Symmetry groups of single-wall nanotubes
This work investigates the symmetry properties of single-wall carbon nanotubes and their structural analogs, which are nanotubes consisting of different kinds of atoms. The symmetry group of a nanotube is studied by looking at symmetries and color fixing symmetries associated with a coloring of the tiling by hexagons in the Euclidean plane which, when rolled, gives rise to a geometric model of the nanotube. The approach is also applied to nanotubes with non-hexagonal symmetry arising from other isogonal tilings of the plane.
De Las Peñas, M. L. A. N., Loyola, M. L., Basilio, A. M., & Santoso, E. B. (2014). Symmetry groups of single-wall nanotubes. Acta Crystallographica Section A: Foundations and Advances, 70(1), 12-23.