Square-hexagonal antiprismatic duoprism

The square-hexagonal antiprismatic duoprism or squahap is a convex uniform duoprism that consists of 4 hexagonal antiprismatic prisms, 2 square-hexagonal duoprisms and 12 triangular-square duoprisms. Each vertex joins 2 hexagonal antiprismatic prisms, 3 triangular-square duoprisms, and 1 square-hexagonal duoprism. It is a duoprism based on a square and a hexagonal antiprism, which makes it a convex segmentoteron.

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

Representations
A square-hexagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x4o s2s12o (full symmetry; hexagonal antiprisms as alternated dodecagonal prisms)
 * x4o s2s6s (hexagonal antiprisms as alternated dihexagonal prisms)
 * x x s2s12o (hexagonal antiprismatic prismatic prism)
 * x x s2s6s