Decagonal-icosahedral duoprism

The decagonal-icosahedral duoprism or dike is a convex uniform duoprism that consists of 10 icosahedral prisms and 20 triangular-decagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-decagonal duoprisms.

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

Representations
A decagonal-icosahedral duoprism has the following Coxeter diagrams:
 * x10o o5o3x (full symmetry)
 * x5x o5o3x (decagons as dipentagons)