Tetrahedral-hexadecachoric duoprism

The tetrahedral-headecachoric duoprism or tethex is a convex uniform duoprism that consists of 4 triangular-hexadecachoric duoprisms and 16 tetrahedral duoprisms. Each vertex joins 3 triangular-hexadecachoric duoprisms and 8 tetrahedral duoprisms. It is a duoprism based on a tetrahedron and a hexadecachoron, and is thus also a convex segmentoexon, as a hexadecachoron atop triangular-hexadecachoric duoprism.

The tetrahedral-hexadecachoric duoprism can be vertex-inscribed into a demihepteract.

Vertex coordinates
The vertices of a tetrahedral-hexadecachoric duoprism of edge length 1 are given by all even sign changes of the first three coordinates, plus all permutations and sign changes of the last four coordinates, of:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{\sqrt2}{2},\,0,\,0,\,0\right).$$

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


 * x3o3o o4o3o3x (full symmetry)
 * x3o3o x3o3o *e3o (D4×A3 symmetry)