From cube-lovers-errors@mc.lcs.mit.edu Sat May 2 17:23:32 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id RAA09204; Sat, 2 May 1998 17:23:31 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri May 1 22:41:24 1998 Message-Id: <354A8671.730D@idirect.com> Date: Fri, 01 May 1998 22:35:29 -0400 From: Mark Longridge Reply-To: cubeman@idirect.com To: Dan Hoey Cc: cube-lovers@ai.mit.edu Subject: Re: Square like groups References: <9805012356.AA16835@sun28.aic.nrl.navy.mil> Dan Hoey wrote: > > Andrew Walker asks: > > > Does anyone have any information on patterns where each > > face only contains opposite colours, but are not in the square > > group? > > We may call this the "pseudosquare" group P. It consists of > orientation-preserving permutations that operate separately on the > three equatorial quadruples of edge cubies and the two tetrahedra of > corner cubies, and for which the total permutation parity is even. So > Size(P) = 4!^5 / 2 = 3981312. > > > L' R U2 L R' may be an example. R2 F2 R2 U2 R2 F2 R2 U2 F2 > > No, that's in the square group, says GAP. Also, Mark Longridge > noticed (8 Aug 1993) that the square group is mapped to itself under > conjugation by an antislice (though I don't recall a proof--is there > an easy one?). Your position is (L R)' R2 T2 R2 (L R), so this result > would apply. Does anyone have a square process for it? I almost forgot about all that info back in 1993! But I hardly think a proof is necessary. After the moves (L' R) all the following moves are in the square's group. Then we are just doing the inverse of (L` R) at the end. Not very rigourous, but... I'll search for a counter-example. -> Mark <-