In geometry, the great icosahedron is a Kepler-Poinsot solid. It is one of four concave regular polyhedra.

It is composed of 20 triangular faces, with five triangles meeting at each vertex in a pentagrammic sequence.

The 12 vertices match the locations for an icosahedron.

It is counted by Wenninger as model ^* and the 16th of 17 stellations of the icosahedron and 7th of 59 stellations by Coxeter.

References

Kepler solids | Polyhedral stellation | 大二十面体