Why is fullerene considered a third well-defined form of pure carbon?

Fullerene is considered a third well-defined allotrope of carbon because it possesses a distinct molecular structure compared to the two previously known forms: diamond and graphite.1

While diamond consists of an infinite three-dimensional crystalline array and graphite is composed of stacked two-dimensional hexagonal sheets, fullerenes are hollow, closed-cage molecules (often called "buckyballs") or cylinders (carbon "nanotubes"). Specifically, the most well-known fullerene, $C_{60}$, is a spherical molecule composed of 60 carbon atoms arranged in 12 pentagonal and 20 hexagonal faces, resembling a soccer ball.12

The discovery of fullerenes in 1985 revealed that carbon could form these unique, discrete molecular structures, bridging the gap between traditional crystalline solids and complex systems at the atomic scale. This discovery expanded the understanding of carbon chemistry and established fullerenes as a structurally unique third form of the element.13