Small covers over products of a polygon with a simplex

The equivariant homeomorphism class of an (orientable) small cover over a simple convex polytope P^n bijectively corresponds to the equivalence class of its (orientable) coloring under the action of automorphism group of face poset of Pn . By calculating the number of orbits of group actions we determine the number of equivariant homeomorphism classes of small covers over products of a polygon with a simplex. Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.