  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 is a
natural number depending on the considered nanotube. We obtain an alternate
rather different description by starting from a description of the honeycomb
lattice in terms of Miller indices. 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.
