Like all closed geodesic structures, it has the 12 pentagons that are required to transform a network into a spheroid, as demonstrated by the 18th-century Swiss mathematician Leonhard Euler. The remaining carbon atoms are configured as 20 hexagons to form the molecule's soccerball shape. As hexagons are added or removed, the molecule begins to loose its roundness. C70, which has 25 hexagons, is shaped more like a rugby ball. Giant fullerenes take on a pentagonal shape.
Smaller fullerenes look like asteroids.
With the loss of roundness comes a loss of stability. The versatility of fullerenes stems in part from the belief that they also can be doped either by attaching atoms to the outer bonds of the ball or by inserting one or more atoms inside the cage. To learn more about the properties of fullerenes and how they can best be used, scientists eventually have to produce the materials in a crystalline form large enough for electronic transport and mechanical measurements. Zettl is used to being at the forefront of making exotic materials. Together, Zettl and his group have been able to successfully synthesize and characterize the highest quality of sizable single crystals of both pure and doped buckyballs.