Decagonal duoprismatic prism

The decagonal duoprismatic prism or daddip, also known as the decagonal-decagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 decagonal duoprisms and 20 square-decagonal duoprisms. Each vertex joins 4 square-decagonal duoprisms and 1 decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a pentagonal duoantiprismatic antiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of an decagonal duoprismatic prism of edge length 2sin(π/9) are given by:
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right).$$

Representations
A decagonal duoprismatic prism has the following Coxeter diagrams:
 * x x10o x10o (full symmetry)
 * x x5x x5x (decagons as dipentagons)
 * xx10oo xx10oo&#x (decagonal duoprism atop decagonal duoprism)
 * xx5xx xx5xx&#x