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Any star antiprism with regular convex or star polygon bases can be made a right star antiprism (by translating and/or twisting one of its bases, if necessary). In the retrograde forms, but not in the prograde forms, the triangles joining the convex or star bases intersect the axis of rotational symmetry.
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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 .
A octagonal antiprismatic prism or octagonal antiduoprism is a convex uniform 4-polytope (four-dimensional polytope). It is formed as two parallel octagonal antiprisms connected by cubes and triangular prisms.
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 .
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.