# Platonic Solids Art

The Platonic solids are prominent in the philosophy of Plato, their namesake. Plato wrote about them in the dialogue Timaeus c. 360 B. C. in which he associated each of the four classical elements (earth, air, water, and fire) with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. There was intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). Air is made of the octahedron; its minuscule components are so smooth that one can barely feel it. Water, the icosahedron, flows out of one's hand when picked up, as if it is made of tiny little balls. By contrast, a highly nonspherical solid, the hexahedron (cube) represents "earth". These clumsy little solids cause dirt to crumble and break when picked up in stark difference to the smooth flow of water. Moreover, the cube's being the only regular solid that tessellates Euclidean space was believed to cause the solidity of the Earth.

In our last unit we studied some polygons, and I said that one of these, the triangle, was thought by Plato to be the building block of the universe. He presented that idea and others about creation, such as the universe being created to resemble a geometric progression, in one of his books, the Timaeus .

In three-dimensional space , a Platonic solid is a regular , convex polyhedron . It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex. Five solids meet those criteria:

PLATONIC SOLIDS In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are five Platonic solids; their names are derived from their numbers of faces.

The so-called Platonic Solids are regular polyhedra. “Polyhedra” is a Greek word meaning “many faces.” There are five of these, and they are characterized by the fact that each face is a regular polygon , that is, a straight-sided figure with equal sides and equal angles: