bgcolor=#e7dcc3 colspan=2 | Compound of n p/q-gonal antiprisms | |
---|---|---|
align=center colspan=2 | n=2 | |
Type | Uniform compound | |
Index |
| |
Polyhedra | n p/q-gonal antiprisms | |
Schläfli symbols (n=2) | ß ßr | |
Coxeter diagrams (n=2) | ||
Faces | 2n (unless p/q=2), 2np triangles | |
Edges | 4np | |
Vertices | 2np | |
Symmetry group |
| |
Subgroup restricting to one constituent |
|
This infinite family can be enumerated as follows:
Where p/q=2, 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
\left(\cos
k\pi | |
n |
,\sin
k\pi | |
n |
,(-1)kh\right)
\left(\cos
k\pi | |
n |
,\sin
k\pi | |
n |
,(-1)k+1h\right)
with k ranging from 0 to 2n−1; if the triangles are equilateral,
| |||||
2h | -\cos |
2\pi | |
n |
.
The duals of the prismatic compound of antiprisms are compounds of trapezohedra:
For compounds of three digonal antiprisms, they are rotated 60 degrees, while three triangular antiprisms are rotated 40 degrees.