

Honeycomb Shape
Name: Mew
Status: student
Grade: 912
Location: Outside U.S.
Country: Hong Kong
Date: Spring 2012
Question:
During a biology class, a question popped into my head when we were studying about bees. The question is why are honeycombs only hexagonal in shape and not square or pentagonal in shape?
Replies:
Hi Mew,
In nature, geometry that serves the bees to further multiply will be retained, those geometries that are less able to support formation of more colonies of bees, do not. For bees, which form colonies by swarming, the building must be flexible, compact, resistant to collapse and highly versatile. In terms of natural selection, the hexagon wins out over the square or pentagon in terms of collapse resistance.
A hexagon stretched into a column is a hexagonal prism. The strength and stability of the hexagonal prism allows for maximum flex and dissolution of forces from virtually any direction. The hexagonal prisms are able to be tightly packed, called tessellations.
Please consider the image above. One can visualize the packing and fluidic flex in every dimension. This flexibility allows a swarm of bees to su
http://hexnet.org/library/hexnet/hexagonalgeometry
Image: http://upload.wikimedia.org/wikipedia/commons/5/
5a/Honeycomb_3d_rot.png
Incidentally, the hexagonal nature of the honeycomb has also crossed the minds of Winnie the Pooh and myself! J
Peter E. Hughes, Ph. D.
Milford, NH
Hexagonal lattices have the advantage of being able to completely fill
a twodimensional space (pentagons do not), and utilize much less
material to fill a given area than a square or triangular lattice. In
other words, hexagons require the least effort (work, and wax) by the
bees!
Hope this helps,
Burr
The hexagonal shape of honeycombs has been shown mathematically to be the most efficient two dimensional tiling structure from a perspective of the surface area of the edges. Put simply, this structure allows the bees to use the smallest amount of wax to fill the hive with repeating 'cells' of honey.
S. Unterman
The most common explanation is that the hexagonal structure is the most efficient use of the wax for construction. Making wax is a big investment for bees, so to get the most efficient use of it is important.
"The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter. The conjecture was proposed by Pappus of Alexandria (c. 290 – c. 350) and proved by mathematician Thomas C. Hales" (from Wikipedia).
Others have proposed that the shape is more of an accident of many individual bees working in the same small space. Queen cells are not as regularly shaped as honey cells.
J. Elliott
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Update: June 2012

