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.