Prismatic compound of antiprisms - AbsoluteAstronomy.com

Each member of this infinite family of uniform polyhedron compound

Uniform polyhedron compound

A uniform polyhedron compound is a polyhedral compound whose constituents are identical uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.The uniform polyhedron compounds were first enumerated by John Skilling...

s is a symmetric arrangement of antiprisms

Prismatic uniform polyhedron

In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms...

sharing a common axis of rotational symmetry.

This infinite family can be enumerated as follows:

For each positive integer n>1 and for each rational number p/q>3/2 (expressed with p and q coprime
Coprime
In number theory, a branch of mathematics, two integers a and b are said to be coprime or relatively prime if the only positive integer that evenly divides both of them is 1. This is the same thing as their greatest common divisor being 1...

), there occurs the compound of n p/q-gonal antiprisms, with symmetry group:
- D_npd if nq is odd
- D_nph if nq is even

Where p/q=2, the component is the tetrahedron

Tetrahedron

In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...

(or dyadic antiprism).