A fullerene is a molecule of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes. Spherical fullerenes are also called buckyballs, and they resemble the balls used in football (soccer). Cylindrical ones are called carbon nanotubes or buckytubes.he smallest fullerene is the dodecahedral C 20. There are no fullerenes with 22 vertices. The number of fullerenes C 2n grows with increasing n = 12, 13, 14, ..., roughly in proportion to n 9 (sequence A007894 in OEIS). For instance, there are 1812 non-isomorphic fullerenes C 60.