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 dicovered by Johannes Kepler (1571-1630) and Louis Poinsot (1777-1859), and were unknown to the ancient world. Three of the Keplar-Poinsot Star Polyhedra are the three stellations of the regular dodecahedron. Namely:
The fourth is one of the many stellations of the icosahedron.
These solids' faces intersect one-another due to their 'star' faces or vertices (hence they are known as star polyhedra). This shown by the fractional '5/2' value in their vertex symbols.