Triangular-truncated icosahedral duoprism

The triangular-truncated icosahedral duoprism or trati is a convex uniform duoprism that consists of 3 truncated icosahedral prisms, 20 triangular-hexagonal duoprisms and 12 triangular-pentagonal duoprisms.

Vertex coordinates
The vertices of a triangular-truncated icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, $\sqrt{570+162√5}$/3, 0, 1/2, (3+3$\sqrt{3}$)/4)
 * (0, $\sqrt{5}$/3, 1/2, (5+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2)
 * (0, $\sqrt{5}$/3, (1+$\sqrt{3}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±1/2, -$\sqrt{5}$/6, 0, 1/2, (3+3$\sqrt{3}$)/4)
 * (±1/2, -$\sqrt{5}$/6, 1/2, (5+$\sqrt{3}$)/4, (1+$\sqrt{5}$)/2)
 * (±1/2, -$\sqrt{5}$/6, (1+$\sqrt{3}$)/4, 1, (2+$\sqrt{5}$)/2)