Johannes Kepler - Platonic Solid Model of the Solar System, “Mysterium Cosmographicum” (The Cosmographic Mystery), 1600.
Kepler’s Cosmological theory, based on the Copernican system, states that five Pythagorean regular Polyhedra dictate the structure of the Universe and reflect God’s plan through Geometry. This was the first attempt since Copernicus to say that the theory of Heliocentrism is physically true.
Kepler claimed to have had an epiphany on July 19, 1595, demonstrating the periodic conjunction of Saturn and Jupiter in the Zodiac: he realized that regular Polygons bound one inscribed and one circumscribed Circle at definite Ratios, which might be the Geometrical basis of the Universe. After failing to find a unique arrangement of Polygons that fit known Astronomical observations, Kepler began experimenting with 3-dimensional Polyhedra. He found that each of the five Platonic Solids could be uniquely inscribed and circumscribed by Spherical Orbs; nesting these Solids, each encased in a Sphere, within one another would produce six layers, corresponding to the six known Planets - Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the Solids correctly - Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube - Kepler found that the Spheres could be placed at intervals corresponding to the relative sizes of each Planet’s path, assuming the Planets circle the Sun. Kepler also found a formula relating the size of each Planet’s orb to the length of its orbital period: from inner to outer Planets, the ratio of increase in orbital period is twice the difference in orb radius.