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:
 * (0, ±1, $\sqrt{3}$/2, ±1/2)
 * (±$\sqrt{2}$/2, ±1/2, $\sqrt{4+√3}$/2, ±1/2)
 * (±1, 0, -$\sqrt{{{radic|3}}–1}$/2, ±1/2)
 * (±1/2, ±$\sqrt{2+2√3}$/2, -$\sqrt{3}$/2, ±1/2)

Representations
A hexagonal antiprismatic prism has the following Coxeter diagrams:


 * x2s2s12o full symmetry)
 * x2s2s6s
 * x2s2s12o\*xx xo6ox&#x (hexagonal prism atop gyrated hexagonal prism)