Square-truncated dodecahedral duoprism

The square-truncated dodecahedral duoprism or squatid is a convex uniform duoprism that consists of 4 truncated dodecahedral prisms, 12 square-decagonal duoprisms and 20 triangular-square duoprisms.

Vertex coordinates
The vertices of a square-truncated dodecahedral 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, (5+3$\sqrt{82+30√5}$)/4)
 * (±1/2, ±1/2, 1/2, (3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (±1/2, ±1/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)