From cube-lovers-errors@mc.lcs.mit.edu Mon May 4 10:31:18 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id KAA12732; Mon, 4 May 1998 10:31:18 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Sun May 3 17:19:27 1998 Message-Id: <199805032117.RAA07495@life.ai.mit.edu> Date: Sun, 3 May 1998 17:18:53 -0400 From: michael reid To: cube-lovers@ai.mit.edu Subject: Re: Square like groups andrew walker asks > Does anyone have any information on patterns where each > face only contains opposite colours, but are not in the square > group? L' R U2 L R' may be an example. the set of such patterns is what i called the "target subgroup" for my optimal solver. it is the intersection of the three subgroups , and (or the intersection of any two of them). the position he mentions is in the square group (mark longridge gives a minimal maneuver for it). dan hoey remarks that the square group has index 6 in this "pseudo-square" group. christoph bandelow's book "inside rubik's cube and beyond" gives a nice criterion for a pseudo- square pattern to be in the square group. bandelow's criterion (slightly paraphrased) is the four U corners must be coplanar, the four F corners must be coplanar, and the four R corners must be coplanar. (equivalently, all twelve sets of four coplanar corners remain coplanar.) in fact, this forces the parity of the corner permutation to be even (and thus the same for the edge permutation). this reminds me of an interesting idea i had for a puzzle: a 3x4x5 box, whose faces and slices are restricted to 180 degree turns. this sort of thing could also be done with any dimensions. mike