Icosahedrons and the Platonic Solids

As some of you might have seen in class, Natassia and I have been working on constructing an origami icosahedron (it is a regular polygon with 20 identical equilateral triangular faces, 12 vertices, and 30 edges, for those of you who were wondering).

Now that it is finished, I started doing some research on icosahedrons. I found out that it is one of the five Platonic solids. A Platonic solid is a convex polyhedron, where the same number of congruent, regular polygon faces meet at each vertex. Only five of these polyhedrons exist: 

They were admired for their aesthetic beauty and symmetry, and were extensively studied by the ancient Greeks. The philosopher Plato theorized that each regular polygon was associated with one of the classical elements-- the tetrahedron with fire, the icosahedron with water, the octahedron with air, and the cube with earth (the dodecahedron represented the universe itself). Euclid called these solids the atoms of the Universe. Basically, they believed that all physical matter was composed of the atoms of the Platonic solids.

What I found really fascinating in my research was discovering where these Platonic solids could be found in nature. The tetrahedron, cube, and octahedron all occur in crystal structures. For example, here's a Franklinite octahedral crystal:

In addition, many viruses, such as herpes, have icosahedral shells. The viral structure is made from identical protein subunits, and it is easiest to assemble them as an icosahedron. 

Pretty cool, huh?