Platonic solids

In Euclidean geometry, Platonic solids are regular, convex polyhedrons with congruent faces of regular polygons and the same number of faces meeting at each vertex. 

Five solids meet those criteria, and each is named after its number of faces.


Tetrahedron - 4 faces


Hexahedron (cube) - 6 faces


Octahedron - 8 faces


Dodecahedron - 12 faces


Icosahedron - 20 faces

Brief 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 are even absent. 

 Dice go back to the dawn of civilization with shapes that augured formal charting of Platonic solids.


Polyhedral dice are often used in different types of games. image: wikipedia

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.

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.