KeplerPoinsot Solids 
The KeplerPoinsot solids are the four selfintersecting regular polyhedra. Two of them (the Small Stellated Dodecahedron and the Great Stellated Dodecahedron) were discovered by Johannes Kepler (15711630). The other two (the Great Dodecahedron and Great Icosahedron) were discovered by Louis Poinsot (17771859) 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 selfintersecting. The KeplerPoinsot solids are the only selfintersecting regular polyhedra.





References:  [1]  Johannes Kepler, Harmonices Mundi (1619). 
[2]  Johannes Kepler with E. J. Aiton, A. M. Duncan, and J. V. Field, translators, The Harmony of the World, American Philosophical Society (1997).  
[3]  Louis Poinsot, Mémoire sur les Polygones et Polyèdres, Journal de l'École polytechnique 10 (1810), 1648. 