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It is difficult to identify a G-C fullerene directly from its dimensions asits lattice is not proportional to that of its archetype in general, althoughthey have the same three-dimensional shape. In this paper, the area scalefactor of a G-C fullerene is proved to be an integer, which can be calculatedfrom its dimensions. All the G-C transformations are k-inflations that can beeasily identified and inversed, primary transformations whose area scalefactors are prime numbers, or composite transformations whose area scalefactors are the product of those of its sub-transformations. As the result, amethod to identify any G-C fullerenes according to the area scale factor waspresented.

Transformation, Identification, and Inversion of Goldberg-Coxeter Fullerenes