Pentagonal-dodecagonal duoprismatic prism

The pentagonal-dodecagonal duoprismatic prism or petwip, also known as the pentagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 pentagonal-dodecagonal duoprisms, 5 square-dodecagonal duoprisms, and 12 square-pentagonal duoprisms. Each vertex joins 2 square-pentagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 pentagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

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

Representations
A pentagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x5o x12o (full symmetry)
 * x x5o x6x (dodecagons as dihexagons)
 * xx5oo xx12oo&#x (pentagonal-dodecagonal duoprism atop pentagonal-dodecagonal duoprism)
 * xx5oo xx6xx&#x