Hexagonal antiprismatic prism

The hexagonal antiprismatic prism or happip is a prismatic uniform polychoron that consists of 2 hexagonal antiprisms, 2 hexagonal prisms, and 12 triangular prisms. Each vertex joins 1 hexagonal antiprism, 1 hexagonal prism, and 3 triangular prisms. As the name suggests, it is a prism based on a hexagonal antiprism. It is also a CRF segmentochoron designated K-4.53 on Richard Klitzing's list.

Vertex coordinates
The vertices of a hexagonal antiprismatic prism of edge length 1 are given by:
 * $$\left(0,\,±1,\,\frac{\sqrt{\sqrt3-1}}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,\frac{\sqrt{\sqrt3-1}}{2},\,±\frac12\right),$$
 * $$\left(±1,\,0,\,-\frac{\sqrt{\sqrt3-1}}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,-\frac{\sqrt{\sqrt3-1}}{2},\,±\frac12\right).$$

Representations
A hexagonal antiprismatic prism has the following Coxeter diagrams:
 * x2s2s12o (full symmetry)
 * x2s2s6s
 * xx xo6ox&#x (hexagonal prism atop gyrated hexagonal prism)