# Octagonal antiprism

Uniform Octagonal antiprism Type Prismatic uniform polyhedron
Elements F = 18, E = 32
V = 16 (χ = 2)
Faces by sides 16{3}+2{8}
Schläfli symbol s{2,16}
sr{2,8}
Wythoff symbol | 2 2 8
Coxeter diagram          Symmetry group D8d, [2+,16], (2*8), order 32
Rotation group D8, [8,2]+, (822), order 16
References U77(f)
Dual Octagonal trapezohedron
Properties convex Vertex figure
3.3.3.8

In geometry, the octagonal antiprism is the 6th 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.

In the case of a regular 8-sided base, one usually considers the case where its copy is twisted by an angle 180°/n. Extra regularity is obtained by the line connecting the base centers being perpendicular to the base planes, making it a right antiprism. As faces, it has the two n-gonal bases and, connecting those bases, 2n isosceles triangles.

If faces are all regular, it is a semiregular polyhedron.