Classification and covering of class C polyhedrons

The first part of the article deals with the classification of convex polyhedra. In this paper we proved that to cover any convex polyhedron, the boundary of which contains at least one surface of the transition type, eight polyhedra of smaller size homothetic to this polyhedron are enough. The problem considered is related to the problem of Hadwiger convex geometric bodies covering by their images at homothety.