On the existence and completeness of enumeration of three-dimensional $RR$-polyhedra

An $RR$-polyhedron is a closed convex polyhedron in $E^3$ whose set of faces can be divided into two nonempty disjoint class: the class of regular polygons of the same type and the class of faces that form stars of symmetric rhombic vertices. A theorem on the existence and completeness of enumeration of closed convex three-dimensional $RR$-polyhedra is proved.