From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Wed Dec 8 10:04:52 1993 Return-Path: <@mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU> Received: from mitvma.mit.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA02610; Wed, 8 Dec 93 10:04:52 EST Message-Id: <9312081504.AA02610@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 1780; Wed, 08 Dec 93 10:04:53 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 0159; Wed, 8 Dec 1993 10:04:54 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 4368; Wed, 8 Dec 1993 10:02:17 -0500 X-Acknowledge-To: Date: Wed, 8 Dec 1993 10:02:15 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Unique antipode of edges only In-Reply-To: Message of 12/07/93 at 20:13:08 from hoey@aic.nrl.navy.mil On 12/07/93 at 20:13:08 hoey@aic.nrl.navy.mil said: >My (very cheap) guess for where we will find the other two M-symmetric >positions is opposite to Jerry Bryan's. On a cube with faces, the >central reflection of the edges with respect to the faces is Pons >Asinorum, which has the easy 12-qt tight lower bound we've seen before >(or if not, you can of course get it from me with email). I'm >guessing that this bound happens to be tight on the cube without >faces, as well. But I have no proof of this guess, and I'm very >grateful we won't have to settle for guesses for very long. >Dan Hoey >Hoey@AIC.NRL.Navy.Mil Dan Hoey is correct. Mirror-Image-of-Start is at level 12. Edges-Flipped is at level 9. Mirror-Image-of-Start-and-Edges-Flipped is at level 15. And, of course, Start is at Level 0. This exhausts the list of configurations with order-24 symmetry. I am still thinking about the easiest way to extract sequences of operators from my data base. I gather from Dan's comments that a 12-qt operator is known for Mirror-Image-of-Start. Are operators known for the other two cases? This is going to be sufficiently time-consuming that I don't want to try to find operators that are already known. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU If you don't have time to do it right today, what makes you think you are going to have time to do it over again tomorrow?