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A honeycomb is a mass of hexagonal prismatic cells built from
beeswax Bee hive wax complex Beeswax (also known as cera alba) is a natural wax produced by honey bees of the genus ''Apis''. The wax is formed into scales by eight wax-producing glands in the abdominal segments of worker bees, which discard it in o ...
by
honey bee A honey bee (also spelled honeybee) is a eusocial flying insect within the genus ''Apis'' of the bee clade, all native to mainland Afro-Eurasia. After bees spread naturally throughout Africa and Eurasia, humans became responsible for the ...
s in their
nests A nest is a structure built for certain animals to hold eggs or young. Although nests are most closely associated with birds, members of all classes of vertebrates and some invertebrates construct nests. They may be composed of organic materi ...
to contain their brood (
egg An egg is an organic vessel grown by an animal to carry a possibly fertilized egg cell (a zygote) and to incubate from it an embryo within the egg until the embryo has become an animal fetus that can survive on its own, at which point the ...
s,
larva A larva (; : larvae ) is a distinct juvenile form many animals undergo before metamorphosis into their next life stage. Animals with indirect development such as insects, some arachnids, amphibians, or cnidarians typically have a larval phase ...
e, and
pupa A pupa (; : pupae) is the life stage of some insects undergoing transformation between immature and mature stages. Insects that go through a pupal stage are holometabolous: they go through four distinct stages in their life cycle, the stages th ...
e) and stores of
honey Honey is a sweet and viscous substance made by several species of bees, the best-known of which are honey bees. Honey is made and stored to nourish bee colonies. Bees produce honey by gathering and then refining the sugary secretions of pl ...
and
pollen Pollen is a powdery substance produced by most types of flowers of seed plants for the purpose of sexual reproduction. It consists of pollen grains (highly reduced Gametophyte#Heterospory, microgametophytes), which produce male gametes (sperm ...
.
Beekeepers A beekeeper is a person who keeps honey bees, a profession known as beekeeping. The term beekeeper refers to a person who keeps honey bees in beehives, boxes, or other receptacles. The beekeeper does not control the creatures. The beekeeper ...
may remove the entire honeycomb to harvest honey. Honey bees consume about of honey to secrete of wax, 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 A honey extractor is a mechanical device used in the extraction of honey from honeycombs. A honey extractor extracts the honey from the honey comb without destroying the comb. Extractors work by centrifugal force. A drum or container holds a ...
. If the honeycomb is too worn out, the wax can be reused in a number of ways, including making sheets of comb
foundation Foundation(s) or The Foundation(s) may refer to: Common uses * Foundation (cosmetics), a skin-coloured makeup cream applied to the face * Foundation (engineering), the element of a structure which connects it to the ground, and transfers loads f ...
with a hexagonal pattern. Such foundation sheets allow the bees to build the comb with less effort, and the hexagonal pattern of
worker Worker may refer to: * Worker, a person who performs work for a living * Laborer, a person who performs unskilled physical labour, especially in construction * Worker, a member of the working class * Worker, a member of the workforce ** Designati ...
-sized cell bases discourages the bees from building the larger
drone Drone or The Drones may refer to: Science and technology Vehicle * Drone, a type of uncrewed vehicle, a class of robot ** Unmanned aerial vehicle or aerial drone *** Unmanned combat aerial vehicle ** Unmanned ground vehicle or ground drone ** Unma ...
cells. Fresh, new comb is sometimes sold and used intact as
comb honey Comb honey is honey intended for consumption by humans, which is still contained within its original hexagonal-shaped beeswax cells, called honeycomb. It has received no processing, filtering, or manipulation, and is in the state that honey bees h ...
, especially if the honey is being spread on bread rather than used in cooking or as a sweetener. 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' by beekeepers when seen on frames of comb honey. Honeycomb in the " supers" that are not used for brood (e.g. by the placement of a
queen excluder In beekeeping, a queen excluder is a selective barrier inside the beehive that allows worker bees but not the larger queens and drones to traverse the barrier. The bars have a distance of 4.2 millimeters. The barrier grid was probably invented a ...
) stays light-colored. Numerous
wasp A wasp is any insect of the narrow-waisted suborder Apocrita of the order Hymenoptera which is neither a bee nor an ant; this excludes the broad-waisted sawflies (Symphyta), which look somewhat like wasps, but are in a separate suborder ...
s, especially
Polistinae The Polistinae is a subfamily of eusocial wasps belonging to the family Vespidae. They are closely related to the wasps (“yellowjackets” as they are called in North America) and true hornets of the subfamily Vespinae, containing four tribes ...
and
Vespinae The subfamily Vespinae contains the largest and best-known groups of eusocial wasps, including true hornets (the genus ''Vespa''), and the "yellowjackets" (genera ''Dolichovespula'' and ''Vespula''). The remaining genus, '' Provespa'', is a smal ...
, construct hexagonal prism-packed combs made of paper instead of wax; in some species (such as ''
Brachygastra mellifica ''Brachygastra mellifica'', commonly known as the Mexican honey wasp, is a neotropical social wasp. It can be found in North America. ''B. mellifica'' is one of few wasp species that produces honey. It is also considered a delicacy in some cultur ...
''), honey is stored in the nest, thus technically forming a paper honeycomb. However, the term "honeycomb" is not often used for such structures.


Geometry

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 In mathematics, the slope or gradient of a Line (mathematics), line is a number that describes the direction (geometry), direction of the line on a plane (geometry), plane. Often denoted by the letter ''m'', slope is calculated as the ratio of t ...
slightly upwards, between 9 and 14°, towards the open ends. Two possible explanations exist as to why honeycomb is composed of hexagons rather than any other shape. First, the
hexagonal tiling In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a Truncation (geometry), truncated triangular tiling ...
creates a partition with equal-sized cells, while minimizing the total
perimeter A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimet ...
of the cells. Known in
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
as the
honeycomb theorem The honeycomb theorem, formerly the honeycomb conjecture, states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area. The conjecture was proven in 1999 by mathematic ...
, this was conjectured by
Jan Brożek Jan Brożek or Johannes Broscius (November 1585 – 21 November 1652) was the most prominent Polish mathematician of his era and an early biographer of Copernicus. He held numerous ecclesiastical offices in the Catholic Church and was associated ...
and mathematically proven much later by Thomas Hales. Thus, a hexagonal structure uses the least material to create a lattice of cells within a given
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
. A second reason, given by
D'Arcy Wentworth Thompson Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948) was a Scottish biologist, mathematician and classics scholar. He was a pioneer of mathematical and theoretical biology, travelled on expeditions to the Bering Strait ...
, 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 A soap bubble (commonly referred to as simply a bubble) is an extremely thin soap film, film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds b ...
s. In support of this, he notes that queen cells, which are constructed singly, are irregular and lumpy with no apparent attempt at efficiency. The closed ends of the honeycomb cells are also an example of geometric efficiency, though three-
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...
al. The ends are trihedral (i.e., composed of three planes) sections of
rhombic dodecahedra Rhombic may refer to: *Rhombus, a quadrilateral whose four sides all have the same length (often called a diamond) * Rhombic antenna, a broadband directional antenna most commonly used on shortwave frequencies * polyhedra formed from rhombuses, suc ...
, with the dihedral angles of all adjacent surfaces measuring 120°, the angle that minimizes
surface area The surface area (symbol ''A'') of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the d ...
for a given volume. (The angle formed by the edges at the pyramidal apex, known as the
tetrahedral angle In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary conv ...
, is approximately 109° 28' 16" ()
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 show this geometric perfection: in a regular comb, deviations of a few
percent In mathematics, a percentage () is a number or ratio expressed as a fraction of 100. It is often denoted using the ''percent sign'' (%), although the abbreviations ''pct.'', ''pct'', and sometimes ''pc'' are also used. A percentage is a dime ...
from the "perfect" hexagonal shape occur. 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. In 1965,
László Fejes Tóth László Fejes Tóth (, ; 12 March 1915 – 17 March 2005) was a Hungarian mathematician who specialized in geometry. He proved that a lattice pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane (a ge ...
discovered that the trihedral pyramidal shape (which is composed of three
rhombi In plane Euclidean geometry, a rhombus (: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhom ...
) 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.


Role of wax temperature

Bees use their antennae,
mandibles In jawed vertebrates, the mandible (from the Latin ''mandibula'', 'for chewing'), lower jaw, or jawbone is a bone that makes up the lowerand typically more mobilecomponent of the mouth (the upper jaw being known as the maxilla). The jawbone i ...
and legs to manipulate the wax during comb construction, while actively warming the wax. During the construction of hexagonal cells, wax temperature is between , well below the temperature at which wax is assumed to be liquid for initiating new comb construction. The body temperature of bees is a factor for regulating an ideal wax temperature for building the comb.


Gallery

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 A larva (; : larvae ) is a distinct juvenile form many animals undergo before metamorphosis into their next life stage. Animals with indirect development such as insects, some arachnids, amphibians, or cnidarians typically have a larval phase ...
e File:Apis florea nest closeup2.jpg, Closeup of an abandoned ''
Apis florea The dwarf honey bee (or red dwarf honey bee), ''Apis florea'', is one of two species of small, wild honey bees of southern and southeastern Asia. It has a much wider distribution than its cladistics, sister species, ''Apis andreniformis''. First ...
'' nest in
Thailand Thailand, officially the Kingdom of Thailand and historically known as Siam (the official name until 1939), is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. With a population of almost 66 million, it spa ...
. 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 ''Apis dorsata'', the rock bee or giant honey bee, is a honey bee of South and Southeast Asia. They are typically around long and nests are mainly built in exposed places far off the ground, like on tree limbs, under cliff overhangs, and under ...
'' 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 Viļāni () (, ) is a town in Rēzekne Municipality in the Latgale region of Latvia. The railway line Riga-Moscow, and the motor highway Riga-Moscow, and the road Preiļi-Balvi cross Viļāni. The Malta river flows through the town. The populati ...
, Latvia File:Honeycomb 091f.jpg, Langstroth frame of honeycomb with
honey Honey is a sweet and viscous substance made by several species of bees, the best-known of which are honey bees. Honey is made and stored to nourish bee colonies. Bees produce honey by gathering and then refining the sugary secretions of pl ...
in the upper left and
pollen Pollen is a powdery substance produced by most types of flowers of seed plants for the purpose of sexual reproduction. It consists of pollen grains (highly reduced Gametophyte#Heterospory, microgametophytes), which produce male gametes (sperm ...
in most of the rest of the cells File:Waxing Honeycombs on the grill.jpg, Cooking a
grilled honeycomb Grilled honeycomb (, or , ; ; , ; , ) is grilled bee honeycomb with bee larvae. It is considered a street food delicacy in Cambodia, Laos and Northern Thailand. Preparation Honeycomb are harvested from the forest during rain season and the ...
with larvae at the Oudong Market in
Cambodia Cambodia, officially the Kingdom of Cambodia, is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. It is bordered by Thailand to the northwest, Laos to the north, and Vietnam to the east, and has a coastline ...


See also

*
Honeycomb structure Honeycomb structures are natural or man-made structures that have the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal weight and minimal material cost. The geometry of honeycomb structures can ...
*
Wax foundation Wax foundation or honeycomb base is a plate made of wax forming the base of one honeycomb. It is used in beekeeping to give the bees a foundation on which they can build the honeycomb. Wax foundation is considered one of the most important invent ...
*
Hive frame A hive frame or honey frame is a structural element in a beehive that holds the honeycomb or brood comb within the hive enclosure or box. The hive frame is a key part of the modern movable-comb hive. It can be removed in order to inspect the bees ...
* Jan Dzierzon *
Grilled honeycomb Grilled honeycomb (, or , ; ; , ; , ) is grilled bee honeycomb with bee larvae. It is considered a street food delicacy in Cambodia, Laos and Northern Thailand. Preparation Honeycomb are harvested from the forest during rain season and the ...
*
Honeycomb toffee Honeycomb toffee, honeycomb candy, sponge toffee, cinder toffee, seafoam, or hokey pokey is a sugary toffee with a light, rigid, sponge-like texture. Its main ingredients are typically brown sugar (or corn syrup, molasses or golden syrup) and bak ...


References


External links

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