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Kepler on Platonic solids. Illustrations and Latin text from Book V of 'Harmonices Mundi' (The Harmony of the World, 1619) by German mathematician and astronomer Johannes Kepler (1571-1630). From his study of musical harmony and geometry, Kepler developed his third law of planetary motion. Discussed here are the relations and properties of the five regular polyhedra (Platonic solids): octahedron, tetrahedron, cube, icosahedron, and dodecahedron. Kepler assigned these solids to the known planets and tried to make observations of their orbits fit the interlocking of the polyhedra. He invented new forms of the dodecahedron to improve his theory.
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