In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound.

As a compound

It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It has icosahedral symmetry (Ih) and the same vertex arrangement as a rhombic triacontahedron. This can be seen as the three-dimensional equivalent of the compound of two pentagons ({10/2} "decagram"); this series continues into the fourth dimension as the compound of 120-cell and 600-cell and into higher dimensions as compounds of hyperbolic tilings.

As a stellation

This polyhedron is the first stellation of the icosidodecahedron, and given as Wenninger model index 47. The stellation facets for construction are:

In popular culture

In the film Tron (1982), the character Bit took this shape when not speaking. In the cartoon series Steven Universe (2013-2019), Steven's shield bubble, briefly used in the episode Change Your Mind, had this shape.