Square-icosahedral duoprism

The square-icosahedral duoprism or squike is a convex uniform duoprism that consists of 4 icosahedral prisms and 20 triangular-square duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-square duoprisms. It is a duoprism based on a square and an icosahedron, which makes it a convex segmentoteron.

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

Representations
A square-icosahedral duoprism has the following Coxeter diagrams:
 * x4o o5o3x (full symmetry)
 * x x o5o3x (icosahedral prismatic prism)