Octagonal antiprismatic prism

The octagonal antiprismatic prism or oappip is a prismatic uniform polychoron that consists of 2 octagonal antiprisms, 2 octagonal prisms, and 16 triangular prisms. Each vertex joins 1 octagonal antiprism, 1 octagonal prism, and 3 triangular prisms. As the name suggests, it is a prism based on an octagonal antiprism. It is also a CRF segmentochoron designated K-4.65 on Richard Klitzing's list.

Vertex coordinates
The vertices of an octagonal antiprismatic prism of edge length 1 are given by: where $$H=\sqrt{\frac{-2-2\sqrt2+\sqrt{20+14\sqrt2}}8}$$ is the distance between the antiprism's center and the center of one of its bases.
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,H,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,H,\,±\frac12\right),$$
 * $$\left(0,\,±\sqrt{\frac{2+\sqrt2}2},\,-H,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{2+\sqrt2}2},\,0,\,-H,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{2+\sqrt2}}2,\,±\frac{\sqrt{2+\sqrt2}}2,\,-H,\,±\frac12\right),$$

Representations
An octagonal antiprismatic prism has the following Coxeter diagrams:
 * x2s2s16o (full symmetry)
 * x2s2s8s
 * xx xo8ox&#x (octagonal prism atop gyrated octagonal prism)