To the theory of convex regular-hedra (Q951708)

The authors define a regular-hedron to be a polyhedron \(P\) (in 3-space) with the following properties: Each face of \(P\) is either composed by two regular convex polygons or is itself a regular convex polygon, and the sum of planar angles at every vertex of \(P\) is smaller than \(2\pi\). The paper refers to the theory of convex regular-hedra. If such a convex regular-hedron can be divided, by a plane into two regular-hedra, it is called composite (and otherwise non-composite). In the paper various results on composite and non-composite regular-hedra are presented.