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):
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:
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:
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.