Square antiprismatic prism

The square antiprismatic prism or squappip is a prismatic uniform polychoron that consists of 2 square antiprisms, 2 cubes, and 8 triangular prisms. Each vertex joins 1 square antiprism, 1 cube, and 3 triangular prisms. As the name suggests, it is a prism based on the square antiprism. As such it is also a convex segmentochoron (designated K-4.19 on Richard Klitzing's list).

Vertex coordinates
Coordinates for the vertices of a square antiprismatic prism of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac12,\,\frac{\sqrt[4]{8}}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,-\frac{\sqrt[4]{8}}{4},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt[4]{8}}{4},\,±\frac12\right).$$

Representations
A square antiprismatic prism has the following Coxeter diagrams:


 * x2s2s8o (full symmetry)
 * x2s2s4s
 * xx xo4ox&#x (cube atop gyro cube)