The hive is made up of beeswax-walled honeycombs, which have hundreds of tiny cells on each of its faces. All honeycomb cells are exactly at the same size. This engineering miracle is achieved by the collective functioning of thousands of bees. Bees use these cells for food storage and maintenance of the young bees.
Bees have been using the hexagonal structure for the construction of the honeycombs for millions of years. (There is a bee fossil is found dating 100 million years.) It is a wonder why they have chosen the hexagonal structure rather than octagonal, or pentagonal? The answer is given by the mathematicians: "hexagonal structure is the most suitable geometric form for maximum use of unit area" If the honeycomb cells were constructed in another form, then there would be areas left out of use; thus less honey would be stored, and less bees would be able to benefit from it.
As long as their depths are the same, a triangle or quadrangle cell would hold the same amount of honey as a hexagonal cell. But, among all these geometric forms, hexagon is the one with the shortest circumference. Whilst they have the same volume, amount of wax required for hexagonal cells is less than that required for a triangular or quadrangular one.
So, the conclusion is: Hexagonal cell requires minimum amount of wax for construction while it stores maximum amount of honey. This result, obtained after many complex geometrical calculations, can surely not have been calculated by bees themselves. These tiny animals use the hexagon form innately, just because they are "taught" and inspired so by their Lord.
The hexagonal design of the cells is practical in many aspects. Cells fit to each other and they share each other's walls. This, again, ensures maximum storage with minimum wax. Although the walls of the cells are rather thin, they are strong enough to sustain a few times of their own weight.
Besides the side walls, the same principle of maximum saving is considered also while the bottom edges are constructed.
Combs are built as a slice with two lines lying back to back, where the connection point problem occurs. This problem is solved by constructing the bottom surfaces of cells by combining three equilateral quadrangles. When three cells are built on one face of the comb, the bottom surface of one cell on the other face is automatically constructed.
As the bottom surface is composed of equilateral quadrangle wax plaques, the depth increases in these cells, which results in an increase in the volume and thus in the amount of honey to be stored.