Petrial great icosahedron

The petrial great icosahedron is a regular skew polyhedron and is the Petrie dual of the great icosahedron, so it shares its vertices and edges with the great icosahedron. It has an Euler characteristic of -12 and consists of 6 skew decagrams.

Vertex coordinates
The vertices of a petrial icosahedron of edge length 1 centered at the origin are the same as the icosahedron, being all cyclic permutations of:
 * $$\left(0,\,\pm\frac{1}{2},\,\pm\frac{1+\sqrt{5}}{4}\right).$$

Related polyhedra
The rectification of the petrial icosahedron is the great dodecahemidodecahedron, which is uniform.