Regular geometry and hexagonal structure of honeycomb results from the optimisation of cylindrical cells built in close proximity

Abstract

The hexagonal structure of honeycomb maximises storage volume while minimising the amount of wax required for its construction. How honeybee builders achieve this geometry, however, remains unclear. Previously, our group identified behavioural patterns that were triggered in builders when they encountered certain sub-scale features associated with partially constructed comb, which resulted in the alignment of new cells to small concavities and the construction of cell walls between two of these stimuli. This caused new cells to be built in the proper locations without the need for explicit instructions . Here, we investigated whether the hexagonal geometry of honeycomb cells resulted from the dense packing of cells that would otherwise have been circular tubes. We hypothesised that the reaction of a builder to a cell that is not fully enclosed by other cells would be an attempt to maximise the internal space by excavating and re-forming the surrounding walls to create a cylindrical interior. However, the creation of a cylindrical cell would be thwarted by the activities of workers within adjacent cells also acting according to these rules. Eventually an equilibrium will emerge with walls that meet at a junction arranged so that the available angular range (360{degrees}) is sub- divided equally between the cells that meet at the junction (typically, internal angles of 120{degrees} when three cells meet). To test this hypothesis, we offered wax stimuli to comb-building honeybees, shaped to encourage or to constrain the construction of comb cells, recording the bees progress. We found that at an early stage cells could be an irregular shape with curved walls and unequal wall lengths and corner angles, however, when allowed further time and unconstrained access the workers reshaped the cells achieving significantly greater regularity.