Prismatic compound of antiprisms
- Prismatic compound of antiprisms
Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of 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 and "p"/"q"≠2, there occurs the compound of "n" "p"/"q"-gonal antiprisms, with symmetry group:
**D"np"d if "nq" is odd
**D"np"h if "nq" is even
*For each positive integer "n">1, there occurs the compound of "n" tetrahedra (as antiprisms, corresponding to "p"/"q"=2 in the previous case), with symmetry group:
**D2"n"d if "n" is odd
**D2"n"h if "n" is even
In the latter case, the compound with "n"=2 has greater symmetry (Oh): it is the stella octangula.
References
* John Skilling, "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.
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