Pentagonal-octagonal duoprismatic prism

The pentagonal-octagonal duoprismatic prism or pop, also known as the pentagonal-octagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 pentagonal-octagonal duoprisms, 5 square-octagonal duoprisms, and 8 square-pentagonal duoprisms. Each vertex joins 2 square-pentagonal duoprisms, 2 square-octagonal duoprisms, and 1 pentagonal-octagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a pentagonal-octagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right).$$

Representations
A pentagonal-octagonal duoprismatic prism has the following Coxeter diagrams:
 * x x5o x8o (full symmetry)
 * x x5o x4x (octagons as ditetragons)
 * xx5oo xx8oo&#x (pentagonal-octagonal duoprism atop pentagonal-octagonal duoprism)
 * xx5oo xx4xx