Honeycomb formation under geometric frustration

The wax–made comb of the honeybee is a masterpiece of animal architecture. As honeybees build their nests in pre-existing tree cavities, they grew accustomed to dealing with the presence of geometric constrains, resulting in non-regular hexagons and topological defects. In this work, we study how bees collectively adapt their environment to regulate and heal the honeycomb structure. Specifically, we identify the irregularities in honeycomb structure in the presence of various types of geometric frustrations. We 3D-print our experimental frames with imprinted foundations. The resulting constructed comb show clear evidence of reoccurring, self-organized patterns built by the bees in response to specific geometric frustrations in the starter frames. Our computational model can recreate and predict these self-organized patterns which can effectively solve various geometrical miss-match problems while optimizing the cost for comb building. Understanding how bees adapt the topology and geometry of the lattice to conform to different constrains will lead to a set of rules to systematically generate biologically inspired designs in the fields of swarm robotics, collective construction, and lightweight cellular structures.