Buckyball is a member of a class of carbon structures called fullerenes. Fullerenes are an allotrope (solid structure) of the element carbon - the best known being diamond and graphite. Fullerenes can be hollow spheres like buckyball, ellipsoid, or tubes (buckytubes). 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 structure of C60 - buckminsterfullerene - is that of a truncated icosahedron, which resembles a round soccer ball of the type made of hexagons and pentagons, with a carbon atom at the corners of each hexagon and a bond along each edge. The molecule was named for Richard Buckminster Fuller, a noted architect who popularized the geodesic dome.

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