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 polytopes of Sz(q). Moreover, there are no degenerate polyhedra. We also obtain, up to
isomorphism, the number of pairs of involutions.