Platonic Solids

A Platonic Solid is a convex multifaceted 3-D object whose faces are all identical polygons, with sides of equal length and angles of equal degrees. A Platonic solid also has the same number of faces meeting at every vertex. The best-known example of a Platonic solid is the cube, whose faces are six identical squares.
The ancient Greeks recognized and proved that only five Platonic solids can be constructed: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. For example, the icosahedron has 20 faces, all in a shape of equilateral triangles.
Plato described the five Platonic solids in Timaeus in around 350 B.C. He was not only awestruck by their beauty and symmetry, but he also believed that the shapes described the structures of four basic elements thought to compose the cosmos. In particular, the tetrahedron was the shape that represented the fire, perhaps because of the polyhedron's sharp edges. The octahedron was air. Water was made up of icosahedra, which are smoother than the other Platonic solids. Earth consisted of cubes, which look sturdy and solid. Plato decided that God used the dodecahedron for arranging the constellations in the heavens.
Pythagoras of Samos - the famous mathematician and mystic who lived in the time of Buddha and Confucius, around 550 B.C. - probably knew of three of the five Platonic solids (the cube, tetrahedron, and dodecahedron). Slightly rounded versions of the Platonic solids made of stone have been discovered in areas inhabited by the late Neolithic people of Scotland at least 1,000 years before Plato. The German astronomer Johannes Kepler (1571-1630) constructed models of Platonic solids nested within one another in an attempt to describe the orbits of planets about the sun. Although Kepler's theories were wrong, he was one of the first to insist on a geometrical explanation for celestial phenomena.