Hexagonal-pentagonal antiprismatic duoprism

The hexagonal-pentagonal antiprismatic duoprism or hapap is a convex uniform duoprism that consists of 6 pentagonal antiprismatic prisms, 2 pentagonal-hexagonal duoprisms, and 10 triangular-hexagonal duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-hexagonal duoprisms, and 1 pentagonal-hexagonal duoprism.

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

Representations
A hexagonal-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x6o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x6o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)
 * x3x s2s10o (hexagons as ditrigons)
 * x3x s2s5s