The history of regular polyhedrons in Art and Science.

The Greeks, while searching for a perfect order in the multiplicity of reality, elaborated a theory of regular bodies as the prime constituents of nature. Abstract speculation in a continuous cultural tradition of geometry and aesthetic invention led to the development of innumerable variations.

The Egyptian geometrists of the sixth century B.C had already dealt with the tetrahedron , the cube and the octahedron, but it was almost certainly Pythagoras who completed the class with the discovery of the Icosahedron and the Dodecahedron (Vl century B.C.).

Timeo of Locri proposed a correspondence between the four elements and the four simplest regular polyhedrons. That correspondence was taken up by Plato (428-327 B.C.) , who attributed a transcendental value to the fifth element , the dodecahedron . According to Plato, God used the Dodecahedron to shape the universe in a whole and animated fashion. Regular solids are defined as "Platonic bodies" because it was Plato who , for the first time , gave a detailed description of them in the Timaeus. Proclus (410-485 B.C. ) the leader of the Athenian school, demonstrated that Plato wrote a book specially, which has since been lost, about the five regular polyhedrons.

It seems that the first person to write about the five regular solids was Teeteto of Heraclea, a disciple of Socrates (LV century B.C.). Euclid used it extensively for his last book Elements, reordering what his predecessors had said.