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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. Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron.
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In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals .
If p/q is an integer, i.e. if q = 1, the prism or antiprism is convex. (The fraction is always assumed to be stated in lowest terms.) An antiprism with p/q < 2 is crossed or retrograde; its vertex figure resembles a bowtie. If p/q < 3/2 no uniform antiprism can exist, as its vertex figure would have to violate the triangle inequality.
3D model of a (uniform) pentagrammic antiprism. In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams. It has 12 faces, 20 edges and 10 vertices. This polyhedron is identified with the indexed name U 79 as a uniform ...
In this respect, it can be seen as a "capped" square antiprism (a square antiprism with a pyramid erected on one of the square faces). It is very similar to the tricapped trigonal prismatic molecular geometry , and there is some dispute over the specific geometry exhibited by certain molecules.
In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by two parallel polygons separated by a strip of triangles. In the case of the heptagonal antiprism, the caps are two regular heptagons. As a result, this polyhedron has 14 vertices, and 14 equilateral triangle faces.
The snub square antiprism (J 85) can be seen as a square antiprism with a chain of equilateral triangles inserted around the middle. The sphenocorona (J 86) and the sphenomegacorona (J 88) are other Johnson solids that, like the square antiprism, consist of two squares and an even number of equilateral triangles.