摘要： Spongy structures are hollow-containing materials, encountered in natural or synthesized zeolites, spongy carbon, etc. The design and topological study of some hypothetical spongy nanostructures is presented in terms of map operations and genus calculation of their associated graphs, respectively. Among the discussed structures one remarks some novel spongy polyhedra that can evolve with 1-periodicity or radially, to provide multi-shell cages. Filling the space inside such complex nanostructures can be achieved by small fullerenes that self-arrange in aggregates with a well-defined geometry, of which energy trends to a minimal value. The way of space filling varies function of the dimension and shape of composing small fullerenes. An attempt of building and stability evaluating of several fullerene aggregates was made. The calculations were made at the HF, DFT and DFTB level of theory. The design of nanostructures was performed by our original software packages CVNET and Nano Studio.