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Cluj and Omega polynomials were designed to describe the graphs associated to polyhedral nanostructures: their exponents express the extent of partitions of a graph property while the coefficients count the partitions of a given extent. Basic definitions and properties of these and some other related counting polynomials are given, as derived from the cutting procedure of their calculation. Formulas to calculate these polynomials in T(4,4)R[c,n] tori are given and exemplified.

Keywords: Cluj polynomial, Omega polynomial, nanotori