Square-icosidodecahedral duoprism

The square-icosidodecahedral duoprism or squid is a convex uniform duoprism that consists of 4 icosidodecahedral prisms, 12 square-pentagonal duoprisms, and 20 triangular-square duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-square duoprisms, and 2 square-pentagonal duoprisms. It is a duoprism based on a square and an icosidodecahedron, which makes it a convex segmentoteron.

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

Representations
A square-icosidodecahedral duoprism has the following Coxeter diagrams:
 * x4o o5x3o (full symmetry)
 * x x o5x3o (icosidodecahedral prismatic prism)