I have a project in mind that involves the symmetry groups of the
regular four-dimensional polytopes.
I'm told that enumeration of a group from its generators is a
by-product of the Todd-Coxeter algorithm.
Unfortunately, I can't make sense of Wikipedia's description of TC,
nor of the one implementation of it that I've seen (in C++;
jenn3d.org).

I hope that this is not the wrong place to ask, and that one of you
can point me to an implementation of Todd-Coxeter in Sage or Python
(Sage preferred, as I'd like to have the square roots handled
algebraically rather than numerically) -- or, as long as I'm wishing,
a list of the 14400 isometry matrices of the [5,3,3] group.

-- 
*\\* Anton Sherwood *\\* www.bendwavy.org

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