Octagonal-icosidodecahedral duoprism

The octagonal-icosidodecahedral duoprism or oid is a convex uniform duoprism that consists of 8 icosidodecahedral prisms, 12 pentagonal-octagonal duoprisms and 20 triangular-octagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-octagonal duoprisms, and 2 pentagonal-octagonal duoprisms.

Vertex coordinates
The vertices of an octagonal-icosidodecahedral 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:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,0,\,0,\,±\frac{1+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,0,\,0,\,±\frac{1+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,±\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}4\right).$$

Representations
An octagonal-icosidodecahedral duoprism has the following Coxeter diagrams:
 * x8o o5x3o (full symmetry)
 * x4x o5x3o (octagons as ditetragons)