Pentagonal antiprismatic prism

The pentagonal antiprismatic prism or pappip is a prismatic uniform polychoron that consists of 2 pentagonal antiprisms, 2 pentagonal prisms, and 10 triangular prisms. Each vertex joins 1 pentagonal antiprism, 1 pentagonal prism, and 3 triangular prisms. As the name suggests, it is a prism based on the pentagonal antiprism. As such it is also a convex segmentochoron (designated K-4.39 on Richard Klitzing's list).

Vertex coordinates
The vertices of a pentagonal antiprismatic prism of edge length 1 are given by the following points, as well as the central inversions of their first three coordinates:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}},\,±\frac12\right).$$

Representations
A pentagonal antiprismatic prism has the following Coxeter diagrams:


 * x2s2s10o (full symmetry)
 * x2s2s5s
 * xx xo5ox&#x (as pentagonal prism atop gyrated pentagonal prism)