On 10/19/95 at 22:57:15 Dale Newfield said:

On Fri, 20 Oct 1995, Michiel Boland wrote:
> It is clear that the group G of the cube (the one with
> 4.3252x10^19 elements) can be embedded in a symmetrical group, e.g.
> S_48, since each move of the cube can be seen as a permutation of 48
> objects.

Um...If I were a better net.person, I'd look up which version of the cube
has that number of elements, but wouldn't it be correct to say that each
move of the cube is a permutation of the pieces of the cube, i.e. the 26
cubies? (Or even, depending on which cube-model you are using(This is
what I should have looked up), if you ignore center cubie orientation,
the 20 cubies?)

If that logic holds, then the largest possible S_n would be S_20, much
less than the 32 that you claim is minimal...

You are forgetting the twists of the corner cubies and the flips of the
edge cubies.

As an aside, the S_48 upper bound is already based on ignoring the face
centers (i.e., 8 facelets on each of 6 faces of the cube).

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