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

Abstract

The comb of honeybees has long been admired for its even hexagonal layout, but such a regular geometry is possible only if it comprises isodiametric cells arranged in a regular pattern of one surrounded by six others. The support structure of a natural nest will not provide a horizontal smooth surface and so will force irregularities, as will the merging of individual tongues of comb, introduction of accidental errors or the inclusion of larger drone cells. These perturbations force within regular comb the construction of non-equilateral or non-equiangular cells, or those that are non-hexagonal. Using automated image analysis, we extracted cell geometry from naturally built comb and that built on wax stimuli at different stages during comb construction. We show that, when faced with disruption, the bees initially build cells that are uneven and irregular, but that following further construction effort they bees reform those cells. The eventual comb exhibited increased homogeneity of cell area; cells that were more equilateral and equiangular. Overall regularity, or progressive transition of cells from one size or alignment to another arose through adjustments to each cell after the initial steps of comb construction.

Honey bees and social wasps reach convergent architectural solutions to nest-building problems

“…Pairs of 5- and 7-sided cells are known to exist in A . mellifera and are even found in graphene, an abiotic hexagonal lattice, which suggests a basic geometric reason for this pairing [ 7 , 15 , 17 , 29 , 30 ]. Here, we show that paired 5- and 7-sided cells are an architectural feature shared across all species with size dimorphism.…”

“…We would also expect them to have evolved near-optimal behaviors when presented with the challenge of transitioning between cell sizes. While non-hexagonal cells exist in the hexagonal arrays of both honey bees and social wasps [ 7 , 14 – 17 ], these irregular shapes are usually ignored in previous research because measuring them is notoriously tedious. However, it is exactly in those situations, where construction of cells requires a non-trivial trade-off between material and functionality, that we may assess their skills as builders.…”