Tetrahedral-hexateric duoprism

The tetrahedral-hexateric duoprism or tethix is a convex uniform duoprism that consists of 4 triangular-hexateric duoprisms and 6 tetrahedral-pentachoric duoprisms. Each vertex joins 3 triangular-hexateric duoprisms and 5 tetrahedral-pentachoric duoprisms. It is a duoprism based on a tetrahedron and a hexateron, and is thus also a convex segmentozetton, as a hexateron atop triangular-hexateric duoprism.

Vertex coordinates
The vertices of a tetrahedral-hexateric duoprism of edge length 1 are given by all even sign changes of the first three coordinates of:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,0,\,0,\,\frac{\sqrt{10}}{5},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,0,\,0,\,0,\,\frac{\sqrt{15}}{6}\right),$$