The following polyhedra are combinatorially equivalent to the regular polyhedron. The octahedron is a regular polyhedron, and a triangular antiprism. It is the only radially equilateral convex polyhedron. A twelve-faced polyhedron is a dodecahedron. A geodesic polyhedron is a convex polyhedron made from triangles. A regular octahedron is the dual polyhedron of a cube. A polyhedron with eight faces is an octahedron. The octahedron is the dual polyhedron to the cube. The cube is the only convex polyhedron whose faces are all squares. A cross section of a polyhedron is a polygon. Geometrically, the linear constraints define the feasible region, which is a convex polyhedron. Duality preserves the symmetries of a polyhedron. Vertices in the same polyhedron are in the same conjugacy class. Therefore, it is a convex polyhedron. Its dual polyhedron is the rhombic triacontahedron.