Not until the advent of close-up film techniques did scientists know for certain how bees build their honey stores. It is a remarkable feat of high precision engineering. Young worker bees excrete slivers of warm wax, each about the size of a pinhead. Each wax partition is less than 0.1mm thick, accurate to a tolerance of 0.002mm. After all, the warm wax could just as well be formed into curved walls.
Some facts are easy to establish.
Others will leave gaps. Of the three space-filling figures, squares give a smaller total perimeter than triangles and hexagons do even better than squares. But if you allow combinations of polygons of all kinds, or edges that are not straight lines, then things become a lot more complicated. Relatively little was known until 1943, when Hungarian mathematician L Fejes Toth used an ingenious argument to prove that the regular hexagon pattern does give the smallest total perimeter for all patterns made up of any combination of straight-edged polygons. Toth thought the regular hexagon pattern would still be more efficient than anything else, but he could not prove it.