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I confess to not only having no proof to this proposition, but no

longer believing it. The false equivalence of "symmetric" and

"locally maximal" seemed to me visually obvious, given that all symmetric

positions are in fact locally maximal. If one believes this

subconsciously, it is but a short step to the conscious "proof" that

all asymmetric positions are but "on the way" to a symmetric, maximal

one; this of course, is bogus. Now a good definition of symmetric

is also needed here; I assume that what we have been meaning is that

all rotations of the cube are Isomorphic. Note that the Plummer and

Christman crosses don't qualify under this definition. What is a good

definition?