Star Dipyramids

The duals of the regular star prisms are called star dipyramids, and the duals of the regular star antiprisms are called star trapezohedra. Each has one type of face and a constant dihedral angle. Like dipyramids and trapezohedra, they can be distinguished from other uniform polyhedra duals by the fact that they do not have polyhedral group (tetrahedral, octahedral, or icosahedral) rotational symmetries.