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. 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". Of the fifth Platonic solid, the dodecahedron, Plato obscurely remarks, "...the god used [it] for arranging the constellations on the whole heaven". Aristotle added a fifth element, aithēr (aether in Latin, "ether" in English) and postulated that the heavens were made of this element, but he had no interest in matching it with Plato's fifth solid.
Euclid mathematically described the Platonic solids in the Elements, the last book (Book XIII) of which is devoted to their properties.
In the 16th century, the German astronomer Johannes Kepler attempted to relate the five extraterrestrial planets known at that time to the five Platonic solids. Kepler proposed a model of the Solar System in which the five solids were set inside one another and separated by a series of inscribed and circumscribed spheres. The six spheres each corresponded to one of the planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn).
In the 20th century, attempts to link Platonic solids to the physical world were expanded to the electron shell model in chemistry by Robert Moon in a theory known as the "Moon model".