Prismatic compound of antiprisms with rotational freedom

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:
*For each positive integer "n">0 and for each rational number "p"/"q">3/2 and "p"/"q"≠2, there occurs the compound of 2"n" "p"/"q"-gonal antiprisms (with rotational freedom), with symmetry group:
**D_"np"d if "nq" is odd
**D_"np"h if "nq" is even
*For each positive integer "n">0, there occurs the compound of 2"n" tetrahedra (as antiprisms, corresponding to "p"/"q"=2 in the previous case, and with rotational freedom), with symmetry group:
**D_2"n"d if "n" is odd
**D_2"n"h if "n" is even

References

* John Skilling, "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.