polyhedron (a Platonic solid ). There are 5 cases like that: a. n = 3, m = 3: tetrahedron , a self-dual polyhedron, the 3-dimensional simplex b. n = 3, m = 4: octahedron , the 3-dimensional cross-polytope c. n = 3, m = 5: icosahedron d. n = 4, m