Using potentials to model the crystallography of bee honeycomb under geometric frustration

Honeybees are known to collectively construct highly regular hexagonal structures of the honeycomb in a distributive manner, that optimizes the use of wax. When faced with various geometric constraints, such as boundaries or connecting combs with different orientations, the resulting comb is irregular, with several topological defects. In this work, we study this process using 3D-print experimental frames with imprinted foundations, which impose a precise geometric frustration. We find that the structure of the honeycomb under various frustrations show clear evidence of recurring patterns. We show that these patterns can be explained as the results of an energy minimization process through simulated annealing. We explore different potentials, ranging from interactions inspired from atomistic crystallography (e.g., Lennard-Jones) to potentials that aim to rationalize the minimization process that rules the honeybee behavior.