Prismatic compound of antiprisms
In geometry, a prismatic compound of antiprism is a category of uniform polyhedron compound. Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry.
Infinite family
This infinite family can be enumerated as follows:- For each positive integer n≥1 and for each rational number p/q>3/2, there occurs the compound of n p/q-gonal antiprisms, with symmetry group:
- *Dnpd if nq is odd
- *Dnph if nq is even
Compounds of two antiprisms
Compounds of two n-antiprisms share their vertices with a 2n-prism, and exist as two alternated set of vertices.Cartesian coordinates for the vertices of an antiprism with n-gonal bases and isosceles triangles are
with k ranging from 0 to 2n−1; if the triangles are equilateral,
| 2 digonal antiprisms | 2 triangular antiprisms | 2 square antiprisms | 2 hexagonal antiprisms | 2 pentagrammic crossed antiprism |
Compound of two trapezohedra (duals)
The duals of the prismatic compound of antiprisms are compounds of trapezohedra:Two cubes |
Compound of three antiprisms
For compounds of three digonal antiprisms, they are rotated 60 degrees, while three triangular antiprisms are rotated 40 degrees.| Three tetrahedra | Three octahedra |