Date: 6 December 1980 1836-est From: Bernard S. Greenberg Subject: Re: That 28 move Plummer Cross To: McKeeman.PA at PARC-Maxc Cc: Cube-Lovers at MIT-MC, Plummer.SIPBADMIN at MIT-Multics 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?