Crystallography of honeycomb formation under geometric frustration

The wax-made comb of honeybees is a masterpiece of animal distributed construction. As bees build their nests in preexisting tree cavities, they grow accustomed to dealing with geometric constraints, resulting in nonregular hexagons and topological defects. We study how bees collectively adapt to their environment by 3D-printing experimental frames with a variety of constraints imposed on the imprinted foundations. The combs constructed by the bees show clear evidence of recurring patterns and can be modeled and replicated through a computational model of crystallographic lattice formation. Our model reproduces global irregularities in the honeycomb structure using local rules and information. It also extends the application of the Lennard-Jones model beyond the physical domain to encompass biological systems, thereby demonstrating its universality.