Prismatic compound of prisms with rotational freedom
From HandWiki
Short description: Polyhedral compound
| Compound of 2n p/q-gonal prisms with rotational freedom | |
|---|---|
 (n=2, p=4, q=1)
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| 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
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (3): 447–457, doi:10.1017/S0305004100052440.
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