Prismatic compound of prisms with rotational freedom

Compound of 2n p/q-gonal prisms with rotational freedom
(n=2, p=4, q=1)
Type Uniform compound
Index UC20
Polyhedra 2n p/q-gonal prisms
Faces 4n {p/q}, 2np squares
Edges 6np
Vertices 4np
Symmetry group np-fold prismatic (Dnph)
Subgroup restricting to one constituent p-fold rotation (Cph)

Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of prisms sharing a common axis of rotational symmetry. It arises from superimposing two copies of the corresponding prismatic compound of prisms (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>2 (expressed with p and q coprime), there occurs the compound of 2n p/q-gonal prisms (with rotational freedom), with symmetry group Dnph.

References

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  • 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.