Platonic solid

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, and each is named after its number of faces.

Geometers have studied the mathematical beauty and symmetry of the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato who theorized in his dialogue, the Timaeus, that the classical elements were made of these regular solids.

History

The Platonic solids have been known since antiquity. Carved stone balls created by the late Neolithic people of Scotland lie near ornamented models resembling them, but the Platonic solids do not appear to have been preferred over less-symmetrical objects, and some of the Platonic solids may even be absent. Dice go back to the dawn of civilization with shapes that predated formal charting of Platonic solids.

The ancient Greeks studied the Platonic solids extensively. Some sources (such as Proclus) credit Pythagoras with their discovery. Other evidence suggests that he may have only been familiar with the tetrahedron, cube, and dodecahedron and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. In any case, Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that no other convex regular polyhedra exist.