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. Each vertex joins 2 truncated icosahedral prisms, 1 square-pentagonal duoprism, and 2 square-hexagonal duoprisms. It is a duoprism based on a square and a truncated icosahedron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a square-truncated icosahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,0,\,±\frac12,\,±3\frac{1+\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{5+\sqrt5}4,\,±\frac{1+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+\sqrt5}4,\,±1,\,±\frac{2+\sqrt5}2\rightt).$$

Representations
A square-truncated icosahedral duoprism has the following Coxeter diagrams:
 * x4o o5x3x (full symmetry)
 * x x o5x3x (truncated icosahedral prismatic prism)