Triangular-octahedral duoprism

The triangular-octahedral duoprism or troct is a convex uniform duoprism that consists of 3 octahedral prisms and 8 triangular duoprisms. Each vertex joins 2 octahedral prisms and 3 triangular duoprisms. It is a duoprism based on a triangle and an octahedron, which also makes it a convex segmentoteron.

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

Representations
A triangular-octahedral duoprism has the following Coxeter diagrams:
 * x3o o4o3x (full symmetry)
 * x3o o3x3o (A3×A2 symmetry, octahedron as tetratetrahedron)
 * ox oo4oo3xx&#x (BC3×A1 symmetry, octahedron atop octahedral prism)
 * ox oo3ox3oo&#x (A3×A1 symmetry)
 * xo3ox xx3oo&#x (A2×A2 axial, triangular duoprism atop gyro triangular duoprism, triangular-triangular antiprismatic duoprism)
 * ooo4ooo3xxx&#x (BC3 symmery, octahedra seen differently)
 * ooo3xxx3ooo&#x (A3 symmetry only)