Pack the Comb

A honeycomb is built out of six-sided cells, and it is worth asking why. Bees are not geometers. Nobody in the hive picked the hexagon because it looked strong or clever. It is the shape that is left over once you ask for two ordinary things at the same time.

The first is no wasted space. Push round cells together as tightly as they will go and they still cannot touch all the way around — there is a little curved hole between every three of them. Add those holes up across a whole comb and a surprising amount of room has gone nowhere. Six-sided cells have no holes at all: each one sits flush against its neighbours the whole way round.

The second is no wasted wall. Every wall costs the hive wax, and wax is expensive — a bee eats a lot of honey to make a little of it. Two cells side by side share the wall between them, so the shapes that share the most wall are the cheapest. Line up cells of exactly the same size and count the walls: triangles need the most, squares need fewer, and hexagons need the fewest of all. It is not a big saving on one cell. It is an enormous saving on fifty thousand.

The surprising part is the third thing, and it is the reason the hexagon is not really a choice. Pack equal circles as tightly as they will go, with each row sitting in the dips of the row below, and then let every circle swell until it presses against its neighbours and the holes close up. Each circle flattens where it meets another one. Six neighbours means six flat sides — and you are looking at a hexagon. Pack the circles in straight lines instead, rows directly above each other, and the same squeeze gives you squares.

So the shape is a consequence of the packing, not a decision. The bees build round cells and push them together, and the hexagons appear.