Decagonal-square antiprismatic duoprism

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

Vertex coordinates
The vertices of a decagonal-square antiprismatic duoprism of edge length 1 are given by:
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right).$$

Representations
A decagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x10o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x10o s2s4s (square antiprisms as alternated ditetragonal prisms)
 * x5x s2s8o (decagons as dipentagons)
 * x5x s2s4s