The Kepler–Poinsot Star Polyhedra
In addition to the five convex regular polyhedra (the Platonic Solids) there are four non-convex regular polyhedra. These four solids were discovered by Johannes Kepler (1571-1630) and Louis Poinsot (1777-1859), and were unknown to the ancient world. Three of the Kepler–Poinsot Star Polyhedra are the three stellations of the regular dodecahedron. Namely:
The fourth is one of the many stellations of the icosahedron.