Honeybees are pretty talented, but they didn't come up with the hexagonal design of the honeycomb. That's just physics. What bees do is build cells in a cylindrical shape and stack them together. The wax then just naturally formed a hexagon.
A regular geometric array of identical cells with simple polygonal cross sections can take only one of three forms: triangular, square or hexagonal. Of these, hexagons divide up the space using the smallest wall area, and thus, for a honeycomb, the least wax.
This economy was noted in the fourth century ad by the mathematician Pappus of Alexandria, who contended that the bees had “a certain geometrical forethought”. But in the seventeenth century, the Danish mathematician Erasmus Bartholin suggested that the insects need no such forethought. He said that hexagons would result automatically from the pressure of each bee trying to make its cell as large as possible, much as the pressure of bubbles packed in a single layer creates a hexagonal foam.
Engineer Bhushan Karihaloo of the University of Cardiff managed to catch honeybees in the act of cell building wax cells. The newest cells were circular, and as they got older, they settled into hexagons, aided by the slight warmth of the worker bees bodies. Read more about how that happens at Nature. Link -via Not Exactly Rocket Science
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