 Plato establishes at the physical and chemical level a correspondence between them and the five elements—earth, water, air, fire and ether—and tries to provide this correspondence with geometrical grounds. A further source of historically decisive importance is the fact that the five regular polyhedra are treated in Euclid’s Elements of Geometry, a work that for Kepler, especially in the Platonic approach of Proclus, has a central position. At the very beginning of HM Kepler complains about the fact that the modern philosophical and mathematical school of Peter Ramus (1515–1572) had not been able to understand the architectonic structure of the Elements, which are crowned with the treatment of the five regular polyhedra. In addition, a revival of Platonic philosophy was taking place in Kepler’s time and inspired not only philosophers and mathematicians but also architects, artists and illustrators (see Field 1997).