An -gonal antiprism is a polyhedron with two parallel congruent -gon bases, one rotated relative to the other, and a band of triangular side faces joining them. For the usual convex regular realization, both bases are regular and all side triangles are equilateral triangles.
Its combinatorial counts are , , and : the bases contribute edges and the zigzag side band another . Hence , agreeing with Euler characteristic. A triangular antiprism is an octahedron; a square antiprism has eight vertices, two square bases and eight triangular side faces.
A prism instead joins corresponding base vertices with a band of quadrilateral faces. The relative rotation and triangular band are the defining differences in the antiprism construction.
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An antiprism is a type of polyhedron that consists of two parallel polygonal bases connected by a band of triangular faces. It can be described as a generalized version of a prism, where instead of the bases being congruent and aligned, the bases are offset from each other and connected by equilateral triangles. Key features of an antiprism include: 1. **Polygonal Bases**: The two bases are identical polygons, such as triangles, squares, or pentagons.