Comb

Each bee digs a round basin and stops where it meets a neighbour's, leaving a flat wall. That's the whole rule. Slide from careless spacing to careful spacing and watch the hexagons appear on their own.

From Darwin's On the Origin of Species, chapter 7. He argued that no bee needs to know geometry: dig basins at an even distance, stop when the wax gets thin, build a wall where two basins meet, and the hexagons follow. Wax is expensive (he cites twelve to fifteen pounds of sugar for one pound of wax), so colonies whose spacing was a little better got through more winters. The counter compares the walls you get with a perfect comb of the same number of cells. When I measured it, the surprise was how little the spacing matters by itself: even the most careless comb here uses only about a tenth more wax. The big saving is sharing walls at all. A humble-bee's separate round cells each need their own wall, which comes to roughly 80% more wax than a shared comb. Neighbours first, neatness second.