Decagonal-truncated tetrahedral duoprism

The decagonal-truncated tetrahedral duoprism or datut is a convex uniform duoprism that consists of 10 truncated tetrahedral prisms, 4 hexagonal-decagonal duoprisms and 4 triangular-decagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-decagonal duoprism, and 2 hexagonal-decagonal duoprisms.

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

Representations
A decagonal-truncated tetrahedral duoprism has the following Coxeter diagrams:
 * x10o x3x3o (full symmetry)
 * x5x x3x3o (decagons as dipentagons)