- Plato believed that atoms have the shapes of regular polyhedra: cubes, tetrahedrons, octahedrons, and so on.
- He submitted his first paper on this topic then, encouraged by Legendre and Malus, he submitted a further paper on polygons and polyhedra in 1812.
- Kepler connected the planetary orbits with the five regular polyhedra, or Platonic solids.
- For example, fair dice don't have to be in the shape of regular polyhedra, such as cubes, icosahedra, and so on.
- The icosahedron is one of only five regular convex polyhedrons, the symmetric ‘Platonic solids’ that fascinated the ancient Greeks (the cube is another).