[DannyTN]

"The bees do no calculus. The combs grow like crystals-once an initial hexagon is created the bees simply replicate that shape and size. The original hexagon is an optimum shape programmed through instinctive behavior."

I don't assume the bees do calculus but your use of the word "programmed" is appropriate. I don't believe it's an evolved instinct.

The bees build the original hexagon shape. And while they can be coaxed to build smaller hexagons through the use of a starter row, I doubt they can be coaxed to build anything other than hexagons.

[Pete]

I don't assume the bees do calculus but your use of the word "programmed" is appropriate

Just to clarify, the calculus I was referring to comes into play when setting the displacement of the pointed tetrahedral apex (on the hidden part of the comb) so that the surface area is minimized - not on the choice of a hexagon (although that minimizes as well).

[Elsie]

Then they need to read "Tiling the Plane" for a bit of diversity in their busy, humdrum lives.