Octagonal-cuboctahedral duoprism

The octagonal-cuboctahedral duoprism or oco is a convex uniform duoprism that consists of 8 cuboctahedral prisms, 6 square-octagonal duoprisms and 8 triangular-octagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-octagonal duoprisms, and 2 square-octagonal duoprisms.

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

Representations
An octagonal-cuboctahedral duoprism has the following Coxeter diagrams:
 * x8o o4x3o (full symmetry)
 * x4x o4x3o (octagons as ditetragons)
 * x8o x3o3x
 * x4x x3o3x