Pentagonal-cubic duoprism

The pentagonal-cubic duoprism or pecube, also known as a square-pentagonal duoprismatic prism, is a convex uniform duoprism that consists of 5 tesseracts and 6 square-pentagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-pentagonal duoprisms. It is a duoprism based on a square and a pentagonal prism, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a pentagonal-cubic duoprism of edge length 1 are given by:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt{5}}{10}},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}},\,±\frac12,\,±\frac12,\,±\frac12\right).$$

Representations
A pentagonal-cubic duoprism has the following Coxeter diagrams:
 * x5o x4o3o (full symmetry)
 * x x4o x5o (square-pentagonal duoprismatic prism)
 * x x x x5o (pentagonal prismatic prismatic prism)