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:
 * (±1/2, ±(1+$\sqrt{2+√2}$)/2, H, ±1/2),
 * (±(1+$\sqrt{2}$)/2, ±1/2, H, ±1/2),
 * (0, ±$\sqrt{(8+2√2+√20+14√2)/8}$, –H, ±1/2),
 * (±$\sqrt{(–2–2√2+√20+14√2)/2}$, 0, –H, ±1/2),
 * (±$\sqrt{4+2√2+2√146+103√2}$/2, ±$\sqrt{2+√2}$/2, –H, ±1/2),

where H = ($\sqrt{(7+4√2–2√20+14√2)/3}$)/2 is the distance between the antiprism's center and the center of one of its bases.

Representations
An octagonal antiprismatic prism has the following Coxeter diagrams:


 * x2s2s16o (full symmetry)
 * x2s2s8s
 * xx xo8ox&#x (octagonal prism atop gyrated octagonal prism)