Octagonal-pentagonal antiprismatic duoprism

The octagonal-pentagonal antiprismatic duoprism or opap is a convex uniform duoprism that consists of 8 pentagonal antiprismatic prisms, 2 pentagonal-octagonal duoprisms and 10 triangular-octagonal duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-octagonal duoprisms, and 1 pentagonal-octagonal duoprism.

Vertex coordinates
The vertices of a octagonal-pentagonal antiprismatic duoprism of edge length 1 are given by all central inversions of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right).$$

Representations
An octagonal-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x8o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x8o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)
 * x4x s2s10o (octagons as ditetragons)
 * x4x s2s5s