Iijima et al. then reported Transmission Electron Microscopy (TEM) observations of hollow graphitic tubes, nanotubes, and the large-scale nanotube synthesis by Ebbesen and Ajayan has seen an explosive research effort into these unusual graphitic forms.

TEM observations of graphitic tubes synthesised using pyrolytic methods, (e.g. pyrolysis of acetylene over cobalt) and their derivatives have revealed fullerene geometries with closed cage arrangements, and also other "oddly" shaped fullerene structures such as "bucky-onions".

It is generally recognised that C₆₀, which consists of pentagons and hexagons formed with carbon atoms, the pentagons play an essential role in creating the convex plane. By wrapping a cylinder in a sheet of graphite we get nanotubes, and in a study of the growth of nanotubes, Iijima found that heptagons of carbon atoms appear in the negatively curved surface. The positive curvature is achieved by inserting pentagons into the graphite sheet. This can be visualised below, where the pentagonal carbons are shown in red and the heptagonal carbons are shown in yellow. Structures incorporating pentagons, hexagons and heptagons include torroidal and helical forms.

Theoretical studies have shown that many of the new graphitic arrangements are very stable, in some cases more that C₆₀ itself, and related structures appear naturally in certain graphitic materials. One derivative, helical in structure, is analagous to that seen in crystal growth affected by screw disslocations.

It is felt that nanotubes may act as precursors to closed shell fullerene formation and the recent advances in the fundamental understanding of carbon structures heralds a new age in nanoscale materials engineering. These novel structures have interesting geometrical properties and may lead to compounds with new magnetic and electrical properties. Other materials (e.g. tungsten disulphide, molybdenum disulphide and boron nitride) also show similar properties in that they can also form nanotube and polyhedral structures.