Buckyballs, also called fullerenes, were one of the first nanoparticles discovered. This discovery happened in 1985 by a trio of researchers working out of Rice University named Richard Smalley, Harry Kroto, and Robert Curl.
Buckyballs are composed of carbon atoms linked to three other carbon atoms by covalent bonds. However, the carbon atoms are connected in the same pattern of hexagons and pentagons you find on a soccer ball, giving a buckyball the spherical structure.
The shape defined by Bucky balls is also found in the Carbon 60 molecule, a form of pure carbon with 60 atoms in a nearly spherical configuration, the truncated icosahedron and soccer balls.
Bucky balls consist of 60 points on the surface of a spherical shape where the distance from any point to its nearest neighboring three points on the sphere is identical for all points.