It has icosahedral symmetry (Ih) and it has the same vertex arrangement as a great rhombic triacontahedron.
This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} "decagram"); this series continues into the fourth dimension as compounds of star 4-polytopes.
This polyhedron is a stellation of the icosidodecahedron, and given as Wenninger model index 61.
It has the same vertex arrangement as a rhombic triacontahedron, its convex hull.
The stellation facets for construction are: This polyhedron-related article is a stub.