Platonic solids were named after Plato, who was one of the first philosophers to be struck by their beauty and rarity. But Plato did more than admire them: he made them the center of his theory of the universe.
Plato believed that the world was composed entirely of four elements: fire, air, water, and earth. He was one of the originators of atomic theory, believing that each of the elements was made up of tiny fundamental particles. The shapes that he chose for the elements were the Platonic solids.
In Plato's system, the tetrahedron was the shape of fire, perhaps because of its sharp edges.
The octahedron was air.
Water was made up of icosahedra, which are the most smooth and round of the Platonic solids.
And the earth consisted of cubes, which are solid and sturdy.
This analysis left one solid unmatched: the dodecahedron. Plato decided that the it was the symbol of the "quintessence," writing, "God used this solid for the whole universe, embroidering figures on it."
Plato's description of the universe made a deep impression on his disciples, but it failed to satisfy his most illustrious student, Aristotle.
Aristotle reasoned that if the elements came in the forms of the Platonic solids, then each of the Platonic solids should stack together, leaving no holes, since for example water is smooth and continuous, with no gaps. But, Aristotle pointed out, the only Platonic solids that can fill space without gaps are the cube and the tetrahedron, hence the other solids cannot possibly be the foundation for the elements. His argument struck his followers as so cogent that the atomic theory was discarded, to be ignored for centuries.
Aristotle's analysis contained a famous error: the tetrahedron does not fill space without gaps.
Incredibly, Aristotle's mistake was not discovered for more than 17 centuries. Aristotle was so highly esteemed by his followers that they confined themselves to trying to calculate how many tetrahedra would fit around one corner in space, rather than considering the possibility that the great man was mistaken.
Funny how one guy could have SUCH in impact on history.