Link between hexagonal honeycomb structures and hexagonal patterns in bees’ eyes

Determine whether a link exists between the hexagonal pattern used by bees in constructing honeycombs and the hexagonal pattern observed in bees’ eyes.

Background

In discussing the ubiquity of hexagonal patterns in nature, the paper notes that bees build honeycombs with hexagonal cells, a choice often associated with material efficiency, and also that hexagons appear in the structure of bees’ eyes.

The author explicitly identifies an unresolved question in biology regarding whether these two occurrences of hexagonal patterning are related, without proposing a mechanism or hypothesis, leaving the relationship—if any—open.

References

Yes, when bees make their honeycombs (Fig. 1) using hexagonal patterns, they are trying to minimize the amount of wax they need. Fascinating, is not it? And more fascinating indeed is that hexagons are also found on bees' eyes. Actually, an open question in biology is to understand whether there is a link between the two phenomena or not.

— Mathematics in art, for art and as art  (2503.03541 - Esteban, 5 Mar 2025) in Introduction