Pentagonal-hexagonal antiprismatic duoprism

The pentagonal-hexagonal antiprismatic duoprism or pehap is a convex uniform duoprism that consists of 5 hexagonal antiprismatic prisms, 2 pentagonal-hexagonal duoprisms and 12 triangular-pentagonal duoprisms. Each vertex joins 2 hexagonal antiprismatic prisms, 3 triangular-pentagonal duoprisms, and 1 pentagonal-hexagonal duoprism.

Vertex coordinates
The vertices of a pentagonal-hexagonal antiprismatic duoprism of edge length 1 are given by:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac{\sqrt3}2,\,\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±1,\,0,\,\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt3}2,\,±\frac12,\,-\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,±1,\,-\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac{\sqrt3}2,\,\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±1,\,0,\,\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt3}2,\,±\frac12,\,-\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,±1,\,-\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac{\sqrt3}2,\,\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±1,\,0,\,\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt3}2,\,±\frac12,\,-\frac{\sqrt{\sqrt3-1}}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±1,\,-\frac{\sqrt{\sqrt3-1}}2\right).$$

Representations
A pentagonal-hexagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x5o s2s12o (full symmetry; hexagonal antiprisms as alternated dodecagonal prisms)
 * x5o s2s6s (hexagonal antiprisms as alternated dihexagonal prisms)