Hales, with his “ The Honeycomb Conjecture.” Bees figured it out long ago, and it’s a good thing, too: beeswax, because it is hard for bees to produce, is precious. For millennia, scientists assumed that it was the most efficient way to fill a plane, but it took until 1999 for someone to prove it: Thomas C. Tessellation ensures that there’s neither wasted space nor wasted energy. Hexagons, which are themselves composed of tessellated triangles, do. Triangles and squares tessellate circles and pentagons do not. Some shapes tessellate, meaning they can be repeated across a surface without leaving gaps or overlapping. Hexagons appear in honeycombs because they’re the most efficient way to fill a space with the least amount of material. Hexagons are the shape closest to a perfect circle that can be placed in a series next to eachother without leaving spaces. Their hives are wondrous constructions, and their hexagonal nature is part brilliance and part accident. But beyond that, they themselves are encoded with the shape: the hexagon is written into their eyes.

Bees worldwide are extraordinarily adept at constructing uniform hexagons. But the most obvious natural hexagon is the honeycomb, the geometrically perfect home for bees and their honey.

Hexagon nature's perfect shape