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.

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:
 * (0, $\sqrt{2}$/3, $\sqrt{102}$/4, $\sqrt{3}$/4, $\sqrt{6}$/4)
 * (±1/2, -$\sqrt{2}$/6, $\sqrt{6}$/4, $\sqrt{3}$/4, $\sqrt{2}$/4)

Representations
A triangular-tetrahedral duoprism has thee 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, tetrahedar have mirror symmetry only)
 * oooo3xxxx&#x (A2 symmetry, tetrahedra have no symmetry)
 * xxoo xoox3oooo&#xr (A2×A1 symmetry)