  The positions of atoms forming a carbon nanotube are usually described by
using a system of generators of the symmetry group. Each atomic position
corresponds to an element of the set Z x {0,1,...,n} x {0,1}, where n depends
on the considered nanotube. We obtain an alternate rather different description
by starting from a three-axes description of the honeycomb lattice. In our
mathematical model, which is a factor space defined by an equivalence relation
in the set {(v_0,v_1,v_2)\in Z^3 | v_0+v_1+v_2\in {0,1}}, the neighbours of an
atomic position can be described in a simpler way, and the mathematical objects
with geometric or physical significance have a simpler and more symmetric form.
We present some results concerning the linear representations of single-wall
carbon nanotubes in order to illustrate the proposed approach.
