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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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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 .
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 .
Note that the pentagram face has an ambiguous interior because it is self-intersecting. The central pentagon region can be considered interior or exterior depending on how interior is defined. One definition of interior is the set of points that have a ray that crosses the boundary an odd number of times to escape the perimeter.
A pentagrammic antiprism is made of two regular pentagrams and 10 equilateral triangles. In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms. All have their vertices in parallel planes and are therefore prismatoids.
The regular 600-cell can be decomposed with the symmetry of the grand antiprism, with each of the 20 blue pentagonal antiprisms being divided into 15 regular tetrahedra. The grand antiprism can be constructed by diminishing the 600-cell: subtracting 20 pyramids whose bases are three-dimensional pentagonal antiprisms. Conversely, the two rings ...
The apeirogonal tiling is the arithmetic limit of the family of prisms t{2, p} or p.4.4, as p tends to infinity, thereby turning the prism into a Euclidean tiling.. An alternation operation can create an apeirogonal antiprism composed of three triangles and one apeirogon at each vertex.