 Amidst this general interest in the regular polyhedra during the Renaissance, Kepler was specifically concerned with their application in the resolution of a cosmological problem, namely the reality of the Copernican system (see Section 5 below). To achieve this goal, he introduced his polyhedral hypothesis already in MC, where he looked for an “a priori” foundation of the Copernican system (see Aiton 1977, Di Liscia 2009). The background for such an approach seems to be that the “a posteriori” way, which according to Kepler was taken over by Copernicus himself, cannot lead to a necessary affirmation of the reality of the new world system, but only to a probable, and hence to an “instrumental”, representation of it as a computational device. This is the “Osiander” or “Wittenberg Interpretation” of Copernicus which Kepler directly attacked not only in his MC but also later in his AN (see Westman 1972, 1975 and 2011). In MC, he claimed to have found an answer to the following three main questions: 1) the number of the planets; 2) the size of the orbits, i.e., the distances; 3) the velocities of the planets in their orbits. By referring to the polyhedral hypothesis (see Figure 1), Kepler found a definitive and simple answer to the first question. By intercalating the polyhedra between the spheres which carry the planets, one must inevitably finish with the sphere of Saturn surrounding the cube—there are no more polyhedra to be intercalated and, as remains the standard case for Renaissance and modern astronomy, there are no more planets to be carried by the spheres. It is absolutely decisive for the consistency of the argument that the necessity of the hypothesis is guaranteed by the fact that it already exists as a mathematical demonstration (by Euclid, Elements XIII, prop. 18, schol.), according to which there are only five regular (“Platonic” for the tradition) polyhedra. For the second and third questions the answer is, of course, not as evident as for the first one. However, Kepler was able to show that distances which are derived from the geometrical model of the five regular bodies fit much better with the Copernican system than with that of Ptolemy. The answer to the third question needs, in addition, the introduction of a notion of power that emanates from the Sun and extends to the outer limit of the universe (see Stephenson 1987, pp. 9–20).