The five Platonic solids made from index cards. I suppose the Platonic solids are just innately beautiful in their symmetry - look how perfect and congruent they are!
Did you know that the five Platonic solids were associated with the elements? There is actually rationale behind these associations - the tetrahedron is fire because of the sharpness of its edges and vertices, the stable cube is earth, water flows out of one's hand like an icosahedron might, between the tetrahedron (fire) and the icosahedron (water) is the intermediary octahedron (air). I particularly like the dodecahedron's representation of the universe - Plato said, "There remained a fifth construction which God used for embroidering the constellations on the whole heaven."
Another particularly awesome bit of Platonic solid history is when astronomer Johannes Kepler proposed that the spacing of the planets could be explained with a series of nested polyhedra and spheres. Starting with the octahedron, followed by the icosahedron, dodecahedron, tetrahedron, and finally the cube, this elegant geometric arrangement was said to explain the locations of the six known planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn). Though the theory had to be abandoned eventually, the research that Kepler did led to his discovery that the planets have elliptical rather than circular orbits.
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