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Dual Space Approach to the Classification of Toroidal Carbon Nanotubes

We apply the dual space approach to the classification of toroidal carbon nanotubes. We show that the realizations of most of the geometric manipulations described in the literature become explicit in the dual space of the original molecular graph. In particular, dual graph can be easily constructed on a rectangular strip in the parametric plane of the torus. Generalization to other forms of graphitic cages with different topologies can also be done. Manifested chirality and the criteria for the existence of highly symmetric isomers are discussed.