From JBRYAN@pstcc.cc.tn.us Tue Feb 20 10:51:48 1996 Return-Path: Received: from PSTCC4.PSTCC.CC.TN.US by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA05232; Tue, 20 Feb 96 10:51:48 EST Resent-From: JBRYAN@pstcc.cc.tn.us Resent-Message-Id: <9602201551.AA05232@life.ai.mit.edu> Received: from pstcc.cc.tn.us by pstcc.cc.tn.us (PMDF V5.0-3 #11457) id <01I1FMFANMA48X1JD9@pstcc.cc.tn.us> for cube-lovers@ai.mit.edu; Tue, 20 Feb 1996 10:50:33 -0400 (EDT) Resent-Date: Tue, 20 Feb 1996 10:50:33 -0400 (EDT) Date: Tue, 20 Feb 1996 10:50:31 -0400 (EDT) From: Jerry Bryan Subject: Re: Cube Musings In-Reply-To: <60.1289.5834.0C20A152@canrem.com> Sender: JBRYAN@pstcc.cc.tn.us To: Cube-Lovers Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: 7BIT On Wed, 7 Feb 1996, Mark Longridge wrote: > Further Cube Musings > ==================== > > We usually think of positions antipodal to start only, but there are > positions antipodal to any given position. > > Given a small enough subgroup of the cube, i.e. one which we can > exhaustively study, it is not hard to determine some examples. I guess I didn't understand the thrust of this note. Isn't it a bit simpler? Let H be some subgroup of G, let A be the set of antipodes of Start within H, and let h be some element of H. Then, don't we simply have that the antipodes of h are the set hA, where hA={ha | a in A}? = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7127 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990