Pentagonal-decagonal duoprismatic prism

The pentagonal-decagonal duoprismatic prism or peddip, also known as the pentagonal-decagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 pentagonal-decagonal duoprisms, 5 square-decagonal duoprisms, and 10 square-pentagonal duoprisms. Each vertex joins 2 square-pentagonal duoprisms, 2 square-decagonal duoprisms, and 1 pentagonal-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a pentagonal-decagonal duoprismatic prism of edge length 1 are given by:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right).$$

Representations
A pentagonal-decagonal duoprismatic prism has the following Coxeter diagrams:
 * x x5o x10o (full symmetry)
 * x x5o x5x (decagons as dipentagons)
 * xx5oo xx10oo&#x (pentagonal-decagonal duoprism atop pentagonal-decagonal duoprism)
 * xx5oo xx5xx&#x