Carbon nanotubes  are tubes made of carbon with diameters typically measured in nanometers.Carbon nanotubes often refer to single-wall carbon nanotubes with diameters in the range of a nanometer. They were discovered independently by Iijima and Ichihashi  and Bethune et al. in carbon arc chambers similar to those used to produce fullerenes. Single-wall carbon nanotubes are one of the allotropes of carbon, intermediate between fullerene cages and flat graphene.Although not made this way, single-wall carbon nanotubes can be thought of as cutouts from a two-dimensional hexagonal lattice of carbon atoms rolled up along one of the Bravais lattice vectors of the hexagonal lattice to form a hollow cylinder. In this construction, periodic boundary conditions are imposed over the length of this roll up vector to yield a lattice with helical symmetry of seamlessly bonded carbon atoms on the cylinder surface.Carbon nanotubes also often refer to multi-wall carbon nanotubes consisting of nested single-wall carbon nanotubes.If not identical, these tubes are very similar to Oberlin, Endo and Koyama's long straight and parallel carbon layers cylindrically rolled around a hollow tube. Multi-wall carbon nanotubes are also sometimes used to refer to double- and triple-wall carbon nanotubes.