, 2 and 4 respectively. This time all the centres
are effected the same!

Naturally there are 3 more positions in SG's <U, R> as well.

A pity there is no "Centre All-Twist" process in any of the cube

-> Mark <-

I'll leave a superflip process for the Magic Dodecahedron as a
'exercise for the reader' ;-)

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