Antiprism
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented by the Conway notation An.
| Set of uniform n-gonal antiprisms | |
|---|---|
Uniform hexagonal antiprism (n = 6) | |
| Type | uniform in the sense of semiregular polyhedron |
| Faces | 2 regular n-gons 2n equilateral triangles |
| Edges | 4n |
| Vertices | 2n |
| Vertex configuration | 3.3.3.n |
| Schläfli symbol | { }⊗{n} s{2,2n} sr{2,n} |
| Conway notation | An |
| Coxeter diagram | |
| Symmetry group | Dnd, [2+,2n], (2*n), order 4n |
| Rotation group | Dn, [2,n]+, (22n), order 2n |
| Dual polyhedron | convex dual-uniform n-gonal trapezohedron |
| Properties | convex, vertex-transitive, regular polygon faces, congruent & coaxial bases |
| Net | |
| Net of uniform enneagonal antiprism (n = 9) | |
Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron.
Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are 2n triangles, rather than n quadrilaterals.
The dual polyhedron of an n-gonal antiprism is an n-gonal trapezohedron.
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