Square-truncated icosahedral duoprism

The square-truncated icosahedral duoprism or squati is a convex uniform duoprism that consists of 4 truncated icosahedral prisms, 20 square-hexagonal duoprisms and 12 square-pentagonal duoprisms.

Vertex coordinates
The vertices of a square-truncated icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (±1/2, ±1/2, 0, 1/2, (3+3$\sqrt{66+18√5}$)/4)
 * (±1/2, ±1/2, 1/2, (5+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2)
 * (±1/2, ±1/2, (1+$\sqrt{5}$)/4, 1, (2+$\sqrt{5}$)/2)