Pentagonal-pentagonal antiprismatic duoprism

The pentagonal-pentagonal antiprismatic duoprism or pepap is a convex uniform duoprism that consists of 5 pentagonal antiprismatic prisms, 2 pentagonal duoprisms, and 10 triangular-pentagonal duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-pentagonal duoprisms, and 1 pentagonal duoprism.

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

Representations
A pentagonal-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x5o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x5o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)