largest possible space for a given length of wall.  Although we have some examples of circular buildings, including those here in Oxford, it isn't a good choice for the shape of rooms within a building. [ Why aren't circular rooms common? ] Circles don't fit neatly together and wasted gaps of space would be left between circular rooms. In order to make the most of your space you need a shape that tessellates or tiles the floor space of your building, just like the paving stones that neatly cover the courtyard near the Beehive. There are only three regular shapes that can tile the plane -- triangles, squares and hexagons.  So by choosing hexagons, the architects of the beehive, both this building and that of the bee, have chosen the most efficient shape for a room -- the hexagonal walls enclose the largest possible areas while wasting no space between them. Bees have known about the benefits of hexagons for millennia, and we have suspected that hexagons were the most efficient way to divide up a flat plane from at least 300AD when Pappus of Alexandria posed this as a question.  However this Honeycomb Conjecture was only proved mathematically just over a decade ago, by Thomas Hales in 1999. Making the most of your energy Although the architects of the Beehive were aware of all this maths, we can be pretty sure that the bees haven't learnt any geometry.  But nature, like mathematicians and architects, is keen on efficiency and