Decagonal-cuboctahedral duoprism

The decagonal-cuboctahedral duoprism or daco is a convex uniform duoprism that consists of 10 cuboctahedral prisms, 6 square-decagonal duoprisms, and 8 triangular-decagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-decagonal duoprisms, and 2 square-decagonal duoprisms.

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

Representations
A decagonal-cuboctahedral duoprism has the following Coxeter diagrams:
 * x10o o4x3o (full symmetry)
 * x5x o4x3o (decagons as dipentagons)
 * x10o x3o3x
 * x5x x3o3x