Hexagonal-icosahedral duoprism

The hexagonal-icosahedral duoprism or hike is a convex uniform duoprism that consists of 6 icosahedral prisms and 20 triangular-hexagonal duoprisms.

Vertex coordinates
The vertices of a hexagonal-icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, ±1, 0, 1/2, (1+$\sqrt{26+2√5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, 0, 1/2, (1+$\sqrt{3}$)/4)