Square-pentachoric duoprism

The square-pentachoric duoprism or squapen is a convex uniform duoprism that consists of 4 pentachoric prisms and 5 square-tetrahedral duoprisms. Each vertex joins 2 pentachoric prisms and 4 square-tetrahedral duoprisms. It is a duoprism based on a square and a pentachoron, and is thus also a convex segmentopeton, as a pentachoric prism atop pentachoric prism.

Vertex coordinates
The vertices of a square-pentachoric duoprism of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,0,\,0,\,0,\,\frac{\sqrt{10}}{5}\right),$$

Representations
A square-pentachoric duoprism has the following Coxeter diagrams:


 * x4o x3o3o3o (full symmetry)
 * x x x3o3o3o (square as rectangle, pentachoric prismatic prism)
 * xx4oo ox3oo3oo&#x (A3×B2 symmetry, square atop square-tetrahedral duoprism)
 * xx xx3oo3oo3oo&#x (A4×A1 symmetry, pentachoric prism atop pentachoric prism)
 * ox xo3oo xx4oo&#x (A2×B2×A1 symmetry, cube atop orthogonal triangular-square duoprism)