From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 15 20:32:05 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id UAA18522; Fri, 15 Aug 1997 20:32:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From reid@math.brown.edu Fri Aug 15 19:48:02 1997 Message-Id: <199708152344.TAA05912@life.ai.mit.edu> Date: Fri, 15 Aug 1997 19:49:54 -0400 From: michael reid To: cube-lovers@ai.mit.edu Subject: Re: isoglyphs perhaps i am missing something, but doesn't D2 R2 U2 D2 R2 U D (12q, 7f) produce an isoglyph of type 4D ? are there any isoglyphs of type 21 or 23 ? i haven't found any. each has three possible patterns: ... .*. .*. *** .** *** *** , *** and *.* , .*. ... ... .*. **. .*. *.* , *.* and *** . i hadn't even considered chiral versus achiral isoglyphs. indeed, all the "continuous" isoglyphs given by herbert are chiral. achiral isoglyphs certainly exist, for example D2 R2 U' B' L B U B L F2 R D' L2 U2 B2 D (22q, 16f) of type 11; pattern *.. *** *** and others can be derived from this. i suspect that there is no chiral form of this isoglyph, but i'm not absolutely certain. another interesting note is that the inverses of the "continuous" isoglyphs are also isoglyphs; in fact the same pattern, perhaps in a different orientation. however, there is at least one (probably more) isoglyph whose inverse is not an isoglyph. instead of giving it right here, i'll challenge other readers to find it/them. mike