Prismatic compound of antiprisms with rotational freedom
# Prismatic compound of antiprisms with rotational freedom

Compound of 2n p/q-gonal antiprisms :

| (n=2, p=3, q=1) (n=1, p=7, q=2) ||
| - | - |
| Type | Uniform compound |
| Index | q odd: $UC_{22}$ q even: $UC_{24}$ |
| Polyhedra | 2n p/q-gonal antiprisms |
| Faces | 4n {p/q} (unless p/q=2), 4np triangles |
| Edges | 8np |
| Vertices | 4np |
| Symmetry group | nq odd: np-fold antiprismatic $(D_{npd})$ nq even: np-fold prismatic $(D_{nph})$ |
| Subgroup restricting to one constituent | q odd: 2p-fold improper rotation $(S_{2p})$ q even: p-fold rotation $(C_{ph})$ |

Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry. It arises from superimposing two copies of the corresponding prismatic compound of antiprisms (without rotational freedom), and rotating each copy by an equal and opposite angle.

This infinite family can be enumerated as follows:

Where p/q=2 the component is a tetrahedron, sometimes not considered a true antiprism.

