Triangular-icosahedral duoprism

The triangular-icosahedral duoprism or trike is a convex uniform duoprism that consists of 3 icosahedral prisms and 20 triangular duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-pentagonal duoprisms. It is a duoprism based on a triangle and an icosahedron, which makes it a convex segmentoteron.

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