Triangular-dodecahedral duoprism

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

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