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Subject:

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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