|Set of uniform antiprisms|
|Faces||2 n-gons, 2n triangles|
|Properties||convex, semi-regular vertex-transitive|
Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterials.
In the case of a regular n-sided base, one usually considers the case where its copy is twisted by an angle Extra regularity is obtained by the line connecting the base centers being perpendicular to the base planes, making it a right antiprism. It has, apart from the base faces, 2n isosceles triangles as faces.
A uniform antiprism has, apart from the base faces, 2n equilateral triangles as faces. They form an infinite series of vertex-uniform polyhedra, as do the uniform prisms. For n=2 we have as degenerate case the regular tetrahedron, and for n=3 the non-degenerate regular octahedron.
Cartesian coordinates for the vertices of a right antiprism with n-gonal bases and isosceles triangles are
with k ranging from 0 to 2n-1; if the triangles are equilateral,
The symmetry group of a right n-sided antiprism with regular base and isosceles side faces is Dnd of order 4n, except in the case of a tetrahedron, which has the larger symmetry group Td of order 24, which has three versions of D2d as subgroups, and the octahedron, which has the larger symmetry group Oh of order 48, which has four versions of D3d as subgroups.
The rotation group is Dn of order 2n, except in the case of a tetrahedron, which has the larger rotation group T of order 12, which has 3 versions of D2 as subgroups, and the octahedron, which has the larger rotation group O of order 24, which has four versions of D3 as subgroups.
- Prismatic uniform polyhedron
- Apeirogonal antiprism
- Prism (geometry)