Triangular-cuboctahedral duoprism

The triangular-cuboctahedral duoprism or traco is a convex uniform duoprism that consists of 3 cuboctahedral prisms, 6 triangular-square duoprisms and 8 triangular duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular duoprisms, and 2 triangular-square duoprisms. It is a duoprism based on a triangle and a cuboctahedron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-cuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 * $$\left(0,\,\frac{\sqrt3}3,\,0,\,±\frac{\sqrt2}2,\,±\frac{\sqrt2}2\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,0,\,±\frac{\sqrt2}2,\,±\frac{\sqrt2}2\right).$$

Representations
A triangular-truncated icosahedral duoprism has the following Coxeter diagrams:
 * x3o o4x3o (full symmetry)
 * x3o x3o3x
 * ox oo3xx4oo&#x (cuboctahedron atop cuboctahedral prism)
 * ox xx3oo3xx&#x
 * ooo3xxx4ooo&#x
 * xxx3ooo3xxx&#x