A honecomb is the pattern honeybees use to build their hives. It consists of waxen, hexagonal prisms, one end of which is capped in such a way that individual cells can be stacked and tesselated into a hive. Mother Nature is a mathematician at heart. Really, I should say Mother Nature is an engineer, but some things are too elegant to be left to engineers.
In nature, evolution is the mother of all design. In order to produce an ounce of beeswax, bees have to collect eight times as much pollen. Collecting pollen is a very dangerous activity, as compared to hanging around the hive. So one could speculate that bees that made effecient use of their wax had more "disposable income" to deal with contingencies, and it just so happens that the honeycomb shape is very, very close to the optimal shape, in terms of unit volume per unit area.
Math teachers (and Platonist mathematicians) point to things like the honeycomb as examples of mathematics realized in nature, descended from some higher Form. But bees, as smart as they are — and they're quite intelligent — are only acting on an instinct passed down from generation to generation. Bees start their lives as eggs, each in its own honeycomb, weaned on royal jelly until they are grown and able to serve their queen. Is it right to see beauty in a purely functional form? There is no originality in the honeycomb. There is no complexity of emotion. No bee has ever felt freedom, or love, or any of the higher emotions from which our creative spirit descends. The somber gold of the honeycomb is a fluke, determined by the bee's environment and not the bee itself. So why does it fill the mind with awe that these beasts have discovered the penultimate in architectural design?
One could say that the honeycomb is the height of bee culture: comparable to the songs of whales, the cities of ants, and the social dynamics of a wolf pack. Too easily we forget that humans aren't the only designers. The only ones blessed with the creative spirit, perhaps: but who is to say that today's design principles aren't "evolved" from the design principles of the past? The bees, with their hive mind, are linked, so that the quantum of evolution is the community and not the self.
At the risk of anthropomorphism, I say that the honeycomb is a symbol of a societial ideal we are incapable of attaining: the incorruptable utilitarian monarchy, ruled by unquestionable instinct and evolutionary designs.
Adapted from an old notebook of mine on mathematical aesthetics, written during a class on aesthetics. To paraclete, with sapphic love. | 
