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