Triangular-pentachoric duoprism

The triangular-pentachoric duoprism or trapen is a convex uniform duoprism that consists of 3 pentachoric prisms and 5 triangular-tetrahedral duoprisms. Each vertex joins 2 pentachoric prisms and 4 triangular-tetrahedral duoprisms. It is a duoprism based on a triangle and a pentachoron, and is thus also a convex segmentopeton, as a pentachoron atop pentachoric prism.

Vertex coordinates
The vertices of a triangular-pentachoric duoprism of edge length 1 are given by:
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,0,\,0,\,\frac{\sqrt{10}}{5}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,0,\,0,\,\frac{\sqrt{10}}{5}\right).$$

Representations
A triangular-tetrahedral duoprism has the following Coxeter diagrams:


 * x3o x3o3o3o (full symmetry)
 * xx3oo ox3oo3oo&#x (A3×A2 symmetry, triangle atop triangular-tetrahedral duoprism)
 * ox xx3oo3oo3oo&#x (A4×A1 symmetry, pentachoron atop pentachoric prism)
 * ox xo3oo xx3oo&#x (A2×A2×A1 symmetry, triangular prism atop orthogonal triangular-square duoprism)
 * xxx3ooo3ooo3ooo&#x (A4 symmetry, 3 pentachoric layers)