From dseal@armltd.co.uk Tue Dec 7 12:02:56 1993 Return-Path: Received: from eros.britain.eu.net by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA08106; Tue, 7 Dec 93 12:02:56 EST Received: from armltd.co.uk by eros.britain.eu.net with UUCP id ; Tue, 7 Dec 1993 16:42:43 +0000 Received: by armltd.co.uk (5.51/Am23) id AA04366; Tue, 7 Dec 93 16:13:04 GMT Date: Tue, 07 Dec 93 16:13:51 GMT From: dseal@armltd.co.uk (David Seal) To: (Cube) cube-lovers@ai.mit.edu Subject: Re: Unique antipode of edges only Message-Id: <2D04ABBF@dseal> > Someone else remarks that it's "got to be all edges flipped in place", > and Jerry Bryan remarks that it is. > > > *6* *6* > > 6*6 3*4 > > *6* *1* > > *2* *5* > > 2*2 3*4 > > *2* *2* > > *3**1**4* *1**1**1* > > 3*31*14*4 5*23*42*5 > > *3**1**4* *6**6**6* > > *5* *2* > > 5*5 3*4 > > *5* *5* > > I disagree. Look at the 1-2 edge. If it's "flipped in place", then > since it appears to be fixed, the cube must flip around it. But then > the four 3 faces would be where the 4 faces actually are. No, it's > more complicated than just all-edges-flipped. > > "[Q]uite extraordinary and wonderful" it is. It is in fact the position arrived at by flipping all edges in place, *then* reflecting the entire configuration. I believe this also tells us what the other two equivalence classes with just 24 elements are: they are the results of doing each of these two operations separately. David Seal dseal@armltd.co.uk