 Poinsot did not know if he had discovered all the regular star polyhedra.Three years later, Augustin Cauchy proved the list complete by stellating the Platonic solids, and almost half a century after that, in 1858, Bertrand provided a more elegant proof by faceting them.The following year, Arthur Cayley gave the Kepler–Poinsot polyhedra the names by which they are generally known today.