Buckminster Fullerene is a new(ish) carbon structure. Unlike diamond, which is a rigid 3D tetrahedral lattice, or graphite, which is planes of hexagons, Bucky Balls are truncated icosahedra.
There's loads about Bucky Balls on the web, but here's a good page:
Scott Kellog loves bucky balls and the buckytubes built from them; his Internet comic 21st Century Fox is full of that stuff. Check it out at: