Date: Wed, 29 Nov 95 12:14:40 -0500 (EST) From: Dan Hoey To: Cube Lovers Subject: Generating Rubik's Cube About generating the cube's group with arbitrary elements of that group, mschoene@Math.RWTH-Aachen.DE (Martin Schoenert) writes: ... Rubik's cube can be generated by 2 elements. Moreover almost any random pair of elements will do the trick.... Actually, I think it's more accurate to say that a random pair of elements has nearly a 75% probability of generating the cube. At least, I'm pretty sure that's an upper bound, and I don't see any reason why it shouldn't be fairly tight. That's for the group where the whole cube's spatial orientation is irrelevant. I think it's more like 56% (9/16) if you also need to generate the 24 possible permutations of face centers. About the minimal presentation of the cube group on the usual generators, frb6006@cs.rit.edu (Frank R Bernhart) writes: The answers may be in SINGMASTER, et.al. "Handbook of Cubic Math" or BANDEMEISTER (sp?) "Beyond R. Cube" I recall Singmaster wanted to know if anyone found a reasonably-sized presentation; I don't know if any have been found in the intervening fifteen years. The best I know of is a few thousand relations, some of them several thousand letters long. I've been meaning to try chopping that down a bit. Dan posted and e-mailed Hoey@AIC.NRL.Navy.Mil