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To jump the gun slightly on the group-theoretic explanation,

any sequence of rotations of any number of faces can be

thought of as an atomic "transformation" for the purposes of

group theory. One of the precepts of this theory is that any

such transformation, repeated often enough, will return the

cube to the original state. For instance, given the transform

"rotate top ccw 90", 4 iterations suffice to return the cube

to the original state.

Mike Speciner, a fellow Camexian, claims that no transformation

can be created that requires more than 216 (=6^3) iterations to

return to the virgin state. (He doesn't yet have a cube, but

has been stealing his daughter's blocks and modeling the cube

with them.)

Where does this number come from, and is it true?

I have been playing with various transforms, and have found

at least one reasonably trivial one that requires the 216

iterations: rotate a face 90, then turn the cube 90 and repeat.

The transform here is 4 twists in a band around the axis of

cube rotation. The patterns generated in the process are interesting,

too, though none of them are as unique as the cruciform or center-face patterns.