The Kepler-Poinsot solids are the four self-intersecting regular polyhedra.
Two of them (the Small Stellated Dodecahedron and the Great Stellated
Dodecahedron) were discovered by Johannes Kepler (1571-1630).
The other two (the Great Dodecahedron and Great Icosahedron) were discovered
by Louis Poinsot (1777-1859) and are the duals of the two Kepler solids.
Like the Platonic solids, these solids are regular because each uses the same
regular polygon or star polygon for each face, with the same number of faces
meeting at each vertex.
The difference is that these four solids are self-intersecting.
The Kepler-Poinsot solids are the only self-intersecting regular polyhedra.