There are only 5 Platonic Solids – each of which is constructed of regular polygons having congruent sides and angles. In Timaeus (ca. 360 B.C.), Plato associated each solid with a specific attribute: tetrahedron = fire (4 vertices, 6 edges, 4 faces) cube = earth (8 vertices, 12 edges, 6 faces) octahedron = air (6 vertices, 12 edges, 8 faces) icosahedron = water (12 vertices, 30 edges, 20 faces) dodecahedron = the fifth element, i.e., quintessence (20 vertices, 30 edges, 12 faces) Plato called this regular polyhedron “universe” and Aristotle called it “ether.” Keith Devlin, The Language of Mathematics. W. H.Freeman and Company, New York, 1998. Image: This image comes from the Brockhaus and Efron Encyclopedic Dictionary (1890-1907). The copyrights for that book have expired and this image is in the public domain.

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