Triangular-icosahedral duoprism

The triangular-icosahedral duoprism or trike is a convex uniform duoprism that consists of 3 icosahedral prisms and 20 triangular duoprisms.

Vertex coordinates
The vertices of a triangular-icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, $\sqrt{138+18√5}$/3, 0, 1/2, (1+$\sqrt{3}$)/4)
 * (±1/2, -$\sqrt{5}$/6, 0, 1/2, (1+$\sqrt{3}$)/4)