On Mon, 23 Oct 2000, Michael Churchill wrote:
  In summary (based on my memory of the article), the hexagon is the
most efficient means of covering a 2-dimensional area with a regular,
repeating pattern.  This is why honeycomb cells are hexagonal in cross
section.

Hi Michael:

It is tempting to say that bees make their cells hexagonal because
that is the most efficient way to do it, but I don't believe that is
the case. I think they make a bunch of cells simultaneously and the
bees working on one cell pushing against the bees working on adjacent
cells give a hexagon by default. When making queen cells there are no
competing cell builders and there is no hexagon. I don't know much
about bumble bees, but when their queen makes her first "honey pots"
and there are no competing constructors the results are probably not
hexagons. Any bumble bee experts out there?

Other features of the hive probably have a prosaic
origin as well. If a bee can just barely get into a space she probably
can't make much of a comb there. One expects "bee space" to be
determined by the size of the bee. The size of cells built without
foundation is likely to be determined by the size of the worker as
well.

Best regards,

Donald Aitken
Edmonton Alberta Canada