From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 15 16:56:00 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id QAA17814; Fri, 15 Aug 1997 16:56:00 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From Hoey@AIC.NRL.Navy.Mil Fri Aug 15 15:27:45 1997 Date: Fri, 15 Aug 1997 15:27:33 -0400 Message-Id: <199708151927.PAA03768@sun30.aic.nrl.navy.mil> From: Dan Hoey To: reid@math.brown.edu Cc: cube-lovers@ai.mit.edu In-Reply-To: <199708150145.VAA22661@life.ai.mit.edu> (message from michael reid on Thu, 14 Aug 1997 21:50:27 -0400) Subject: Re: isoglyphs Mike, I'm glad you like glyphs, and I'd also like to know about the other isoglyphs (by which I don't want to minimize my interest in the wealth of optimal processes you've been producing!). In particular, we've seen isoglyphs with all corner types except D (which we know is impossible) and with all edge types. So we might wonder if all the glyph types not involving corner type D are achievable. But I know there is no isoglyph of type 4D (stripe). Are there others? One superset of the isoglyphs that might be worth looking is the partial isoglyphs, in which all faces are either the same glyph or blank (type 00). This allows corner type D (laughter is 4 type D4 + 2 type 00). These even come in continuous varieties (slice is 4 type 4D + 2 type 00). Is there a partial isoglyph pattern for every glyph? And what about chiral partial isoglyphs, for which isoglyphicity is redefined to require the same handedness for orientable patterns? I'm pretty sure all the isoglyphs we've seen so far are chiral, but are there isoglyphs achievable only non-chirally? Dan Hoey@AIC.NRL.Navy.Mil