Octagonal-icosahedral duoprism

The octagonal-icosahedral duoprism or oike is a convex uniform duoprism that consists of 8 icosahedral prisms and 20 triangular-octagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-octagonal duoprisms.

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

Representations
An octagonal-icosahedral duoprism has the following Coxeter diagrams:
 * x8o o5o3x (full symmetry)
 * x4x o5o3x (octagons as ditetragons)