The Platonic Solids

The Platonic Solids - the intermediate (octahedron) to air...

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The Platonic Solids The Platonic Solids belong to the group of geometric figures called polyhedra. A polyhedron is a solid bounded by plane polygons. The polygons are called faces ; they intersect in edges , the points where three or more edges intersect are called vertices . A regular polyhedron is one whose faces are identical regular polygons. Only five regular solids are possible cube tetrahedron octahedron icosahedron dodecahedron These have come to be known as the Platonic Solids The Elements Linked to the Platonic Solids Plato associates four of the Platonic Solid with the four elements. He writes, We must proceed to distribute the figures [the solids] we have just described between fire, earth, water, and air. . . Let us assign the cube to earth, for it is the most immobile of the four bodies and most retentive of shape the least mobile of the remaining figures (icosahedron) to water the most mobile (tetrahedron) to fire
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Unformatted text preview: the intermediate (octahedron) to air Note that earth is associated with the cube, with its six square faces. This lent support to the notion of the foursquaredness of the earth. The Cosmos But there are five regular polyhedra and only four elements. Plato writes, "There still remained a fifth construction, which the god used for embroidering the constellations on the whole heaven." Plato's statement is vague, and he gives no further explanation. Later Greek philosophers assign the dodecahedron to the ether or heaven or the cosmos. The dodecahedron has 12 faces, and our number symbolism associates 12 with the zodiac. This might be Plato's meaning when he writes of "embroidering the constellations" on the dodecahedron. Note that the 12 faces of the dodecahedron are pentagons. Recall that the pentagon contains the golden ratio. Perhaps this has something to do with equating this figure with the cosmos....
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