From mschoene@math.rwth-aachen.de Wed Dec 7 19:49:39 1994 Return-Path: Received: from samson.math.rwth-aachen.de by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA17943; Wed, 7 Dec 94 19:49:39 EST Received: from hobbes.math.rwth-aachen.de by samson.math.rwth-aachen.de with smtp (Smail3.1.28.1 #11) id m0rFSLJ-000MPZC; Wed, 7 Dec 94 20:48 MET Received: by hobbes.math.rwth-aachen.de (Smail3.1.28.1 #19) id m0rFSLI-0000PsC; Wed, 7 Dec 94 20:48 PST Message-Id: Date: Wed, 7 Dec 94 20:48 PST From: "Martin Schoenert" To: cube-lovers@life.ai.mit.edu Subject: Permutation Representations for Magic Polyhedra Dan Hoey writes in his e-mail message of 1994/11/08 Wow, I didn't realize this sort of calculation had been automated. Hey, we do this stuff every day. Really. Well at least with a loose interpretation of ``this sort of''. Dan Hoey continues gap-3.4 -b -g 4m gap> Sum( ConjugacyClasses( M ), > c -> Size( Centralizer(G,Representative(c)) ) / 48 * Size(c) ); 901083404981813616 Well, call me John Henry. Say, do you have gap libraries for other magic polyhedra? For higher-dimensional magic? I also have a permutation representation for the 2x2x2 and the 4x4x4 cube. I must confess that I was never interested in other magic polyhedra. I once started writing a GAP function that creates a premutation representation for any (hyper-)cube, i.e., 'Cube( 3, 3, 3, 2 )' would create a 4-dimensional magic domino. The largest problem was to define what the ``faces'' and ``slices'' are, i.e., are they 2 or n-1 dimensional? If there is interest, I would finish this project and also collect permutation representations for other magic polyhedra and distribute them together with future versions of GAP. Have a nice day. Martin. -- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany