“By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, cube—Kepler found that the spheres could be placed at intervals corresponding (within the accuracy limits of available astronomical observations) to the relative sizes of each planet’s path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet’s orb to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula, because it was not precise enough.”–Via

Platonic solids, as ideas and concepts, have been with us ever since Plato decided to tell an origin story of the universe. Plato’s universe originated with a master craftsman, a demiurge, that created the essential elements that make up reality, ourselves included:

“[T]he Craftsman begins by fashioning each of the four kinds “to be as perfect and excellent as possible…” (53b5–6). He selects as the basic corpuscles (sômata, “bodies”) four of the five regular solids: the tetrahedron for fire, the octahedron for air, the icosahedron for water, and the cube for earth.”–Via Stanford Encyclopaedia of Philosophy

These polyhedra are everywhere. If you’re aware of crystals and how they form in nature, you’ve come across platonic solids. Also, with just a few minutes of proper web research, you’ll find that many microscopic organisms, including many species of algae, may have one of the following shapes (Captions are linked to examples of platonic solids):

“Since silicon is the most common semiconductor used in solid-state electronics, and silicon has a valence of four, the tetrahedral shape of the four chemical bonds in silicon is a strong influence on how crystals of silicon form and what shapes they assume.”–Tetrahedrons in electronics (Wikipedia)

“[A] completely symmetrical structure can always keep the walking capability when any of its six faces of the hexahedron touches the ground.”–Application in robotics, via.

Octahedral Pyrite

“A scanning electron microscope (SEM) image of quasicrystalline aluminum-copper-iron showing the dodecahedral shape of the grain.”—Via.

Nowadays, we all know that there are many more elements that make up the physical world; nevertheless, 2000 years after Plato’s Timaeus–the text that the previous quote was taken from–, these figures have been observed outside Plato’s mind. Take the example of the carbon allotrope known as a fullerene:

An isochaedron shaped fullerene.

Made out of 540 carbons, this allotrope–or “alternative form”, diamonds are ‘allotropes’ of  carbon–has the shape of an isochaedron, our last platonic solid. These molecules have many useful applications, including nanotechnology and biomedical research.

Viruses, biological entities that blur the line between living and nonliving, also exhibit isochaedral shapes. The outer protein shell of many viruses–including HIV and herpes–are regular polyhedrons. And, in many cases, these polyhedrons are isochaedrons:

“Schematic diagram (left) and cryoreconstruction (right) of the ssRNA insect virus FHV (family Nodaviridae). The capsid of FHV consists of 180 copies of a single subunit arranged with T=3 icosahedral symmetry.”

Many more instances of platonic polyhedrals can be found in nature. I encourage you to do some research. For more information on platonic solids, you should check out the following link: Some Solid (Three-dimensional) Geometrical Facts about the Golden Section.

The following video summarizes a lot of the information presented here: