  The $f$-vector of a polytope consists of the numbers of its $i$-dimensional
faces. An open field of study is the characterization of all possible
$f$-vectors. It has been solved in three dimensions by Steinitz in the early
19th century. We state a related question, i.e. to characterize $f$-vectors of
three dimensional polytopes respecting a symmetry, given by a finite group of
matrices. We give a full answer for all three dimensional polytopes that are
symmetric with respect to a finite rotation or rotary reflection group. We
solve these cases constructively by developing tools that generalize Steinitz's
approach.
