On a Class of Polyhedra with Symmetrical Vertex Stars

Abstract

The influence of the local symmetry of stars of some vertices of a closed convex polyhedron in E3 on its geometry is considered. A theorem on the complete classification of symmetric polyhedra some of whose vertices possess symmetric stars of deltoid or rhombic faces is proved. In the proof, we use so-called strongly symmetric polyhedra and the lemma on local symmetry conditions previously introduced by the author.