On the Classification of 3D Periodic Polyhedral Cellular Systems
In several fields of materials science space-filling polyhedral systems are generally used for modeling and characterizing the microstructure of polycrystalline and cellular materials. In this paper a simple quantitative method designated to classify 3D triply periodic, space-filling, cellular systems is outlined. The concept of the proposed method is based on the known analogy between the combinatorial structure of 3D space-filling polyhedral systems and of 4D polytopes. For classification purposes various topological shape indices are defined and tested. It is demonstrated that using two appropriately selected shape factors (asymmetry and compactness coefficients) a global combinatorial classification of cellular systems can be performed.
P.J. Szabó, T. Réti, T. Czigány
T. Réti and E. Bitay, "On the Classification of 3D Periodic Polyhedral Cellular Systems", Materials Science Forum, Vol. 589, pp. 341-348, 2008