Pentagonal-square antiprismatic duoprism

The pentagonal-square antiprismatic duoprism or pesquap is a convex uniform duoprism that consists of 5 square antiprismatic prisms, 2 square-pentagonal duoprisms, and 8 triangular-pentagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-pentagonal duoprisms, and 1 square-pentagonal duoprism.

Vertex coordinates
The vertices of a pentagonal-square antiprismatic duoprism of edge length 1 are given by:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\, \sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right).$$

Representations
A pentagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x5o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x5o s2s4s (square antiprisms as alternated ditetragonal prisms)