Symmetry groups of single-wall nanotubes

An approach to the determination of the symmetry groups of structural analogs of single-wall carbon nanotubes using ideas in color symmetry theory is described. The line group structures of the symmetry groups of BN, BC₃, BCN and BC₂N nanotubes are identified. An extension of the method to address nanotubes with non-hexagonal symmetry is also presented.