Triangular-truncated dodecahedral duoprism

The triangular-truncated dodecahedral duoprism or tratid is a convex uniform duoprism that consists of 3 truncated dodecahedral prisms, 12 triangular-decagonal duoprisms and 20 triangular duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular duoprism, and 2 triangular-decagonal duoprisms. It is a duoprism based on a triangle and a truncated dodecahedron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-truncated dodecahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
 * $$\left(0,\,\frac{\sqrt3}3,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,0,\,±\frac12,\,±\frac{5+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{2+\sqrt5}2\right).$$