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For other uses, see Honeycomb (disambiguation).

A honeycomb is a mass of hexagonal wax cells built by honeybees in their nests to contain their larvae and stores of honey and pollen. The term is also used for manmade materials that resemble it in appearance or structure. In addition, Polistinae and Vespinae wasps construct hexagonal prism packed combs, which are made of paper instead of wax.

Honeycomb is essentially the furniture and pantry in the bees' home. Beekeepers may remove the entire honeycomb to harvest honey. The honey can be extracted from the comb by uncapping and spinning in a centrifugal machine - the honey extractor. Fresh, new comb is sometimes sold and used intact as comb honey, especially if the honey is being spread on bread rather than used in cooking or to sweeten tea.

Broodcomb becomes dark over time, because of the cocoons embedded in the cells and the tracking of many feet, called travel stain by beekeepers when seen on frames of comb honey. Honeycomb in the "supers" that are not allowed to be used for brood stays light colored.

[edit] Honeycomb geometry

The axes of honeycomb cells are always quasi-horizontal, and the non-angled rows of honeycomb cells are always horizontally (not vertically) aligned. Thus, each cell has two vertical walls, with "floors" and "ceilings" composed of two angled walls. The cells slope slightly upwards, between 9 and 14 degrees, towards the open ends.

There are two possible explanations for the reason that honeycomb is composed of hexagons, rather than any other shape. One is that the hexagon tiles the plane with minimal perimeter per piece area. Thus a hexagonal structure uses the least material to create a lattice of cells with a given volume. Another, given by D'Arcy Wentworth Thompson, is that the shape simply results from the process of individual bees putting cells together: somewhat analogous to the boundary shapes created in a field of soap bubbles. In support of this he notes that queen cells, which are constructed singly, are irregular and lumpy with no apparent attempt at efficiency.

It is likely that the honeybee constructs the honeycomb based on instinct, and the prevailing theory of biology is that the appearance of such efficient shapes in nature is a result of natural selection.

The closed ends of the honeycomb cells are also an example of geometric efficiency, albeit three-dimensional and little-noticed. The ends are trihedral (i.e., composed of three planes) pyramidal in shape, with the dihedral angles of all adjacent surfaces measuring 120°, the angle that minimizes surface area for a given volume. (The angle formed by the edges at the pyramidal apex is approximately 109° 28' 16" (= 180° - arccos(1/3)).)

The shape of the cells is such that two opposing honeycomb layers nest into each other, with each facet of the closed ends being shared by opposing cells.

Individual cells do not, of course, show this geometrical perfection: in a regular comb, there are deviations of a few percent from the "perfect" hexagonal shape. In transition zones between the larger cells of drone comb and the smaller cells of worker comb, or when the bees encounter obstacles, the shapes are often distorted.

In 1965, László Fejes Tóth discovered that the trihedral pyramidal shape (which is composed of three rhombi) used by the honeybee is not the theoretically optimal three-dimensional geometry. A cell end composed of two hexagons and two smaller rhombuses would actually be .035% (or approximately 1 part per 2850) more efficient.

[edit] References

• Graham, Joe. The Hive and the Honey Bee. Hamilton/IL: Dadant & Sons; 1992; ISBN 0-915698-09-9
• Thompson, D'Arcy Wentworth (1942). On Growth and Form. Dover Publications. ISBN 0-486-67135-6.
• "The Mathematics of the Honeycomb" (June 1985). Science Digest, pp. 74-77.de:Bienenwabe

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