How are carbon nanotubes related to spherical fullerene molecules?

Carbon nanotubes are considered members of the fullerene family, which consists of hollow carbon molecules that form either closed cages, known as "buckyballs," or cylinders, known as nanotubes.12

The relationship between these structures is defined by their geometry and composition:

• Structural Connection: Carbon nanotubes are essentially elongated fullerenes. While a buckyball is a hollow sphere composed of carbon atoms, a single-walled carbon nanotube can be described as a graphene sheet rolled into a cylinder.312
• Capping: The ends of carbon nanotubes are generally capped by fullerene domes, which include pentagonal rings necessary to close the tubular structure.32
• Shared Origins: Both forms are composed of carbon atoms arranged in hexagonal rings. The discovery of nanotubes occurred while investigating materials produced under conditions similar to those used for forming C60 (buckyballs).3
• Functional Integration: Because of their structural compatibility, nanotubes can be "decapped" and filled with other materials, including buckyballs themselves.3

While both are allotropes of carbon, their distinct shapes—spherical versus cylindrical—result in different mechanical and electronic properties, with nanotubes exhibiting unique one-dimensional characteristics.12