Polygons and PolyhedraPolyhedra Applications

Many viruses, bacteria and other small organisms are shaped like icosahedra. Viruses, for example, must enclose their genetic material inside a shell of many identical protein units. The icosahedron is the most efficient way to do this, because it consists of a few regular elements but is almost shaped like a sphere.

Many molecules are shaped like regular polyhedra. The most famous example is C60 which consists of 60 carbon atoms arranged in the shape of a Truncated Icosahedron.

It was discovered in 1985 when scientists researched interstellar dust. They named it “Buckyball” (or Buckminsterfullerene) after the architect Buckminster Fuller, famous for constructing similar-looking buildings.

Most crystals have their atoms arranged in a regular grid consisting of tetrahedra, cubes or octahedra. When they crack or shatter, you can see these shapes on a larger scale.

Tetrahedra and octahedra are incredibly rigid and stable, which makes them very useful in construction. Space frames are polygonal structures that can support large roofs and heavy bridges.

Platonic solids are also used to create dice. because of their symmetry, every side has the probability of landing facing up – so the dice are fair.

The Truncated Icosahedron is probably the most famous polyhedron in the world: it is the shape of the football.