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Platonic Solids

13 12 the dodecahedron 12 faces 30 edges 20 vertices The beautiful dodecahedron has twelve regular pentagonal faces, three of which meet at every vertex. Its symmetry is icosahedral below. Like the tetrahedron, or pyramid, and the cube, the dodecahedron was known to the early Pythagoreans and was commonly referred to as the sphere of twelve pentagons. Having detailed the other four solids and ascribed them to the elements, Platos Timaeus says enigmatically There remained a fifth construction which God used for embroidering the constellations on the whole heaven. A dodecahedron sitting on a horizontal surface has vertices lying in four horizontal planes which cut the dodecahedron into three parts. Surprisingly, the middle part is equal in volume to the others, so each is one third of the total Also, when set in the same sphere, the surface areas of the icosahedron and dodecahedron are in the same ratio as their volumes, and their inspheres are identical. Fools Gold, or iron pyrite, forms crystals much like the dodecahedron, but dont be fooled, their pentagonal faces are not regular and their symmetry is tetrahedral.
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