Decagonal-truncated icosahedral duoprism

The decagonal-truncated icosahedral duoprism or dati is a convex uniform duoprism that consists of 10 truncated icosahedral prisms, 20 hexagonal-decagonal duoprisms, and 12 pentagonal-decagonal duoprisms. Each vertex joins 2 truncated icosahedral prisms, 1 pentagonal-decagonal duoprism, and 2 hexagonal-decagonal duoprisms.

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

Representations
A decagonal-truncated icosahedral duoprism has the following Coxeter diagrams:
 * x10o o5x3x (full symmetry)
 * x5x o5x3x (decagons as dipentagons)