Octagonal-small rhombicosidodecahedral duoprism

The octagonal-small rhombicosidodecahedral duoprism or osrid is a convex uniform duoprism that consists of 8 small rhombicosidodecahedral prisms, 12 pentagonal-octagonal duoprisms, 30 square-octagonal duoprisms and 20 triangular-octagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-octagonal duoprism, 2 square-octagonal duoprisms, and 1 pentagonal-octagonal duoprism.

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

Representations
An octagonal-small rhombicosidodecahedral duoprism has the following Coxeter diagrams:
 * x8o x5o3x (full symmetry)
 * x4x x5o3x (octagons as ditetragons)