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Kepler on polyhedral geometry. Polyhedra in '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. Some geometrical properties of polyhedra are shown here, including two new stellated forms of the dodecahedron (lower left) discovered by Kepler. At centre right are the five regular polyhedra (Platonic solids) representing the Aristotelian elements: octahedron (air), tetrahedron (fire), cube (earth), icosahedron (water), and the dodecahedron (aether).
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