On the number of abstract regular polytopes whose automorphism group is a Suzuki simple group

We determine, up to isomorphism and duality, the number of abstract regular polytopes of rank three whose automorphism group is a Suzuki simple group Sz ( q ) , with q an odd power of 2. No polytope of higher rank exists and, therefore, the formula obtained counts all abstract regular polytopes of Sz ( q ) . Moreover, there are no degenerate polyhedra. We also obtain, up to isomorphism, the number of pairs of involutions.