Octagonal-truncated icosahedral duoprism

The octagonal-truncated icosahedral duoprism or oti is a convex uniform duoprism that consists of 8 truncated icosahedral prisms, 20 hexagonal-octagonal duoprisms and 12 pentagonal-octagonal duoprisms. Each vertex joins 2 truncated icosahedral prisms, 1 pentagonal-octagonal duoprism, and 2 hexagonal-octagonal duoprisms.

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

Representations
An octagonal-truncated icosahedral duoprism has the following Coxeter diagrams:
 * x8o o5x3x (full symmetry)
 * x4x o5x3x (octagons as ditetragons)