Editing Honeycomb

{{Short description|Collection of wax cells built by honeybees}}
{{other uses}}
[[File:Honeycombs for Sale - Saraeyn - Iranian Azerbaijan - Iran (7421128352).jpg|thumb|300px|Honeycombs for sale in [[Sareyn]], Iran]]
A '''honeycomb''' is a mass of [[Triangular prismatic honeycomb#Hexagonal prismatic honeycomb|hexagonal prismatic]] cells built from [[beeswax]] by [[honey bee]]s in their [[beehive|nests]] to contain their brood ([[egg]]s, [[larva]]e, and [[pupa]]e) and stores of [[honey]] and [[pollen]].

[[beekeeping|Beekeepers]] may remove the entire honeycomb to harvest honey. Honey bees consume about {{cvt|8.4|lb|kg}} of honey to secrete {{cvt|1|lb|g}} of wax,<ref>Graham, Joe. The Hive and the Honey Bee. Hamilton/IL: Dadant & Sons; 1992; ISBN.</ref> and so beekeepers may return the wax to the hive after harvesting the honey to improve honey outputs. The structure of the comb may be left basically intact when honey is extracted from it by uncapping and spinning in a centrifugal [[honey extractor]]. If the honeycomb is too worn out, the wax can be reused in a number of ways, including making sheets of comb [[Wax foundation|foundation]] with a hexagonal pattern. Such foundation sheets allow the bees to build the comb with less effort, and the hexagonal pattern of [[Worker bee|worker]]-sized cell bases discourages the bees from building the larger [[Drone (bee)|drone]] cells. 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 as a sweetener.

[[Brood (honey bee)|Broodcomb]] becomes dark over time, due to empty cocoons and shed larval skins embedded in the cells, alongside being walked over constantly by other bees, resulting in what is referred to as a 'travel stain'<ref>{{cite web |url=https://montgomerycountybeekeepers.com/glossary-bee-terms/#t |title=Glossary of Bee Terms |author=<!--Not stated--> |website=Montgomery County Beekeepers Association |access-date=2018-02-08 |quote="dark discoloration on the surface of comb honey left on the hive for some time, caused by bees tracking propolis over the surface."}}</ref> by beekeepers when seen on frames of comb honey. Honeycomb in the "[[honey super|supers]]" that are not used for brood (e.g. by the placement of a [[queen excluder]]) stays light-colored.

Numerous [[wasp]]s, especially [[Polistinae]] and [[Vespinae]], construct hexagonal prism-packed combs made of paper instead of wax; in some species (such as ''[[Brachygastra mellifica]]''), honey is stored in the nest, thus technically forming a paper honeycomb. However, the term "honeycomb" is not often used for such structures.

==Geometry==
{{further|Patterns in nature}}

The axes of honeycomb cells are always nearly horizontal, with the open end higher than the back end. The open end of a cell is typically referred to as the top of the cell, while the opposite end is called the bottom. The cells [[slope]] slightly upwards, between 9 and 14°, towards the open ends.{{citation needed|date=March 2017}}

Two possible explanations exist as to why honeycomb is composed of hexagons rather than any other shape. First, the [[hexagonal tiling]] creates a partition with equal-sized cells, while minimizing the total [[perimeter]] of the cells. Known in [[geometry]] as the [[honeycomb theorem]], this was conjectured by [[Jan Brożek]] and mathematically proven much later by [[Thomas Callister Hales|Thomas Hales]]. Thus, a hexagonal structure uses the least material to create a lattice of cells within a given [[volume]].  A second reason, 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 bubble]]s. In support of this, he notes that queen cells, which are constructed singly, are irregular and lumpy with no apparent attempt at efficiency.<ref>Thompson, D'Arcy Wentworth (1942). ''[[On Growth and Form]]''. Dover Publications. ISBN.</ref>

The closed ends of the honeycomb cells are also an example of geometric efficiency, though three-[[dimension]]al.<ref name="nazzi">{{cite journal|pmc=4913256|year=2016|last1=Nazzi|first1=F|title=The hexagonal shape of the honeycomb cells depends on the construction behavior of bees|journal=Scientific Reports|volume=6|pages=28341|doi=10.1038/srep28341|pmid=27320492|bibcode=2016NatSR...628341N}}</ref> The ends are trihedral (i.e., composed of three planes) sections of [[rhombic dodecahedron|rhombic dodecahedra]], with the [[dihedral angle]]s 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, known as the [[tetrahedral angle]], is approximately 109° 28' 16" ({{nowrap|{{=}} arccos(−1/3)}})

<div style="text-align:center;">[[File:Honeycomb cell 3d rot.svg|alt=A computer-generated model of a honeycomb cell, showing a hexagonal tube terminating in three equal rhombuses that meet at a point on the axis of the cell.|The three-dimensional geometry of a honeycomb cell]]</div>

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.<ref name=nazzi/>
<div style="text-align:center;">[[File:Honeycomb 3d rot.svg|alt=A computer-generated model of two opposing honeycomb layers, showing three cells on one layer fitting together with three cells on the opposing layer.|Opposing layers of honeycomb cells fit together]]</div>

Individual cells do not show this geometric perfection: in a regular comb, deviations of a few [[percent]] from the "perfect" hexagonal shape occur.<ref name=nazzi/> 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. Cells are also angled up about 13° from horizontal to prevent honey from dripping out.<ref>{{cite book|last=Frisch|first=Karl von|title=Animal Architecture|url=https://archive.org/details/animalarchitect00fris|url-access=registration|year=1974|publisher=Harcourt Brace Jovanovich|location=New York|isbn=9780151072514}}</ref>

In 1965, [[László Fejes Tóth]] discovered that the trihedral pyramidal shape (which is composed of three [[rhombus|rhombi]]) used by the honeybee is not the theoretically optimal three-dimensional geometry. A cell end composed of two hexagons and two smaller rhombi would actually be .035% (or about one part per 2850) more efficient. This difference is too minute to measure on an actual honeycomb, and irrelevant to the hive economy in terms of efficient use of wax, considering wild comb varies considerably from any mathematical notion of "ideal" geometry.<ref>
{{cite book
 | last = Bessiere
 | first = Gustavo
 | title = Il Calcolo Differenziale e Integrale—Reso Facile ed Attraente.IL
 | publisher = Hoepli
 | edition = VII
 | year = 1987
 | location = Milan
 | language = it
 | url = http://www.hoepli.it/libro/il-calcolo-differenziale-e-integrale-/9788820310110.html
 | isbn = 9788820310110
}}</ref><ref>
Gianni A. Sarcone.
[http://www.archimedes-lab.org/monthly_puzzles_72.html "The solved angular puzzle of the honeycombs' cells"].
2004.
</ref>

===Role of wax temperature===
Bees use their [[antenna (biology)|antennae]], [[Mandible (insect mouthpart)|mandibles]] and legs to manipulate the wax during comb construction, while actively warming the wax.<ref name="bauer">{{cite journal|pmid=23149932|year=2013|last1=Bauer|first1=D|title=Hexagonal comb cells of honeybees are not produced via a liquid equilibrium process|journal=Naturwissenschaften|volume=100|issue=1|pages=45–9|last2=Bienefeld|first2=K|doi=10.1007/s00114-012-0992-3|bibcode=2013NW....100...45B|s2cid=11552726}}</ref> During the construction of hexagonal cells, wax temperature is between {{cvt|33.6|-|37.6|°C}}, well below the {{cvt|40|°C}} temperature at which wax is assumed to be liquid for initiating new comb construction.<ref name=bauer/> The body temperature of bees is a factor for regulating an ideal wax temperature for building the comb.<ref>{{cite journal|pmid=15257392|year=2004|last1=Pirk|first1=C. W.|title=Honeybee combs: Construction through a liquid equilibrium process?|journal=Naturwissenschaften|volume=91|issue=7|pages=350–3|last2=Hepburn|first2=H. R.|last3=Radloff|first3=S. E.|last4=Tautz|first4=J|doi=10.1007/s00114-004-0539-3|bibcode=2004NW.....91..350P|s2cid=31547154}}</ref>

==Gallery==
<gallery mode="packed" style="font-size:88%; line-height:130%">

File:Western honey bee on a honeycomb.jpg|A Western honey bee on a honeycomb
File:Honeycomb-Process.png|The bees begin to build the comb from the top of each section. When a cell is filled with honey, the bees seal it with wax.
File:BDHoneycomb.JPG|Natural honeycombs on a building
File:Bienenwabe mit Eiern und Brut 5.jpg|Honeycomb with eggs and [[larva]]e
File:Apis florea nest closeup2.jpg|Closeup of an abandoned ''[[Apis florea]]'' nest in [[Thailand]]. The hexagonal grid of wax cells on either side of the nest are slightly offset from each other. This increases the strength of the comb and reduces the amount of wax required to produce a robust structure.
File:Honey comb.jpg|Honeycomb
File:Natural Beehive and Honeycombs.jpg|The lower part of the natural comb of ''[[Apis dorsata]]'' has a number of unoccupied cells
File:Bienenwabe Ausbau der Mittelwand 79a.jpg|"Artificial honeycomb" foundation plate in which bees have already completed some cells
File:TransitionalHoney.jpg|Honeycomb section containing transition from worker to drone (larger) cells – here bees make irregular and five-cornered cells (marked with red dots)
File:Western Honey Bees and Honeycomb.JPG|Western honeybees and honeycomb
File:Machine-made honeycombs.jpg|Honeycombs made by machine with beeswax and with the whole structure of the hexagonal cell already built
File:Coat of Arms of Viļāni.svg|Coat of arms of the town of [[Viļāni]], Latvia
File:Honeycomb 091f.jpg|[[Langstroth hive|Langstroth]] frame of honeycomb with [[honey]] in the upper left and [[pollen]] in most of the rest of the cells
File:Waxing Honeycombs on the grill.jpg|Cooking a [[grilled honeycomb]] with larvae at the Oudong Market in [[Cambodia]]
</gallery>

==See also==
* [[Honeycomb structure]]
* [[Wax foundation]]
* [[Hive frame]]
* [[Jan Dzierzon]]
* [[Grilled honeycomb]]
* [[Honeycomb toffee]]

==References==
{{reflist}}

==External links==
{{Commons category|Honeycombs}}
{{Wiktionary}}
{{BeeColonyMemberTypes}}

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