On dihedral angle sums and number of facets for product polytopes

Abstract In this paper we present a method for computing the dihedral angle sums (and their two-sided estimates) of cartesian and skew product polytopes provided the sums of dihedral angles (or their estimates) are known for the factors. In addition, a formula for computing the number of facets of such product polytopes is derived. The method proposed is very universal and illustrated by several examples. The estimates are in a full agreement with known results for prisms and hexahedra.