Decagonal-tetrahedral duoprism

The decagonal-tetrahedral duoprism or datet is a convex uniform duoprism that consists of 10 tetrahedral prisms and 4 triangular-decagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-decagonal duoprisms.

Vertex coordinates
The vertices of a decagonal-tetrahedral duoprism of edge length 1 are given by all even sign changes of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,0,\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$

Representations
A decagonal-tetrahedral duoprism has the following Coxeter diagrams:
 * x10o x3o3o (full symmetry)
 * x5x x3o3o (decagons as dipentagons)