Tetrahedral-pentachoric duoprism

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

Vertex coordinates
The vertices of a tetrahedral-pentachoric duoprism of edge length 1 are given by all even permutations of the first three coordinates of:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,0,\,0,\,\frac{\sqrt{10}}{5}\right),$$