Degenerate polygonal tilings in simple animal tissues

We study 2D polygonal tilings as models of the en-face structure of single-layer biological tissues. Using numerical simulations, we explore the phase diagram of equilibrium tilings of equal-area, equal-perimeter convex polygons whose energy is independent of their shape. We identify 3 distinct phases, which are all observed in simple epithelial tissues: The disordered phase of polygons with 4-9 sides, the hexatic phase, and the hexagonal phase with perfect 6-fold coordination. We quantify their structure using Edwards' statistical mechanics of cellular systems.