We present the construction dynamics of the simplest pair of mutually polar nonconvex star polyhedra. The first polyhedron in this pair is Coxeter’s uniform small cubicuboctahedron, and the second is its polar-dual polyhedron, the small hexacronic icositetrahedron. We study the structure of these polyhedra and their curvatures. For the polyhedral angles of the small cubicuboctahedron, we obtain an analog of the Gauss–Alexandrov theorem.
L. A. Antipova (Thu,) studied this question.