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Compound of np/q-gonal antiprisms | |||
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n=2
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Type | Uniform compound | ||
Index |
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Polyhedra | np/q-gonal antiprisms | ||
Schläfli symbols (n=2) | ß{2,2p/q} ßr{2,p/q} | ||
Coxeter diagrams (n=2) | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||
Faces | 2n {p/q} (unless p/q=2), 2np triangles | ||
Edges | 4np | ||
Vertices | 2np | ||
Symmetry group |
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Subgroup restricting to one constituent |
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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.
This infinite family can be enumerated as follows:
When p/q = 2, or equivalently p = 2, q = 1, the component is the tetrahedron (or dyadic antiprism). In this case, if n = 2 then the compound is the stella octangula, with higher symmetry (Oh).
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,
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2 digonal antiprisms (tetrahedra) | 2 triangular antiprisms (octahedra) | 2 square antiprisms | 2 hexagonal antiprisms | 2 pentagrammic crossed antiprism |
The duals of the prismatic compound of antiprisms are compounds of trapezohedra:
![]() Two cubes (trigonal trapezohedra) |
For compounds of three digonal antiprisms, they are rotated 60 degrees, while three triangular antiprisms are rotated 40 degrees.
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Three tetrahedra | Three octahedra |
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