Decagonal-truncated octahedral duoprism

The decagonal-truncated octahedral duoprism or datoe is a convex uniform duoprism that consists of 10 truncated octahedral prisms, 8 hexagonal-decagonal duoprisms, and 6 square-decagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-decagonal duoprism, and 2 hexagonal-decagonal duoprisms.

This polyteron can be alternated into a pentagonal-pyritohedral icosahedral duoantiprism, although it cannot be made uniform.

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

Representations
A decagonal-truncated octahedral duoprism has the following Coxeter diagrams:
 * x10o o4x3x (full symmetry)
 * x10o x3x3x
 * x5x o4x3x (decagons as dipentagons)
 * x5x x3x3x