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' ;-)