On the number of abstract regular polytopes whose automorphism group is a Suzuki simple group Sz(q)

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.