Mike,

Are you proposing a truly continuous Rubik sphere with an infinite, nay
uncountable, number of slicings with continuously varying hue to distinguish
"slices"?

Such cubes could differ in the "function" that connects the motion of
"neighboring slices". We could have linear, quadratic, and even
hyperexponential axes of rotation. Then giving the cube a spin about each of its
(many) axes, we would have a continuously shifting pattern of color. Maybe
would should leak this idea to George Lucas for the visuals of StarWars III? Or
maybe one of the LISP machine folks can whip up a simulation overnite?

Bill