Prismatic compound of antiprisms with rotational freedom

Compound of 2n p/q-gonal antiprisms
UC22-2k n-m-gonal antiprisms.png (n=2, p=3, q=1) UC24-2k n-m-gonal antiprisms.png (n=1, p=7, q=2)
Type Uniform compound
Index
  • q odd: UC22
  • q even: UC24
Polyhedra 2n p/q-gonal antiprisms
Faces 4n {p/q} (unless p/q=2), 4np triangles
Edges 8np
Vertices 4np
Symmetry group
Subgroup restricting to one constituent

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 (expressed with p and q coprime), there occurs the compound of 2n p/q-gonal antiprisms (with rotational freedom), with symmetry group:
    • Dnpd if nq is odd
    • Dnph if nq is even

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

ReferencesEdit

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.