Fullerene molecule. Illustration of a spherical fullerene molecule. Fullerenes are a structural type (allotrope) of carbon. The molecular model here shows the arrangement of the carbon atoms in rings of hexagons. The spherical fullerenes are sometimes referred to as buckyballs, after the first such molecule to be discovered (C60, buckminsterfullerene). They are being investigated for their physical and chemical properties, and for medical applications.