f-vectors of symmetric 3-polytopes

The f-vector of a d-dimensional polytope P is the vector (f_0, ..., f_d), where f_i is the number of i-dimensional faces of P. For d=3, a full characterization of the set F of all possible f-vectors was found by Steinitz (1906). Given a finite subgroup G of GL(3,R), one can ask how this set changes when only considering f-vectors of G-symmetric polytopes, i.e. polytopes that are invariant under the action of G. We give a full description of the sets F(G)={f : f is the f-vector of a G-symmetric 3-polytope} for all finite rotation groups G. These sets show expectable regularities as well as some surprising additional restrictions. This is joint work with Robert Schüler.