a fullerene
/ FULL-uh-reen /
Look at a classic black-and-white football (soccer ball): its surface is a patchwork of black pentagons and white hexagons stitched into a closed, round shell. Now imagine a carbon atom sitting at every corner of that pattern, and you have a fullerene — a hollow, closed cage of carbon atoms curved shut into a ball. The most famous, C60, has exactly 60 carbon atoms and looks precisely like a nanoscopic football, less than a nanometre across. It is a third form of pure carbon, alongside graphite and diamond.
The shape is not arbitrary; it obeys a rule of geometry. A flat graphene sheet is all hexagons, which tile the plane forever without curving. To close a sheet of hexagons into a ball you must introduce some pentagons, and Euler's theorem for closed shells demands exactly 12 pentagons, no more and no fewer, whatever the number of hexagons. C60 has those 12 pentagons plus 20 hexagons — a shape mathematicians call a truncated icosahedron — with every pentagon isolated, surrounded by hexagons. Larger fullerenes like C70 add more hexagons and stretch into a rugby-ball shape, still with exactly 12 pentagons.
Fullerenes were discovered in 1985 by Kroto, Curl and Smalley, who won the 1996 Nobel Prize in Chemistry for it, and they opened the whole field of carbon nanostructures — cap a rolled graphene tube with half a fullerene and you have a carbon nanotube. Structurally the family is a beautiful lesson: the same honeycomb bonding that lies flat in graphene can be forced to curve and close simply by sprinkling in pentagons. In the solid state, C60 molecules themselves stack into a face-centred-cubic crystal, each buckyball acting like a single fat atom.
Solid C60 is an orange-brown powder in which each buckyball, about 0.7 nm across, sits at the point of a face-centred-cubic lattice — held to its neighbours only by weak van der Waals forces, exactly as if the molecules were oversized inert atoms. At room temperature the balls even spin freely in place, a molecular crystal of tiny footballs.
Euler's rule forces exactly 12 pentagons to close a honeycomb into a cage: C60 is 12 pentagons + 20 hexagons.
C60 is a molecule, not a bulk lattice — the crystal is a molecular solid of C60 balls, so 'fullerene structure' means the cage, while 'fullerene crystal' means how the cages pack. The 12-pentagon rule is exact and unavoidable; the number of hexagons is what varies from one fullerene to the next.