This model illustrates a simple way of building a buckyball. A sphere and a couple of linking bars are rotated around a point to form a pentagon. Two pentagons are joined together and the assembly is duplicated six times with these constructs being translated and rotated into position.
Notice that it is easy to replace the sphere definition of the Atom by any other shape. Replace it with a face and you get 60 faces in space.
A buckyball is a football shaped carbon 60 mollecule. The name is really Buckminster-Fullerene.