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Fullerenes, or Buckyballs, are molecules composed entirely of carbon, taking the form of a hollow sphere, ellipsoid, tube or ring. Fullerenes are similar in structure to graphite, which is composed of a sheet of linked hexagonal rings, but they contain pentagonal (or sometimes heptagonal) rings that prevent the sheet from being planar. The smallest fullerene in which no two pentagons share an edge (which is destabilizing - see pentalene) is C60, and as such it is also the most common. It is called Buckminsterfullerene in honor of Buckminster Fuller, a noted architect who created the geodesic dome. For a clear picture of the structure of C60, just take a soccer ball and picture a carbon atom at the corner of each hexagon, and a bond along each edge.

Other atoms can be trapped inside fullerenes, and indeed recently evidence for the meteor impact at the end of the Permian was found in analyzing noble gases so preserved. Another neat thing is that fullerenes may be drawn out to form cylinders, called buckytubes or nanotubes.

Until the late twentieth century, graphite and diamond were the only known allotropes of carbon. Then, in molecular beam experiments, discrete peaks were observed corresponding to molecules with the exact mass of 60, 70, or greater numbers of carbon atoms. Harold Kroto, Robert Curl and Richard Smalley were awarded the Nobel Prize for their roles in the discovery of this class of compounds. Buckyball and other fullerenes and fullerene compounds were later noticed occuring outside of a laboratory environment. As of the early twenty-first century, the chemical and physical properties of fullerenes are still under heavy study, in both pure and applied research labs.

Superconductivity is one of the more recently explored properties.