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:
 * ±(0, $\sqrt{5}$, $\sqrt{2}$, ±1/2)
 * ±(±(1+$\sqrt{(7+√5)/8}$)/4, $\sqrt{(5+√5)/10}$, $\sqrt{5}$, ±1/2)
 * ±(±1/2, –$\sqrt{5}$, $\sqrt{(5–2√5)/15}$, ±1/2)

Representations
A pentagonal antiprismatic prism has the following Coxeter diagrams:


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