Decagonal-octahedral duoprism

The decagonal-octahedral duoprism or doct is a convex uniform duoprism that consists of 10 octahedral prisms and 8 triangular-decagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-decagonal duoprisms.

Vertex coordinates
The vertices of a decagonal-octahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,0,\,0,\,\frac{\sqrt2}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,0,\,\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,0,\,\frac{\sqrt2}{2}\right).$$

Representations
A triangular-octahedral duoprism has the following Coxeter diagrams:
 * x10o o4o3x (full symmetry)
 * x5x o4o3x (decagons as dipentagons)
 * x10o o3x3o (octahedra as tetratetrahedra)
 * x5x o3x3o (decagons as dipentagons and octahedra as tetratetrahedra)