Honeybee comb geometry emerges from local redistribution of angular space by worker construction activity

Honeybee comb is unique among animal architectures in its strikingly regular hexagonal cells, yet how this geometry emerges remains debated. Do bees construct perfect hexagons from the outset, or does regularity arise through later adjustments? We examined comb-building dynamics by presenting honeybees (Apis mellifera) with wax stimuli that constrained cell placement and angular space. Across three experiments, we tested predictions about how bees distribute the available angular range at cell junctions, shape cell bases, and correct irregularities over time. Initially, cells were uneven, with curved walls and variable angles. When the angular space was restricted to 180°, bees built cells with 90° internal angles; as construction progressed and barriers eroded, angles shifted toward 120°, equalizing the 360° range among three adjoining cells. Similarly, opposed cells formed flat bases orthogonal to side walls (≈90°), contrasting with the pyramidal bases of natural comb. When separate tongues of comb merged, cells at junctions were highly irregular, but subsequent work significantly reduced disparities in wall angles and cell size. These findings reveal that honeycomb cell geometry emerges through a self-organizing process: bees iteratively redistribute space and adjust cell boundaries until equilibrium is achieved. This dynamic optimization explains the iconic hexagonal pattern without invoking complex cognitive strategies.