Triangular-tetrahedral duoprism

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

Vertex coordinates
The vertices of a triangular-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:
 * $$\left(0,\,\frac{\sqrt3}{3},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

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


 * x3o x3o3o (full symmetry)
 * xx3oo ox3oo&#x (A2×A2 symmetry, triangle atop triangular duoprism)
 * ox xx3oo3oo&#x (A3×A1 symmetry, tetrahedron atop tetrahedral prism)
 * ox xo xx3oo&#x (A2×A1×A1 symmetry, triangular prism atop orthogonal triangular prism)
 * ooo3ooo3xxx&#x (A3 symmetry, tetrahedra considered different)
 * oox ooo3xxx&#x (A2×A1 symmetry, tetrahedra have mirror symmetry only)
 * oooo3xxxx&#x (A2 symmetry, tetrahedra have no symmetry)
 * xxoo xoox3oooo&#xr (A2×A1 symmetry)