Polytopes Derived from Sporadic Simple Groups - Auxiliary Information

This web page contains auxiliary information for the article Polytopes Derived from Sporadic Simple Groups, submitted to Experimental Mathematics in July 2006.

In that article, the twelve smallest sporadic simple groups were studied, and for each one, the polytopes having that group as an automorphism group were enumerated. This page contains links to extra information that could not be adequately contained in the article.

In particular, the generators of the automorphism groups of every polytope discovered are stored in the file sporpolys.tgz (6.7 Mb, uncompresses to 18 Mb), as permutations. These may be read into GAP via the command

Read("all.gap");
issued from the folder into which sporpolys.tgz is unzipped.

I also provide links to tables summarising the polytopes for each group.

The Mathieu Group M11 (0 polytopes)
The Mathieu Group M12 (67 polytopes)
The Mathieu Group M22 (0 polytopes)
The Mathieu Group M23 (0 polytopes)
The Mathieu Group M24 (1260 polytopes)
The McLaughlin Group McL (0 polytopes)
The First Janko Group J1 (300 polytopes)
The Second Janko Group J2 (292 polytopes)
The Third Janko Group J3 (586 polytopes)
The Tits Group 2F4(2)' (525 polytopes)
The Higman-Sims Group HS (580 polytopes)
The Held Group He (2437 polytopes)

There is a small intersection between this work and earlier work by Leemans and Vauthier. Note that the latter does not distinguish polytopes from their duals.