The 'third form' of carbon after diamond and graphite. It forms spherical shells exactly like footballs (Am: soccer:), technically a truncated icosahedron. This, in fact, is the only way in which hexagons can form spheres - in concert with pentagons.
It was discovered by Harry Kroto et al in 1985 (although forseen by Daedalus of New Scientist in 1966! And Japanese and Soviet reports existed before 1980). Although described as 'a solution looking for a problem' for a while, it now has some tentative applications as high temperature superconductors, drugs, or as part of a molecular abacus. It is even possible to encapsulate metal ions inside (so called 'endohedral' complexes).
Its relatives, fullerenes - like carbon tubes or other macrocyclics are also starting to find uses, other than being beautiful...
See: "C60: Buckminsterfullerene" H.W. Kroto, J.R. Heath S.C. O'Brien,R.F Curl and R.E Smalley Nature 318 162(1985)
see also misspelt softlink below.