Decagonal-great rhombicuboctahedral duoprism

The decagonal-great rhombicuboctahedral duoprism or dagirco is a convex uniform duoprism that consists of 10 great rhombicuboctahedral prisms, 6 octagonal-decagonal duoprisms, 8 hexagonal-decagonal duoprisms, and 12 square-decagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-decagonal duoprism, 1 hexagonal-decagonal duoprism, and 1 octagonal-decagonal duoprism.

This polyteron can be alternated into a pentagonal-snub cubic duoantiprism, although it cannot be made uniform. The great rhombicuboctahedra can be edge-snubbed to create a pentagonal-pyritohedral prismantiprismoid, which is also nonuniform.

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

Representations
A decagonal-great rhombicuboctahedral duoprism has the following Coxeter diagrams:
 * x10o x4x3x (full symmetry)
 * x5x x4x3x (decagons as dipentagons)