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 small stellated dodecahedron, its regiment colonel.

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

It is abstractly equivalent to the petrial icosahedron.