In order to simulate the polyhedral grain nucleation in alloys, 3-D cell population growth
processes are studied in space-filling periodic cellular systems. We discussed two different methods
by which space-filling polyhedral cellular systems can be constructed by topological
transformations performed on “stable” 3-D cellular systems. It has been demonstrated that an
infinite sequence of stable periodic space-filling polyhedral systems can be generated by means of a
simple recursion procedure based on a vertex based tetrahedron insertion. On the basis of computed
results it is conjectured that in a 3-D periodic, topologically stable cellular system the minimum
value of the average face number 〈f〉 of polyhedral cells is larger than eight (i.e. 〈f〉 > 8). The
outlined algorithms (which are based on cell decomposition and/or cell nucleation) provide a new
perspective to simulate grain population growth processes in materials with polyhedral
microstructure.
