Honeycomb crystallography: comb formation under geometric frustrations

1As honeybees build their nests in pre-existing tree cavities, they must deal with dealing with the presence of geometric constraints, resulting in non-regular hexagons and topological defects in the comb. In this work, we study how bees adapt to their environment in order to regulate the comb structure. Specifically, we identify the irregularities in honeycomb structure in the presence of various geometric frustrations. We 3D-print experimental frames with a variety of constraints imposed on the imprinted foundations. The combs constructed by the bees show clear evidence of reoccurring patterns built by bees in response to specific geometric frustrations on these starter frames. Furthermore, using an experimental-modeling framework, we demonstrate that these patterns can be successfully modeled and replicated through a simulated annealing process, in which the minimized potential is a variation of the Lennard-Jones potential that only considers first-neighbor interactions according to a Delaunay triangulation. Our simulation results not only confirm the connection between honeycomb structures and other crystal systems such as graphene, but also show that irregularities in the honeycomb structure can be explained as the result of local interactions between honeybees and their immediate surroundings, leading to emergent global order. Additionally, our computational model can be used to describe specific strategies that bees use to effectively solve each geometric mismatch problem while minimizing cost of comb building.