Pentagonal pyramidal prism

The pentagonal pyramidal prism, or peppyp, is a CRF segmentochoron (designated K-4.38 on Richard Klitzing's list). It consists of 2 pentagonal pyramids, 1 pentagonal prism, and 5 triangular prisms.

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

Two pentagonal pyramidal prisms can be attached to the pentagonal prismatic cells of the pentagonal antiprismatic prism to produce the uniform icosahedral prism.

Vertex coordinates
Coordinates of the vertices of a pentagonal pyramidal prism of edge length 1 centered at the origin are given by:


 * (±1/2, -$\sqrt{2}$, 0, ±1/2),
 * (±(1+$\sqrt{2}$)/4, $\sqrt{5}$, 0, ±1/2),
 * (0, $\sqrt{(7+√5)/8}$, 0, ±1/2),
 * (0, 0, $\sqrt{5}$, ±1/2).

Representations
A pentagonal pyramidal prism has the following Coxeter diagrams:


 * xx o54oo&#x (full symmetry)
 * oxxo5oooo&#xr (H2 axial only, pentagonal pyramid atop pentagonal pyramid)