Octagonal antiprism

The octagonal antiprism, or oap, is a prismatic uniform polyhedron. It consists of 16 triangles and 2 octagons. Each vertex joins one octagon and three triangles. As the name suggests, it is an antiprism based on an octagon.

Vertex coordinates
An octagonal antiprism of edge length 1 has vertex coordinates given by:
 * (±1/2, ±(1+$\sqrt{(6+2√2+√20+14√2)/8}$)/2, H),
 * (±(1+$\sqrt{(–2–2√2+√20+14√2)/2}$)/2, ±1/2, H),
 * (0, ±$\sqrt{4+2√2+2√146+103√2}$, –H),
 * (±$\sqrt{2+√2}$, 0, –H),
 * (±$\sqrt{2+√2}$/2, ±$\sqrt{(7+4√2–2√20+14√2)/3}$/2, –H),

where H = $\sqrt{2}$) is the distance between the antiprism's center and the center of one of its bases.

Representations
An octagonal prism can be represented by the following Coxeter diagrams:


 * s2s8s
 * s2s16o (alternated hexadecagonal prism)
 * xo8ox&#x (bases considered separately)

Related polyhedra
A square cupola can be attached to a base of the octagonal antiprism to form the gyroelongated square cupola. If a second square cupola is attached to the other base, the result is the gyroelongated square bicupola.