Pentagonal-hexagonal duoprismatic prism

The pentagonal-hexagonal duoprismatic prism or pehip, also known as the pentagonal-hexagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 pentagonal-hexagonal duoprisms, 5 square-hexagonal duoprisms, and 6 square-pentagonal duoprisms. Each vertex joins 2 square-pentagonal duoprisms, 2 square-hexagonal duoprisms, and 1 pentagonal-hexagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a pentagonal-hexagonal duoprismatic prism of edge length 1 are given by:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,±1,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,±1,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,±1,\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt3}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt3}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt3}2,\,±\frac12,\,±\frac12\right).$$

Representations
A pentagonal-hexagonal duoprismatic prism has the following Coxeter diagrams:
 * x x5o x6o (full symmetry)
 * x x5o x3x (hexagons as ditrigons)
 * xx5oo xx6oo&#x (pentagonal-hexagonal duoprism atop pentagonal-hexagonal duoprism)
 * xx5oo xx3xx&#x