14. HONEYCOMB AND TESSELLATIONS

Bees construct their honeycomb to hold their hoeny and to contain their larvae. The honeycomb cells have an almost perfect regular hexagonal cross-section. It is reasonable to ask why this shape appears here.

In mathematics there are three regular tessellations of the plane – non-overlapping coverings of congruent regular polygons. The polygons here are the regular hexagon, the square, and the equilateral triangle. So why do the bees choose the hexagon? It can be shown that the hexagonal cross-section is the most economical of the three (in terms of wax used) for enclosing a given cell volume. Those clever bees!

The cells have geometrically interesting caps as well, but that is another story.

http://en.wikipedia.org/wiki/Honeycomb