The topological analysis of 2D cellular patterns composed of polygons with various sides has been performed in order to generate new topological invariants by which topologically different finite cellular systems can be numerically characterized and compared. The proposed novel approach is based on the analysis of the correspondences between the topological properties of individual cells and their first order neighbors (i.e. cell coronas). It is shown that from the edge and vertex-coronas of cells, various local and global parameters can be derived, which can be used for the topological comparison and classification of cellular structures. It is demonstrated in an example that the proposed method is an efficient tool for the topological evaluation of fullerene solids.