Pentagonal prism

The pentagonal prism, or pip, is a prismatic uniform polyhedron. It consists of 2 pentagons and 5 squares. Each vertex joins one pentagon and two squares. As the name suggests, it is a prism based on a pentagon.

Semiuniform variants of the pentagonal prism also exist, with the lengths of the edges of the base pentagons and the side edges of the prism being different but still remaining vertex transitive and with full symmetry. In these cases the lateral squares become rectangles. The according Coxeter diagram would then be x y5o.

Vertex coordinates
A pentagonal prism of edge length 1 has vertex coordinates given by:
 * (±1/2, –$\sqrt{(15+2√5)/20}$, ±1/2),
 * (±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$, ±1/2),
 * (0, $\sqrt{2}$, ±1/2).