Polytopes derived from sporadic simple groups

Michael Ian Hartley, Alexander Hulpke

Abstract


In this article, certain of the sporadic simple groups are analysed, and the polytopes

having these groups as automorphism groups are characterised. The sporadic groups considered

include all with order less than 4030387201, that is, all up to and including the order of the Held group.

Four of these simple groups yield no polytopes, and the highest ranked polytopes

are four rank 5 polytopes each from the Higman-Sims group, and the Mathieu group $M_{24}$.

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Contributions to Discrete Mathematics. ISSN: 1715-0868