An atlas of abstract regular polytopes for small groups

Abstract

For each almost simple group G such that S ≤ G ≤ Aut(S) and S is a simple group of order less than 900,000 listed in the Atlas of Finite Groups, we give, up to isomorphism, the number of abstract regular polytopes on which G acts regularly. The results have been obtained using a series of Magma programs. All these polytopes are made available on the first author's website, at http://cso.ulb.ac.be/~dleemans/polytopes/. © Birkhauser Verlag, Basel 2007.