From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 15 16:23:24 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id QAA17354; Wed, 15 Apr 1998 16:23:24 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Wed Apr 15 15:35:06 1998 Date: Wed, 15 Apr 1998 15:38:00 -0400 (Eastern Daylight Time) From: Dale Newfield Reply-To: DNewfield@cs.virginia.edu To: cube-lovers@ai.mit.edu Subject: Re: Hamiltonian circuits on the cube In-Reply-To: <009C4C21.E208C3B3.8@ice.sbu.ac.uk> Message-Id: On Wed, 15 Apr 1998, David Singmaster wrote: > The discussion of isoglyphs, etc., has reminded me of a problem which I > worked on in the early 1980s but never resolved. I took an all white cube and > traced a Hamitonian circuit through all the 54 facelets. If you jumble this > up, it is essentially impossible to restore. Indeed there are probably many > solutions to the problem. This led me to ask some questions about such > Hamiltonian circuits through the 54 facelets. This is quite reminiscent of "Oddmaze," (http://www.edoc.com/zarf/custom-cubes.html) which is a creation by Andrew Plotkin realized using Kristin Looney's "Custom Cube Technology" (http://www.wunderland.com/WTS/Kristin/Technology.html). On its surface is a labyrinth with no branches or dead ends. Each facelet has exactly two paths through it. In the "start" position, at least, the path obeys the Celtic knotwork property (over/under alternations). It is really quite interesting, and well described on the above mentioned page. (This doesn't help answer your questions, but might put you in contact with another that has given them some thought.) -Dale Newfield Dale@Newfield.org