Decagonal-icosidodecahedral duoprism

The decagonal-icosidodecahedral duoprism or daid is a convex uniform duoprism that consists of 10 icosidodecahedral prisms, 12 pentagonal-decagonal duoprisms, and 20 triangular-decagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-decagonal duoprisms, and 2 pentagonal-decagonal duoprisms.

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

Representations
A decagonal-icosidodecahedral duoprism has the following Coxeter diagrams:
 * x10o o5x3o (full symmetry)
 * x5x o5x3o (decagons as dipentagons)