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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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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 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 .
There is an infinite series of convex uniform antiprismatic prisms, starting with the digonal antiprismatic prism is a tetrahedral prism, with two of the tetrahedral cells degenerated into squares.
Notes: Two of these polyhedra may be constructed from the first two snub polyhedra in the list starting with the icosahedron : the pentagonal antiprism is a parabidiminished icosahedron and a pentagrammic crossed-antiprism is a parabidiminished great icosahedron, also known as a parabireplenished great icosahedron .
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.
In geometry, an n-gonal trapezohedron, n-trapezohedron, n-antidipyramid, n-antibipyramid, or n-deltohedron [3], [4] is the dual polyhedron of an n-gonal antiprism.The 2n faces of an n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites.