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I suspect this is why there are (and will probably never be) cubes of

orders greater than 5. I believe (though have not proved) that the 5 cube

contains all the complexity that is possible. Adding more cubies would only

increase the amount of time needed to solve.On the other hand, a 5X (or any cube of odd order) will still have the

constraints imposed by a fixed center. As a single example, the 4X here in

my office is completely "solved" except that two opposite corners are

swapped. That's not something that can happen on a cube of odd order (at

least I don't think so, but I would love to be proved wrong ;).

Wow! I could have sworn I have gotten to this position before, but you are

very definitely correct. The state with two diagonal corners swapped is in

the orbit with edge cubies exchanged.

Ronnie