A mathematical model for TUC4C8(S)TUC4C8(S) nanotubes and their symmetry groups

A C4C8C4C8 net is a trivalent decoration made by alternating squares C4C4 and octagons C8C8. It can cover either a cylinder or a torus. Such a covering can be derived from a square net by the leapfrog operation. In this paper we obtain a mathematical model for the lattice of the TUC4C8(S)TUC4C8(S) nanotube. Using this model, we compute the symmetry group of the lattice and nanotube.