And if you color it continuously, why not have continuous moves, too? For
instance, a smooth twist about an axis (like twisting a rubber ball that's
glued to sticks at its poles -- carries meridians into spirals), or a smooth
bending (like pushing one of those poles sideways while holding the other
fixed -- makes parallels not parallel). I suspect that the groups resulting
from some sets of smooth motions would be very simple, but some might have
interesting interactions. A problem with all this smoothness (a feature?) is
that it would enable approximate solutions, iterative converging infinite
"solutions", and disputes about whether SOLVED has in fact been reached --
none of which occur with the real Rubik's.

Steve

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