Generalized ω -transformation of fullerenes and related structures

We present a generalization of the ω-transformation that we previously proposed for modifying fullerene cages. It is applicable not only to fullerenes but also to any other molecules whose structures correspond to cubic polyhedral graphs. The relationship between the generalized ω-transformation and Fedorov’s operations for generating simple polyhedra is considered. The efficiency of the proposed approach is demonstrated on all cubic polyhedral graphs and all fullerenes containing tetragons. By means of the generalized ω-transformation, each of these families can be combined into a single interconversion map.