Pentagonal cupolic prism

The pentagonal cupolic prism, or pecupe, is a CRF segmentochoron (designated K-4.117 on Richard Klitzing's list). It consiss of 2 pentagonal cupolas, 5 triangular prisms, 5 cubes, 1 pentagonal prism, and 1 decagonal prism.

As the name suggests, it is a prism based on the pentagonal cupola. As such, it is a segmentochoron between two pentagonal cupolas. It can also be viewed as a segmentochoron between a decagonal prism and a pentagonal prism.

It can be obtained as a segment of the small rhombicosidodecahedral prism.

Vertex coordinates
Coordinates of the vertices of a pentagonal cupolic prism of edge length 1 centered at the origin are given by:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,\sqrt{\frac{5-\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,\sqrt{\frac{5-\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5-\sqrt5}{10}},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,0,\,0,\,±\frac12\right).$$