Tetrahedral-octahedral duoprism

The tetrahedral-octahedral duoprism or tetoct is a convex uniform duoprism that consists of 4 triangular-octahedral duoprisms and 8 triangular-tetrahedral duoprisms. Each vertex joins 3 triangular-octahedral duoprisms and 4 triangular-tetrahedral duoprisms. It is a duoprism based on a tetrahedron and an octahedron, and is thus also a convex segmentopeton, as an octahedron atop triangular-octahedral prism.

Vertex coordinates
The vertices of a tetrahedral-octahedral duoprism of edge length 1 are given by all even sign changes of the first three coordinates, plus all permutations and sign changes of the last three coordinates, of:
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4],\,\frac{\sqrt2}{4},\,±\frac{\sqrt2}{2},\,0,\,0\right).$$

Representations
A triangular-tetrahedral duoprism has the following Coxeter diagrams:


 * x3o3o o4o3x (full symmetry)
 * x3o3o o3x3o (A3×A3 symmetry)
 * xo3ox xx3oo3oo&#xt (A3×A2 axial, triangular-tetrahedral duoprism atop triangle-dual triangular-tetrahedral duoprism)
 * ox3oo oo4oo3xx&#x (B3×A2 xaial, octahedron atop triangular-octahedral duoprism)
 * xo ox oo4oo3xx&#x (B3×A1×A1 axial, octahedral prism atop orthogonal octahedral prism)