From cube-lovers-errors@mc.lcs.mit.edu Sat Aug 16 21:30:20 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id VAA22864; Sat, 16 Aug 1997 21:30:19 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From reid@math.brown.edu Sat Aug 16 17:12:29 1997 Message-Id: <199708162109.RAA29706@life.ai.mit.edu> Date: Sat, 16 Aug 1997 17:14:10 -0400 From: michael reid To: cube-lovers@ai.mit.edu Subject: Re: patterns with 24-fold symmetry dan asks > By the way, this isn't a complete list of optimal maneuvers, is it? > Are you looking to find such a list? Or would it be too difficult (or > too voluminous)? for most, it isn't a complete list. the main reason is that it's too time consuming to calculate all of them. (perhaps it is also too voluminous, but i'm not sure.) on an individual basis, here's what i gave: superflip: all 20f maneuvers, up to inversion, cyclic shifting, and conjugation by cube symmetries. all _known_ 24f maneuvers, up to the same transformations. pons asinorum: all 12q maneuvers, up to conjugation by cube symmetries. all 6f maneuvers, up to conjugation by cube symmetries. (the inverse of each maneuver is the same as some conjugate by a cube symmetry.) superflip composed with pons asinorum: all 20q and 19f maneuvers, up to inversion and conjugation by cube symmetries. for the H-symmetric patterns (24-fold symmetry), i was less ambitious. for each, i gave a single minimal maneuver in each metric. also, in the cases where there is a maneuver that is minimal in both metrics, i gave such a maneuver. > And I'm looking forward to seeing optimal maneuvers for the > T-symmetric positions (if I'm not being too presumptuous). how did you know what i'm working on next? ;-) i also plan to examine AC-symmetric positions and X-symmetric positions (if i understand your terminology correctly). however, there are so many of these (124) in the X-symmetric case, that i probably will have to settle for sub-optimal maneuvers. mike