Hexagonal-square antiprismatic duoprism

The hexagonal-square antiprismatic duoprism or hasquap is a convex uniform duoprism that consists of 6 square antiprismatic prisms, 2 square-hexagonal duoprisms and 8 triangular-hexagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-hexagonal duoprisms, and 1 square-hexagonal duoprism.

Vertex coordinates
The vertices of a hexagonal-square antiprismatic duoprism of edge length 1 are given by:
 * $$\left(0,\,±1,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\,±1,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\,±1,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right).$$

Representations
A hexagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x6o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x6o s2s4s (square antiprisms as alternated ditetragonal prisms)
 * x3x s2s8o (hexagons as ditrigons)
 * x3x s2s4s