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.