The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues^{1}, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays^{2}. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of *in vivo* analysis of mitotic cell junction dynamics in *Drosophila* imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.