Dipyramids

The duals of the regular prisms are often called dipyramids, and the duals of the regular antiprisms are often called trapezohedra. The Square Dipyramid and the Trigonal Trapezohedron are the Octahedron and the Cube, respectively. The remaining regular dipyramids and trapezohedra are closely related to Catalan solids in the sense that they have one type of face and they have constant dihedral angles. The distinguishing factor is that regular dipyramids and trapezohedra do not have polyhedral group (tetrahedral, octahedral, or icosahedral) rotational symmetries.