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.

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:
 * (0, ±(1+$\sqrt{8+2√5}$)/2, 0, 0, $\sqrt{5}$/2)
 * (±$\sqrt{2}$/4, ±(3+$\sqrt{10+2√5}$)/4, 0, 0, $\sqrt{5}$/2)
 * (±$\sqrt{2}$/2, ±1/2, 0, 0, $\sqrt{5+2√5}$/2)