[next] [prev] [up] Date: Wed, 07 Dec 94 20:48:00 -0700 (PST)
[next] [prev] [up] From: Martin Schoenert <Martin.Schoenert@math.rwth-aachen.de >
~~~ ~~~ [up] 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) );

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

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

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 Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany

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