Matrix description of the complete topology of three-dimensional cells

A new, efficient method based on a series of matrices is introduced to completely describe the detailed topology of individual domains and their topology evolution in three-dimensional cellular structures. With this approach, we found a lot of new topological grain forms which are never reported before, i.e., there are total 8 and 32 topological forms for 7- and 8-faced grains respectively, other than the reported 7 and 27. This method is proved to be a practical tool to predict all possible grain forms efficiently. Moreover, a connectivity index of grain forms serves as a new convenient differentiator of different multicellular structures.