Pentagonal-octahedral duoprism

The pentagonal-octahedral duoprism or poct is a convex uniform duoprism that consists of 5 octahedral prisms and 8 triangular-pentagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a pentagonal-octahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt{5}}{10}},\,0,\,0,\,\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}},\,0,\,0,\,\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}},\,0,\,0,\,\frac{\sqrt2}{2}\right).$$

Representations
A pentagonal-octahedral duoprism has the following Coxeter diagrams:
 * x5o o4o3x (full symmetry)
 * x5o o3x3o (octahedra as tetratetrahedra)
 * xo3ox xx5oo&#x (triangular-pentagonal duoprism atop gyro triangular-pentagonal duoprism)