From @mitvma.mit.edu,@WVNVM.WVNET.EDU:BRYAN@WVNVM.WVNET.EDU Tue Dec 7 13:42:56 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 AA13489; Tue, 7 Dec 93 13:42:56 EST Message-Id: <9312071842.AA13489@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP V2R2) with BSMTP id 2007; Tue, 07 Dec 93 13:42:57 EST Received: from WVNVM.WVNET.EDU (NJE origin MAILER@WVNVM) by MITVMA.MIT.EDU (LMail V1.1d/1.7f) with BSMTP id 5141; Tue, 7 Dec 1993 13:42:57 -0500 Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.1d/1.7f) with BSMTP id 9473; Tue, 7 Dec 1993 13:40:23 -0500 X-Acknowledge-To: Date: Tue, 7 Dec 1993 13:40:20 EST From: "Jerry Bryan" To: "Cube Lovers List" Subject: Re: Unique antipode of edges only In-Reply-To: Message of 12/07/93 at 12:29:32 from andyl@harlequin.com On 12/07/93 at 12:29:32 Andy Latto said: >The antipodal position is an interesting one. If you take the antipodal >position, and flip all the edges, you get: > *5* > 5*5 > *5* > *1* > 1*1 > *1* > *3**2**4* > 3*32*24*4 > *3**2**4* > *6* > 6*6 > *6* >Antipodal with edges flipped. >This looks like a rotation of the solved state at first glance, since >all the faces on a given side of the cube are the same color. But >look again! This is not the solved state of the original cube, but >of the mirror image cube. If you added in the centers or the corners, >there would be no way to add them to make this a solved state. Indeed. I spoke too quickly when I said the antipodal was simply Start with the edges flipped. I stared at it, flipped the edges in my mind, and it "looked" solved, so I assumed it was Start. I am not yet for sure what they look like, but of the other two states with order-24 equivalence classes, one is at level 9 and the other is at level 12. Since the only one at an even level is at level 12, I am assuming that will be the one which is Start with the edges all flipped. The one at level 9 will probably be the mirror image of Start. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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?