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Analysis of another two symmetry subgroups of order 4
Submitted by Herbert Kociemba on Wed, 03/08/2006 - 12:46.The symmetry class C4 defines a 1/4-rotational symmetry around a face (I chose
the UD-axis). It took about 8 days to show that all 36160 cubes, which exactly
have this symmetry (M-reduced) are solvable in at most 20 moves. There are 39
20f*-cubes. 35 of them also have antisymmetry, 4 only have symmetry, so reduced
wrt M+inv there are 37 cubes.
The class D2 (face) consists of all cubes which have a 1/2-rotational symmetry around all faces. Up to M-symmetry there are 23356 cubes, which exactly have this symmetry. It took about 4 days to show, that all cubes of this symmetry class can be solved in 20 moves. There are only 4 cubes which are 20f*, all of them also are antisymmetric. Here are the results:
The class D2 (face) consists of all cubes which have a 1/2-rotational symmetry around all faces. Up to M-symmetry there are 23356 cubes, which exactly have this symmetry. It took about 4 days to show, that all cubes of this symmetry class can be solved in 20 moves. There are only 4 cubes which are 20f*, all of them also are antisymmetric. Here are the results:
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