Patterns in the Void - Platonic Solids in Nature

Platonic solids, or regular convex polyhedra, are named after the Greek philosopher Plato who theorized that the five classical elements (Empedocles’ wind, water, fire, and earth, with an added element for spirit) were actually comprised of regular polyhedra. They are five in number and named for the number of faces they exhibit. They are the tetrahedron, the hexahedron, the octahedron, the dodecahedron, and the icosahedron. Platonic solids have been the metaphysical and aesthetic inspiration of geometers for thousands of years. 

Plato wrote about these polyhedra in the dialogue Timaeus c.360 B.C. in which he associated each of the four classical elements 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 un-spherical 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 solidity of the Earth was believed to be due to the fact that the cube is the only regular solid that tesselates Euclidean space. The fifth Platonic solid, the dodecahedron, Plato obscurely remarks, “…the god used for arranging the constellations on the whole heaven”. Aristotle added a fifth element, aithêr (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.

Platonic solids occur frequently in nature. Their forms are the complex crystalizations of minerals and appear as the skeletal remains of several species of amoebic sea creatures in the Radiolarian phylum. These creatures were beautifully illustrated by the Victorian-era biologist Ernst Haeckel in his Kunstformen der Nature.

Platonic Solids can be found in atoms in crystals, it commonly occurs in organic and inorganic chemistry, viruses and radiolarian skeletons.

These platonic solids have been found living in the sea.