Octagonal-great rhombicosidodecahedral duoprism

The octagonal-great rhombicosidodecahedral duoprism or ogrid is a convex uniform duoprism that consists of 8 great rhombicosidodecahedral prisms, 12 octagonal-decagonal duoprisms, 20 hexagonal-octagonal duoprisms, and 30 square-octagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-octagonal duoprism, 1 hexagonal-octagonal duoprism, and 1 octagonal-decagonal duoprism.

This polyteron can be alternated into a square-snub dodecahedral duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a snub dodecahedral-square prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of an octagonal-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:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right).$$

Representations
An octagonal-great rhombicosidodecahedral duoprism has the following Coxeter diagrams:
 * x8o x5x3x (full symmetry)
 * x4x x5x3x (octagons as ditetragons)