Decagonal-great rhombicosidodecahedral duoprism

The decagonal-great rhombicosidodecahedral duoprism or dagrid is a convex uniform duoprism that consists of 10 great rhombicosidodecahedral prisms, 12 decagonal duoprisms, 20 hexagonal-decagonal duoprisms, and 30 square-decagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-decagonal duoprism, 1 hexagonal-decagonal duoprism, and 1 decagonal duoprism.

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

Vertex coordinates
The vertices of a decagonal-great rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of: along with all even permutations of the last three coordinates of:
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right).$$

Representations
A decagonal-great rhombicosidodecahedral duoprism has the following Coxeter diagrams:
 * x10o x5x3x (full symmetry)
 * x5x x5x3x (decagons as dipentagons)