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Why honey bees built hive in perfect hexagonal shape instead of irregular shape?

Why honey bees built hive in perfect hexagonal shape instead of irregular shape?


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Why honey bees built hive in perfect hexagonal shape ?

Due to Hexagonal shape, I can go near without any anxious or fear.( Apart from Honey bee's stings)

From this Question, Most creatures look like or tries to look like irregular to fear the other creatures to attack.


Why honey bees built hive in perfect hexagonal shape ?

Honeycomb cells (not the hive or the honeycomb itself) are hexagonal, in some species of bees but not all. The regularity of this shape has puzzled people for a long time, and Darwin (and others before him) addressed the reasons for it. Darwin did a series of experiments with bees, and summarized his results in Origin of Species. You can search for "hexagon" in the linked text for his long explanation, or read the (still long) summary 'Evolution of Honeycomb on the Darwin Correspondence Project, but the short explanation is that it's the most efficient way to pack cells without wasting wax, and Darwin identified a bunch of intermediate (less efficient) cell structures in various bee species that supported his hypothetized mode of evolution.

Thus, as I believe, the most wonderful of all known instincts, that of the hive-bee, can be explained by natural selection having taken advantage of numerous, successive, slight modifications of simpler instincts; natural selection having, by slow degrees, more and more perfectly led the bees to sweep equal spheres at a given distance from each other in a double layer, and to build up and excavate the wax along the planes of intersection. The bees, of course, no more knowing that they swept their spheres at one particular distance from each other, than they know what are the several angles of the hexagonal prisms and of the basal rhombic plates; the motive power of the process of natural selection having been the construction of cells of due strength and of the proper size and shape for the larvae, this being effected with the greatest possible economy of labour and wax; that individual swarm which thus made the best cells with least labour, and least waste of honey in the secretion of wax, having succeeded best, and having transmitted their newly-acquired economical instincts to new swarms, which in their turn will have had the best chance of succeeding in the struggle for existence.


The bees don't make hexagonal cells. This paper shows how bees construct multiple cylindrical tubes which are then molded based on temperature and contact with other cells.

As you can see, the cells start off cylindrical (day 0) and transform into the common hexagonal shape by day 2. The paper also goes into details of the physics involved (it is in a physics journal). I strongly suggest reading the paper if you wish to go more in depth.


in "the origin of species" pages 178 and 179, Darwin has stated that if a bee could build a cell slightly more hexagonal than the other bees then this bee would have a survival benefit since a perfect hexagon is the most economical structure in storing the greatest amount of honey with the least amount of wax, but unfortunately there is nothing in his analysis that proves the point. He concludes on page 179 that the saving of wax by largely saving honey would be an important element in the success in any family of bees. The problem with that analysis is that a slight modification of structure in this case a slightly more regular hexagon cannot provide a survival benefit as the two structures are almost identical.(the old cell and the slightly modified cell)


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Answers and Replies

It is genetically programmed bee-havior (sorry).

Overall, this is more of a why, than a how. AFAIK there is no definitive discussion on exactly how this is programmed into these guys.

In terms of energetics, making wax requires a lot of energy. Resusing it (bees do) and building cells in a shape that maximizes volume and minimizes the use of energetically expensive wall materials is important for colonial insect survival. If I can build my house
as good or better than you do, for less cost, longterm my kind comes out ahead of your kind in the race to survive.

Most of the hymenoptera (bees & wasps) that are colonial make the same hexagonal cell.
So, playing hexagons probably goes back to a common ancestor. Hymenoptera evolved in the Cretaceous and evolved as flowering plants became dominant.

Honey-bees construct wax combs inside their nests. The combs are made of hexagonal prisms – cells – built back to back, and are used to store honey, nectar, and pollen, and to provide a nursery for bee larvae. The combs are natural engineering marvels, using the least possible amount of wax to provide the greatest amount of storage space, with the greatest possible structural stability.

Now the question is how they do it?Any solid idea?what tools they use?!

The process of making a hexagonal bee hive was determined by Charles Darwin. He wrote about the theory and experiments that he himself conducted using his own bee hives in "Origin of the Species". He also discusses other types of hives made by bees. He showed theoretically how a series of cigar shaped nests could evolve into a hexagonal bee hive.

The description is in "Origin of the Species". I am not sure what exact page numbers it is on. It probably varies in the different editions. However, Darwin was quite thorough. I will summarize what I remember.

There are many types of bees, bee hives, and bee social behavior. Bees drink nectar which is very high in carbohydrates, but low on other nutrients. To get other nutrients, they have to drink a lot of nectar. Eating pollen helps them get a few proteins, although pollen contains carbohydrates too. To get all their nutrients, they absorb far more carbohydrate calories then they can possibly use. Therefore, all bees exude wax as a waste product. Wax probably started out as a compact way of disposing of excess carbohydrates.

The bees live in social groups. Each bee inherits a "comfort radius". They try to keep a certain distance away from other bees, with a fixed average distance. So each bee has a comfort zone within which she is the only bee. However, they try to dispose of the wax outside their comfort zone. Although they probably don't think of it this way, orthink at all, each bee would like their wax to pile up in someone elses zone. However, after defecating their wax, they always retreat to their own comfort zone.

The geometrical pattern of the wax that piles up is mathematically determined by both the radius of their comfort zone and the amount they of wax they have to defecate. If the radius is very large and the amount of wax small, then each bee has his own "cubical" of wax. Some bumble bees have evolved that way. However, the geometric pattern changes as the radius changes. A smaller radius places each bee in its own wax cigar. A very small radius results in a hexagonal honeycomb.

Basically, the bees are defecating in each others territory. They are throwing wax cooties around "randomly". The direction of the tossed wax is completely arbitrary. The distance is arbitrary, other than the restriction that the distance is greater than the comfort radius. The shape of the hive is mathematically determined by the comfort radius.

The motion of defecation is not optimal for building a hive. It is literally a pissing contest. Most of the motion in moving the wax around is waster. Most of the wax just keeps moving back and forth without any form taking shape. The shape slowly develops over time after a lot of aimless tossing back and forth.

The motion is not the most efficient necessary to make a stable hive. In fact, most species of bees do not make a stable hexagonal honeycomb. The shape and stability vary a lot among species, each living under different conditions. Honey bees are special not because they are the most common types of bee. Human beings raise them because the shape of the hive is most conducive to taking their honey. The motion of the wax is NOT energetically efficient even in the case of the honey bee.

The radius of comfort, and the rate that wax is produced, is inherited. The ratio is of course influenced by other behavior patterns of the bee. Natural selection causes a behavior pattern to form, which determines both radius and rate of defecation. However

Darwin did an interesting experiment to show that most of the motion in moving the wax was arbitrary. Darwin kept honey bees on his estate. He took a small dollop of bees wax and dyed it dark red. He went to one of his beehives. He placed the red dollop of bees wax in the middle of the hive. The bees broke it to pieces and "tossed" it at each other. Eventually, the red wax became part of the honeycomb. However, the wax did not stay in one place.

The red wax slowly spread over time. It first concentrated in one part of the hive which was dark red. Then it spread out so it was dark pink. It spread out farther until is was light pink. In never was planted firmly in the wax.The red wax went back and forth in random directions. Pieces of red wax diffused in a random walk until it was all over the hive.

Most of the motion of the wax did not contribute to stability of the hive. From the standpoint of making a stable hive, the motion was wasted. However, the wax still served to shelter the bees. The defecating in each others space was what some would call a "preadaption."

There are still a lot of bees that don't make hexagonal honey combs. Some Mexican bees make separate cigar shaped nests, as Darwin pointed out. There are a whole lot of different hives. Some don't make nests at all, just exuding wax. The main difference between the bees is the size of the "comfort zone".

Changing only one parameter gradually by natural selection is sufficient to change the entire geometry of the hive. There is no complicated series of saltations necessary to make different bee hives. The individual changes in radius can be random. It doesn't make a difference to the shape of the hive. At each step of the phylogeny, some geometrical shape has to form for each radius. In honey bees, the size of the comfort zone is small enough to form the hexagon chambers of the hive.


The evolution of honeycomb

Honey-bees construct wax combs inside their nests. The combs are made of hexagonal prisms – cells – built back to back, and are used to store honey, nectar, and pollen, and to provide a nursery for bee larvae. The combs are natural engineering marvels, using the least possible amount of wax to provide the greatest amount of storage space, with the greatest possible structural stability. Darwin recognised that explaining the evolution of the honey-bee’s comb-building abilities was essential if his theory of natural selection was to be taken seriously, and in the 1850s he carried out his own experiments at his home at Down House in Kent, and wrote many letters on the subject.

For natural theologians, who looked on nature as showing the workings of providence, the bee cell was a favourite subject. The question of how little insects could solve correctly a design problem that challenged even expert human geometers, and implement it practically, pointed, they thought, to a governing intelligence. In Lord Brougham’s Dissertations on subjects connected with natural theology (1839), Brougham commented that bees acted with a discipline that in men could only be effected by a superintendent with a design. The bee chose the most advantageous shape for her cells, he wrote, ‘as indeed we might well suppose when we recollect who is her teacher’ (Brougham 1839, 1: 35, 77). William Kirby wrote of the bees as ‘those Heaven-instructed mathematicians, who before any geometer could calculate under what form a cell would occupy the least space without diminishing its capacity, and before any chemist existed to discover how wax might be elaborated from vegetable sweets, instructed by the Fountain of Wisdom, had built their hexagonal cells of that pure material, had closed them at the bottom with three rhomboidal pieces, and were enabled, without study, so to construct the opposite story of combs, that each of these rhomboids should form one of those of three opposed cells, thus giving strength to the structure, that in no other place, could have been given to it’ (Kirby 1852, 2: 246).

Darwin’s copy of Brougham’s Dissertations is heavily annotated. He recognised that the problem of the bee cell was important for his theory. On page 77, he scribbled, ‘very wonderful – it is as wonderful in the mind as certain adaptations in the body – the eye for instance, if my theory explains one it may explain other.’ Darwin, and others working on naturalistic explanations, needed to show how bee cells could arise from simple processes. The theory of evolution by natural selection was supposed to be a comprehensive theory of life on earth: if it could not explain bee cells, it was radically flawed. Darwin needed to show two things: first, how the bees’ abilities had evolved over time, and second, how the bees built their combs using only the instincts and intelligence they had evolved.

The first point was relatively straightforward. Brougham, rejecting the suggestion that hexagonal cells could have arisen from cylindrical cells, asserted that no bee in the world ever made cylindrical cells (Brougham 1839, 1: 32). However, Darwin knew that humble bees made roughly cylindrical or near spherical cells for holding honey and larvae, and was delighted to discover a Mexican bee, Melipona domestica, that made a rough comb of cylindrical or nearly spherical cells, with flat sides where cells happened to meet. Most naturalists accepted that circular structures were the easiest for animals to construct: for example, birds’ nests are usually circular. Darwin argued that if the Melipona put its cells together in a more regular fashion, it would probably develop a structure like that of the honey-bee (Origin, p. 226). Further, there were advantages to a more regular, hexagonal-celled, structure: it used less wax to store more honey. Thus, when under environmental pressure (cold winters, lack of food), bee colonies with the more efficient structure would be more likely to survive and prosper.

The second point, how bees actually built the comb, involved Darwin in a great deal of correspondence and experimentation. When he began working in earnest on the subject for a projected book on the species question, Darwin wrote to George Robert Waterhouse. Waterhouse had written the article on bees for the Penny Cyclopaedia in 1835. He suggested that bees acted according to two antagonistic principles: one causing them to deposit and excavate the wax, the other limiting the degree of excavation. In his view, bees set out to make circular cells, which became hexagonal due to their working under the constraints of the two antagonistic principles and the proximity of other cells. Darwin’s letter has not been found, but from Waterhouse’s reply, it is clear that Darwin was asking for examples of honey-bees making cylindrical structures, either free-standing or at the edges of combs where the cells were not subject to the space constraints of other cells. (Letter from G. R. Waterhouse, 14 April 1857.)

In a later letter Waterhouse gave a detailed account of his observations of a leaf-cutter bee making a circular structure out of clay. After giving the matter due consideration he had realised that the repetitive motions of the bee, which he had at first thought ‘stupid’, were in fact guaranteed to produce a regular circular structure. ‘By keeping the body fixed in one position for some time & by working in all directions as far as she could reach, in her excavating, she would necessarily form a cavity in segments of circles and of definite size— —the diameter being determined by her power of reaching.’ (Letter from G. R. Waterhouse, 10 February 1858.)

By now not only Waterhouse but William Bernhard Tegetmeier (who had helped Darwin with his work on pigeons) and other members of the Entomological Society of London were exercising their minds on the problem. In his next letter, Waterhouse described wasps’ nests exhibited at a meeting of the society. It had been objected to his theory of cell-building that wasps also built combs of hexagonal cells, even though to begin with only one wasp (the queen) worked on the comb. Waterhouse responded that the wasp working alone always worked on several cells at once, and so was subjected to the same formal constraints as a group of bees working together. (Letter from G. R. Waterhouse, 13 February 1858.)

In April 1858, Darwin went to London to meet William Hallowes Miller, a crystallographer, to discuss the geometry of bee cells. Miller had developed a system of crystallography that was ‘far more simple, symmetrical, and adapted to mathematical calculations than any which had yet been devised’ (ODNB). Possibly Darwin consulted Miller simply on geometry, but his choice of expert suggests an interest in how a complex pattern may arise from natural forces. Darwin made notes for their discussion in a memorandum to W. H. Miller, [15 April 1858], summarising his position as follows:

Bees can make apparently true cylinders & spheres. (2) They never begin one cell at time always several (3) they can judge distance to certain extent, & (4) those that make their spheres or cylinders so that if completed, would intersect make an intermediate flat wall. Then assume perfect judge of distance, I thought that all angles might follow, for I cd see they would in hexagonal prism.–— My notion modification of Waterhouses. Ld. Brougham sneers at it.

Meanwhile, Waterhouse was still exercising his mind on the subjects of wasp’s nests. He sent another long letter to Darwin on the subject, this time arguing that where the sides of wasp cells that were not bounded by other cells were straight, this was because of the cues taken by the wasps from the other straight sides that were bounded by other cells (letter from G. R. Waterhouse, 17 April 1858).

Waterhouse also told Darwin of a meeting at the Entomological Society of London on 5 April. Since the notes he promised to send Darwin have not been found, the account given in the Proceedings of the Entomological Society of London n.s. 5: 17–18 is reproduced here:

Some discussion having arisen relating to the construction of the cells of the hive bee, Mr. Waterhouse stated that he was of opinion that the hexagonal form of cell was accidental, so far as the constructors of the cell were concerned and having been called upon to explain his views, he proceeded, in the first place, to call attention to the fact that if a number of cylinders of equal size were packed close together, side by side, each cylinder would be surrounded by six others that, assuming the cylindrical form (or at least a form of cell approaching more or less to the cylindrical, and having a circular section) was the type form of isolated cells constructed by different kinds of bees, and that, in the case of the hive bee, a number of insects worked together, first depositing a small portion of wax, then excavating a small circular cavity in the same, for the commencement of a cell this then being followed by the deposition of more wax and the excavation of more cavities, and these being placed close to the first then neither of the cells could be constructed of their natural diameter, provided the first cavity formed had not attained the full diameter of the complete cell. The diameters of the cells would intersect each other but if partitions be left between them, the cell must be six-sided, if the cells remain equal in size. In order to make the idea more clear, he . . . would assume for a moment that it were a law that a number of equal-sized circles, being packed closely together, side by side, and that each circle was then surrounded by seven others he believed that the cell of the hive bee would, in that case, have been seven-sided. Such were the views entertained many years back by Mr. W., and published by him in the ‘Penny Cyclopaedia’ and having subsequently had his attention particularly directed to the subject, whilst examining the nests of a vast number of Hymenopterous insects, he still believes those views to be essentially correct. He now, however, has reason to believe that it is not absolutely necessary for the supposed natural diameters of the cells to intersect before an angular-formed cell would be produced. The instinct which leads an insect to excavate, in order to form a cell, may lead it to excavate beyond what would be necessary to form a sufficiently large cell, in the case of an insect, which, under ordinary circumstances, burrows until it comes in contact with an adjoining cell. Contact with other cells was the essential condition which influenced the angular form of any particular cell. . . . Mr. Waterhouse said he had possessed a very small nest of a hornet which consisted of three cells only it was built in a small cavity adjoining a large nest, and where there was not room for more than three cells they were circular externally and angular internally,–—that is to say, each cell had two straight sides where it came in contact with two other cells, and was rounded elsewhere. Mr. Tegetmeier remarked that he possessed a small piece of honey-comb which presented the same peculiarities.

Darwin quickly arranged to look at Tegetmeier’s piece of honeycomb (letter to W. B. Tegetmeier, [21 April 1858]) however, it had been mislaid. Nevertheless, Darwin asked Tegetmeier to keep an eye out for the first beginnings of the comb (letter to W. B. Tegetmeier, 9 May [1858]). He suspected that the first cells, built without the constraints of neighbouring cells, would not be hexagonal.

At this time Darwin was much exercised by the work of François Huber. In his copy of Huber 1814, 2: 143, he scribbled a note: ‘If the sides of separate cell one are angular before other cells formed fatal to my theory.’ He wrote to his son William, ‘I am come to heavy grief about my Bees-cells & my only hope is that Huber has not correctly described their manner of building’ (letter to W. E. Darwin, [26 May 1858].) To Tegetmeier, he explained in more detail:

Huber says that first, a very thin & very low little ridge is made & then on one face the base of a single cell is hollowed out, & on the opposite face, the bases of two cells. He states that first the outlines of these 3 primordial cells are arched, (section [DIAGRAM OF CURVED ARCH] ) & then made angular ( [DIAGRAM OF POINTED ARCH] ). Now what I what I want so much to see is this rudiment of the comb in this state. I believe when the arched bases of the cells are made angular, the bases of other adjoining cells have just been commenced. The hexagonal tube or prism has not been at this period hardly been begun & all must be very minute. (See the letter)

Darwin was probably particularly concerned about the pentagonal cell wall that is constructed out of the original curved arch, since Huber’s diagrams show this transition clearly. Darwin thought that the arch was not made angular until the hexagonal cells of the second row had been begun by the bees making further hemispherical scrapes. However, he may also have been concerned about the angular bottoms of the cells that were excavated out of the original hemispherical scrapes. The bottom of a hexagonal cell is a pyramidal structure that fits neatly against the bottoms of three cells on the other side of the wall. Darwin thought that this angular structure too was only formed as a result of the presence of other cells.

Challenging Huber was a serious business he had laid the scientific foundations of the study of the honey-bee, despite being blind from the age of 15. His work was carried on with the help of his wife and manservant, and depended on minute, repeated observations. He too was sceptical about the view of the bee as master geometrician explaining how the necessary angles might arise from the initial circular workings of the bee, he asked, ‘May we not deduce from the preceding facts, that the geometry, which apparently embellishes the productions of these insects, is rather the necessary result than the principle of their proceedings?’ (Huber 1841, p. 269.)

Darwin asked Tegetmeier to observe the beginning of the comb and, having been lent a glass hive by a friend, did the same himself he also asked Tegetmeier to look out for isolated cylindrical cells (letter to W. B. Tegetmeier, 5 June [1858]). Tegetmeier suggested putting a piece of wax in the hive for the bees to work on. Using this method, Darwin ‘got some excavated hemispherical bases in artificial wax—hurrah!’ and was thinking of ordering another hive from Tegetmeier, and buying a swarm (letter to W. B. Tegetmeier, 8 [June 1858]). (Articial wax is probably beeswax, but a block of wax added to the hive rather than wax that the bees in hive were producing and working themselves.)

Darwin tried three different experiments with bees’ cells at Down that he reported in Origin. In one, he put a thick block of wax into the hive. ‘The bees instantly began to excavate minute circular pits in it: and as they deepened these little pits, they made them wider and wider until they were converted into shallow basins, appearing to the eye perfectly true or parts of a sphere, and of about the diameter of a cell. It was most interesting to me to observe that wherever several bees had begun to excavate these basins near together, they had begun their work at such a distance from each other, that by the time the basins had acquired the above stated width (i.e. about the width of an ordinary cell), and were in depth about one sixth of the diameter of the sphere of which they formed a part, the rims of the basins intersected or broke into each other. As soon as this occurred, the bees ceased to excavate, and began to build up flat walls of wax on the lines of intersection between the basins, so that each hexagonal prism was built upon the festooned edge of a smooth basin, instead of on the straight edges of a three-sided pyramid as in the case of ordinary cells.’ (Origin, p. 223.) The cells were built up in a hexagonal shape when their bases intersected with those of other cells but the pyramidal bases were apparently not built, since there was no pressure to accomodate cells on the other side of the wax, which was a thick block.

These experiments were repeated in 2009 by John Williams, a master beekeeper who maintains an observation hive at Down House during the summer. In these photographs, it is possible to see how the bees tended to clump their cells and build them up into hexagons but the circular foundations of seven adjacent unfinished cells are also visible in the second photograph next to the left-hand clump of cells.

Secondly, Darwin put a thin piece of vermilion wax in the hive, a ‘narrow, knife-edged ridge’.

The bees instantly began on both sides to excavate little basins near to each other . . . but the ridge of wax was so thin, that the bottoms of the basins, if they had been excavated to the same depth as in the former experiments, would have broken into each other from the opposite sides. The bees, however, did not suffer this to happen, and they stopped their excavations in due time so that the basins, as soon as they had been a little deepened, came to have flat bottoms and these flat bottoms, formed by thin little plates of the vermilion wax having been left ungnawed, were situated, as far as the eye could judge, exactly along the planes of imaginary intersection between the basins on the opposite sides of the ridge of wax. In parts, only little bits, in other parts, large portions of a rhombic plate had been left between the opposed basins, but the work, for the unnatural state of things, had not been neatly performed. (Origin, pp. 229–30.)

In other words, by starting their excavations in the correct places, the bees produced an approximation to the pyramidal bottoms of cells simply by ceasing to excavate when they were about to break through into another cell.

In his third experiment, Darwin covered edges of the walls of a hexagonal cell, or the extreme margin of a growing comb – the place in which the cells are furthest from hexagonal – with a thin layer of vermilion wax.

‘I invariably found that the colour was most delicately diffused by the bees . . . by atoms of the coloured wax having been taken from the spot on which it had been placed, and worked into the growing edges of cells all around’ (Origin, p. 232).

The bees were continually rebuilding unsatisfactory cells as the comb grew outwards.

The experiments with vermilion wax have also been repeated by John Williams. A ‘knife-edge’ ridge of wax is sometimes applied to the top bar of a hive to encourage the bees to build in the right place, and it is likely that the ‘knife-edged ridge’ used by Darwin was a similar arrangement. The results of this experiment show something that Darwin does not mention, but that beekeepers would no doubt take for granted: the bees add their own wax to the vermilion wax as they work to extend it. The vermilion (as Darwin found in his third experiment) becomes thoroughly mixed with uncoloured beeswax over most of the resulting comb. This is now an on-going experiment and can be seen in the observation hive at Down House during the summer. The result is shown in the photograph below.

In August 1858, Waterhouse’s remarks at the 5 April meeting of the Entomological Society (see extended quotation, above) were reprinted in theZoologist. He no doubt began to regret the wording of his suggestion that hexagonal cells were a necessary consequence of packing cylinders in a small space, as some readers may have understood him to mean that the hexagons were formed as a result of lateral pressure on the comb, a theory that had been current and that had been dismissed by Lord Brougham. At a meeting of the Entomological Society on 7 July 1858 (Proceedings of the Entomological Society of London n.s. 5 (1858–61): 34–5), the issue was discussed. John Edward Gray, the president, using vermicelli as an analogy, supported the idea that compressed cylinders became hexagonal prisms, and added, with characteristic acerbity, that he ‘considered the attempt made by Natural Theologians to prove that the formation of an hexagonal rather than a cylindrical cell indicated the possession of a greater degree of Divine wisdom bestowed on the insect, was the greatest piece of humbug they had ever brought forward.’ Frederick Smith however had apparently made paper cylinders and failed to compress them into hexagons. Waterhouse reviewed the latest controversies in his letter to Darwin of 2 August 1858. The notion that the theory of hexagonal bee cells being formed from cylinders depended on actual physical compression was to dog responses to Darwin’s own theory as well.

Also in August Darwin received a hive from Jamaica, and observed that the cells were larger than those made by European bees. He at once sent for specimens of the actual bees, probably curious to see whether the size of the cell was proportionate to the size of the bee. This would suggest that the famous regularity of bee cell sizes might have a simple explanation. (Letter to Richard Hill, 8 August [1859].) Much later, Jeffries Wyman wrote to Darwin from Cambridge, Massachusetts, that he found that bee cells were not as regular as some had supposed them to be their measurements varied, the pyramidal bases of the cells sometimes had four, not three rhombs, and the transition from worker to drone cells (these are different sizes) was carried out in different ways (letter from Jeffries Wyman, 11 January 1866).

Concurrently with his work on cell formation, Darwin was thinking about why the hexagonal structure was advantageous to bees. It was already well known that the hexagonal cells stored the greatest possible amount of honey and pollen with the least possible expenditure of wax, but in September 1858 Tegetmeier was able to give Darwin figures for just how costly wax production was to bees. He calculated that 15lb of sugar was consumed in the secretion of 1lb of wax. Tegetmeier also confirmed Darwin’s conclusions about the building of cells. (Letter to W. B. Tegetmeier, 8 September [1858].)

In Origin, in November 1859, Darwin published a theory of cell-building that differed from both Huber’s and Waterhouse’s. Huber had believed that although the bees began by making curved arches in the wax partly following the outline of the first hemispherical depressions that they dug into the wall of wax, these were swiftly converted into angular (pentagonal) structures and followed in the second row by hexagonal structures. Waterhouse believed that the bee built the cells up in circles, and that when the circle of one bee threatened to break into the circle of another, they both stopped excavating at the nearest point and switched their attention to excavating the wax where there was no imminent danger of breaking through, thus making hexagons. Darwin, however, had observed that the bees began by making hemispherical scrapes in the wax, and that where the scrapes intersected, they built or excavated straight walls, thus building up hexagonal prisms. Cells at the edge of the comb tended to have roughly curved walls until further cells were built and they were transformed into more regular hexagons.

Thus, in Origin, Darwin explained the development of the honey-bee’s cell-building instinct from simpler forms (the less organised, round cells of other insects), and explained their method of building based on the repetition of simple actions and feedback from simple sensations, rather than on the application of geometry. His observations, and those of Tegetmeier and others, had proved that bees did not build angular structures except at the intersections between cells that they continually rebuilt the roughly finished cells at the margins of the comb into more regular structures as the comb grew outwards that there were measurable advantages to the regular structures of the honey-bee over the more haphazard structures of other bees in times of scarcity and that the unfailing regularity and precision of the bee cell was, when precise measurement was bought to bear, a myth.

In 1865, Darwin received a letter from Edward Cresy (letter from Edward Cresy, 10 September 1865), in which Cresy sent as an illustration of Darwin’s bee-cell theory a description of a plum pie, the crust of which came out of the oven ‘completely mapped out with hexagonal articulations’. ‘By guesswork each plumb should have punched just a swelling & then a round hole for itself like a round shot through a plank but I suppose the strain came to equally on all part of the crust so the spherical plumbs laid the foundation, without any instinctive knowledge of a series of regular hexagonal combs’, Cresy concluded: the plums didn’t need to know how to do it any more than the bees did.


Optimality of the Comb Structure

The honeybee comb is, at first sight, a wonder of animal architecture. In all known species of honeybees, the structure is a double sided sheet of tessellated hexagonal cells where the base (common to both sides) is formed from three rhombi (Figure 2). Obviously, hexagonal cells are more suitable than the round cells used by, e.g., bumblebees, since the latter arrangement wastes a lot of space between cells. Square or triangular cells would have no gaps between cells, but since the larvae to be raised in the cells are neither square nor triangular in cross-section, space would be wasted inside the cells. Thus, hexagonal cells are intuitively suitable, and in fact some species of wasps build them too, albeit of “paper” (chewed wood) rather than wax. But no species of bee except honeybees also builds double-sided hexagonal combs — another notable strategy to save space and material. The bottom of each hexagonal cell has the shape of a pyramid (again a more efficient solution than a square bottom), and the two sides of the comb interface perfectly with one another through these pyramid-shaped bases of the cells. Unlike the combs of some stingless bees, the honeybee comb has to be vertical so that honey can be stored on both sides without dripping out, and the cells of the comb are tipped slightly downward from the opening to the base (Figure 2). In cavity-nesting species (Apis mellifera and A. cerana), multiple combs are built in parallel, leaving just enough space for workers to move about freely (Figure 3). This is despite the fact that cavities in which these species of honeybees nest naturally (e.g., hollow trees) are highly irregular in shape (not like the cuboid boxes beekeepers supply them with). Beyond the intuitive arguments in favor of a double sided hexagonal structure, it has been pointed out that the structure is in fact a mathematically optimal, or close to optimal, solution to economizing on building material while maximizing storage space (Kepler, 1611 Huber, 1814/1926 (Langstroth, 1853). Huber (1814/1926, p. 106) reported that the rhombus angles could beneficially be altered by modifying angles by 10 min. Analysis of the geometry of tessellated polyhedrons (Tóth, 1964) showed that the most economical cell construction (volume per wall area) comprised a hexagonal cell with a base formed from two squares and two hexagons. However, the saving would be less than 0.35%, at the expense of greater complexity of construction. By the use of self-aligning soap bubbles (Weaire and Phelan, 1994) it was shown that at a certain wall thickness, the ideal solution would switch from the optimal arrangement proposed by Tóth to that favored by the bees. We can thus infer that the structure is indeed very close to the theoretical optimum.

FIGURE 2. Schematic structure of hexagonal wax cells and double-sided honeycomb (computer graphic). Top: three walls and the three rhombi (forming the base of a cell) as discrete components. Central: a single cell, joined to three on the other side. The wall of the single cell is shown cutaway to reveal the cell base. Note that the cells slope slightly from the opening on each side, down toward the comb spine. The lower image shows a single drone cell, approximately 30% larger than cells built for worker larvae (as shown in the top panels).

FIGURE 3. Comb construction of multiple parallel combs (computer graphic). The sketch shows how normal comb constructions of cavity-nesting honeybees where comb is begun attached to the top surface of the cavity, and then gradually extended downwards. Multiple combs will be grown, each roughly parallel and separated by a gap sufficient for the bees to work both. Note that the first line of cells (the 𠇏oundation”) is differently shaped to other cells. At the lower end of the construction, partially constructed cells come in a large variety of shapes, and individual workers can in principle continue from any partial construction.


Contents

Chapter 1: Introduction
Chapter 2: Out of the Dark
Chapter 3: A Difficult Diet
Chapter 4: The Chemistry of Social Regulation
Chapter 5: The Reproductive Machine
Chapter 6: The Worker Bee in a Variety of Guises
Chapter 7: Diseases, Pests and Parasites
Chapter 8: The Idiosyncrasies of Sex and Reproduction
Chapter 9: Apiculture and Long Suffering Bees
Chapter 10: Dark Sides of Honey Bee Science
Chapter 11: A Silver Lining for the Future of Bees?


Honeycomb

By: Peter Borst

H ow Do They Do This So Well?

Historical Notes

Since ancient times, people have marveled at the society and the architecture of the honey bees. The following excerpt from “The Fables of Pilpay” gives a glimpse of the thinking two thousand years ago.

They have a king among them, who is bigger than the rest, and whom they all obey he resides in a little square apartment, and has his vizirs, his porters, his Serjeants, and his guards the industry of these, and all his other officers, and people in general, is such, that they frame every one for themselves a little six-cornered chamber of wax, the angles of which differ not at all in shape or dimensions, but are so exactly made to answer one another, that the most expert geometrician could not range them with more regularity (Gaulmin, 1818).

It wasn’t until the 1600s, that Jan Swammerdam established the fact the the big bee is a female, now called the queen. But the marvel of the geometry of the honeycomb has stayed alive in people’s imagination. Mathematicians computed the angles of the cells and Charles Darwin wrote, “the comb of the hive-bee, as far as we can see, is absolutely perfect in economizing labor and wax.”

This became a major puzzle for him to understand how natural selection could have produced the honey bee which appears to have arrived at this complex solution to building the most efficient structure to house not only themselves but their resources of honey and pollen, using only beeswax, which they produce in their own bodies. The explanation that bees rely on divine guidance made more sense to people at the time.

In 1852, William Kirby described bees as those Heaven-instructed mathematicians, who before any geometer could calculate under what form a cell would occupy the least space without diminishing its capacity, and before any chemist existed to discover how wax might be elaborated from vegetable sweets, instructed by the Fountain of Wisdom, had built their hexagonal cells of that pure material, had closed them at the bottom with three rhomboidal pieces, and were enabled, without study, so to construct the opposite story of combs, that each of these rhomboids should form one of those of three opposed cells, thus giving strength to the structure, that in no other place, could have been given to it (Kirby, 1852).

The Geometry of the Cells

Looking at nature, we see the recurrence of geometric shapes, especially the hexagon. Hexagons are notable in geology, such as the six sided pillars of basalt formed by the slow cooling of lava into fantastic rock cliffs, such as “The Devil’s Postpile” in California and “Fingal’s Cave” in Scotland. More ephemeral, but equally enchanting, are the intricate structures made by aggregates of bubbles. Bubbles, as we all know, form spheres out of the tenuous soapy water membranes. When they are piled up, the surfaces where they touch each other become flat. If the bubbles are nearly the same size, they form neat piles of hexagons.

Further, when multiple bubbles intersect, shapes arise that are very similar to the intersection of cells at the midrib of the bees’ comb. Early observers moved past the study of the hexagons to the base of the comb, which consists of equally sized diamonds, or more correctly – rhombs. From “The Garden of Cyrus”:

And the Combes themselves so regularly contrived that their Mutual Intersections make three Lozenges at the Bottom of every Cell which severally regarded make three Rows of neat Rhomboidall Figures, connected at the Angles, and so continue three several Chains throughout the whole Comb (Browne, 1736).

While it’s plain enough that a hexagon must contain six equal angles of 120° each, the angles of the little rhombs are a bit more difficult to predict. Early observers found the angles are 110° and 70°. If the larger angle was 120°, the shape of the base would be flat, like manmade honeycomb structures such as cardboard panels. A much smaller value would increase the depth of the cells. But with the bees, the base forms a shallow three-sided pyramid shape that shares its rhombs with three cells on the other side of the comb.

Why this should be so can easily be explained by physics and mathematics, but how did the bees hit upon this shape and replicate it so faithfully for millions of years? A clue lies in the cells of other species of bees and wasps. Solitary Hymenoptera make single cells out of various materials such as leaves or mud, in which to place a single egg. When bees and wasps congregate, they make nests consisting of many cells. With the bumble bee, we find piles of small waxen spheres used for storing honey and raising the young.

More organized bees such as the stingless bees (Melipona) build elaborate combs, which superficially resemble honey bee combs but with important differences. These bees, and also wasps, make combs with the cells pointing only downward, the comb is not two sided. Looking only at the bases, we see half spheres being used, like groups of bubbles. On the undersides the cells are tightly packed, in the familiar hexagonal rows.

Physicists Step Into It

More recently, a group of scientists theorized that the shape of the honey bee comb is accidental and that honey bees are actually trying to make round bottomed cylinders out of wax. In the hot environment of the the hive, the wax melts and flows into the shapes we see, the same way that bubbles or other fluids organize into geometric shapes.

It certainly cannot be the case with wasps, which make their cells out of paper formed from collected plant fibers. They begin with one hexagonal round bottomed cell and surround it with many more of the same until the comb reaches a certain size. Then they build a parallel comb beneath the first and surround the whole thing with an outer shell of paper. This material is never liquid and hexagons are built from the start.

Responding to the idea that the wax becomes fluid in the hive, other researchers took accurate measurements of the internal temperatures, and concluded that they never reach those necessary for wax to flow. Not only that, but it’s pretty obvious that if they did the wax would melt and the comb would fall apart. Sometimes theory gets too far removed from observation.

There was quite a controversy, generating papers such as “Honeybee combs: construction through a liquid equilibrium process?” in 2004, which asserted that “the comb structure is a result of a thermoplastic wax reaching a liquid equilibrium.” This was followed in 2012 by “Hexagonal comb cells of honeybees are not produced via a liquid equilibrium process” which countered: “the geometry of the developing cells is generated by mechanical shaping and not by the self-organised process postulated by the liquid equilibrium hypothesis.”

The Observations of Huber

François Huber may have been blind, but his study of the comb building behavior of honey bees is without doubt the most painstaking, clear and definitive, despite being carried out two hundred years ago. He began using glass walled hives to scrutinize the internal workings of the hive, employing a trusted and able assistant upon whose eyesight he depended. Being frustrated by the fact that bees generally obscure the view of the comb building, he invented a frame hive which allowed the entire inside of the colony to be observed in real time.

With this access, he could gently brush the bees off the combs they were constructing and study their progress over hours and days by returning to the same comb over time. In 1821 he published “New Observations on the Natural History of Bees,” in which he described comb construction in marvelous and complete detail. His work can be easily verified by anyone with a hive of bees and adequate patience. In his words:

The cells of bees consist of two parts, a prismatic hexagonal tube, and a pyramidal bottom. The latter, which must be considered to be most delicate and essential part of the work, is composed of three equal lozenges, similar, uniting in a common centre, and forming a slight cavity by their reciprocal inclination. Their depression into one face of the comb makes a projection on the other, there corresponding to three cells partially common to the whole (Huber, 1821).

The Building of the Combs

Using details from Huber and others, we know that the procedure for building the combs commences when worker bees form a curtain or “festoon,” either by clinging to the top of the cavity in which they find themselves, or the underside of a wooden bar provided by a beekeeper, or else the lower edge of a previously constructed comb. Each row of bees clings tightly to the one above and they face each other, with the aim of building a two sided comb between themselves. Once the comb is commenced they can hang on it. Wax producing bees engorge with honey and the wax forms in glands in their abdomen. The pure beeswax appears in the form of a “scale” or flake, which they take up with their mandibles and begin to chew it like a piece of gum, adding saliva.

This is the very point at which we can see if the bees make cylinders which then morph themselves spontaneously into prisms. The first shapes to appear are all flat, thin supports built down from the top and are inflected at precisely the correct angles from the very start. It looks as if the bees are working from some sort of a blueprint which contains the shapes, angles and distances. But soon it becomes apparent from close observation that no individual bee works for long on the project. They move here and there, starting some work and continuing that started by others. It seems clear that they simply assess the situation in progress, continue as appropriate, and scurry off.

Blueprint or Stigmergy?

The concept of stigmergy was developed by French zoologist Pierre-Paul Grassé about 1959. This idea proposes that there is not a blueprint or overall design at all. It proposes that each bee works independently, responding with a set of reflexive rules which are a sort of “if this, then this” procedure. Computer programmers used the acronym IFTTT they create branching sequences of procedures that follow one after the other creating an emergent result based on the variable input.

This model can account for why the comb can be constructed in such consistently repeated symmetry when the space is unobstructed, such as inside the wall of a house. Bees can construct combs many feet tall or wide that are perfectly flat and made up of unbroken swaths of hexagons. However, as the need arises, they can change the direction of the comb, winding it to fit irregular spaces, around obstructions, etc. They have the capacity to improvise as needed and to create novel and unexpected shapes and solutions. They do not proceed mechanistically and blindly like a train on the rails, but adjust themselves to whatever space they have occupied.

Stigmergy further supposes that honey bees are not really coöperating in the way that people tend to romanticize that they do. It suggests that each bees is working independently, not really cognizant of the whole structure, or “purpose” of the hive. The great form that we see and admire is the result of thousands of workers proceeding independently, guided by behaviors that have led to success in the past, and have been preserved through time by evolution, which tends to keep successful adaptations while sacrificing those creatures which fail to adapt. Oldroyd and Pratt describe it like this:

Close observation of honey bees shows that each cell emerges from small contributions by many workers rapidly coming and going at the building site. Stigmergy allows any worker to pick up where the last one left off, as long as every worker follows the same rules (Oldroyd, 2015).

Darwin’s Conundrum

Charles Darwin took many years to construct his theory of evolution by natural selection. During this time he challenged himself by looking beyond the apparent results that evolution had produced, to the obstacles his theory would have to overcome to be fully explanatory. One of these was the honeycomb, which had always been seen as an example of the expression of God’s plan by His creatures.

Not only did Darwin intend to challenge this firmly entrenched system of beliefs, but he needed to supplant it with a new system in which people could believe, if it offered a sufficiently strong explanation. In his own words, “I am half mad on the subject to try to make out some simple steps from which all the wondrous angles may result.” According to Sarah Davis:

In the Origin, Darwin wanted to show that simple, repeated actions, such as the excavation of excess wax, could result in complicated structures. This is a lesson that applied not only to honey bees, but also to other creatures’ structures, such as spiders’ webs, birds’ nests and beavers’ dams. The message from Darwin was that instinct could result in seemingly intelligent actions and behaviour, despite the animal not actually reasoning about what it is doing (Davis, 2004).

In order to obtain firsthand observations of honey bees, Darwin made friends with William Tegetmeier, who was an experienced apiarist. They corresponded regularly between 1855 and 1881 Darwin’s son Francis remarked that his father had full trust and respect in the judgement and knowledge of Tegetmeier. Many of the observations were made at the “Experimental Bee House for exhibiting the working of scientific and improved hives” operated in the 1860s by the Apiarian Society of London. It contained numerous glass walled hives so that bees could be observed regardless of the weather outside.

Darwin cited Tegetmeier in his book when he discussed the economy of wax production. Tegetmeier told him that nectar is seldom abundant and that great quantities of it are required to produce small amounts of beeswax. As much as twelve to fifteen pounds of dry sugar would be converted into one pound of wax, he said. Further, even greater quantities would be needed for winter consumption, so there was a strong incentive to use as little nectar as possible to make wax and also to store it in a structure which has the strength and integrity to support the weight of the honey and the bees, which cling to the combs.

Reinforcements

Pure fresh beeswax has great tensile strength, but over time the combs are modified in ways that greatly increases it. Referring again to Huber, he described in detail how the bees gather propolis, which is sap and resins from certain trees, and apply it to the surface of the completed combs. Much attention has been paid to the antiseptic properties of propolis and no doubt the colony benefits from that, but it appears that the chief virtue of it is that it can be used to improve the wax.

Propolis requires much less energy to produce, having only to be gathered and applied where needed. They use it as a sort of varnish, not only on the combs but on all the interior surfaces of the hive. Sometimes they build great structures such as entrance reducers, making the opening to the hive much smaller and easier to guard. Many new beekeepers are concerned by the darkening of the fresh white wax, which over time becomes yellowed, brown and finally dark black. This is mainly caused by the propolizing of the combs. Eventually, the combs become very tough and durable, much less prone to breaking than newly built combs.

The field of beekeeping was revolutionized by the invention by Langstroth of a practical bee hive consisting of boxes fitted with moveable frames in which the bees are induced to build their combs. This was quickly followed by two other revolutionary inventions: the centrifugal honey extractor and honeycomb foundation. While tough old combs could have the honey spun out them using the new machine without damage, new combs were tender and often broke apart in the machine.

The solution was the manufacture of honeycomb foundation, sheets of pure beeswax imprinted with cell bases, that could be mounted in the wooden frames and reinforced with wire. Combs built upon this foundation had the added advantage of being less liable to sag over years of use, although they did tend to stretch and buckle eventually. This fact kept inventors working for a century, trying all sorts of so-called improvements including laminating the beeswax on both sides of a sheet of paper. In the 1920s, the bee magazines were abuzz with talk about bee combs made of aluminum. From the journal “The Western Honey Bee,” April 1922:

These combs present a number of advantages which will appeal to any beekeeper. Drones are effectively controlled. Danger from destruction of combs by wax moth is eliminated. Melting down of combs is rendered impossible. These combs will not break or “buckle” in the extractor, and because the baskets can be revolved more vigorously, they can be extracted much more cleanly (Biggs, 1922).

Aluminum combs proved to be a short-lived fad, I couldn’t find any references to them after 1930. But that didn’t stop the inventors, by the 1960s you could purchase foundation that had embedded wires, or laminated with plastic film.

Finally, in 1971 Paul Pierce patented an entire frame and foundation manufactured out of hard plastic. These days the most popular configuration is a traditional wood frame fitted with a hard plastic comb base, which is lightly sprayed with beeswax coating to make it more acceptable to the honey bees. They faithfully build their comb upon this sturdy foundation, making it nearly indestructible and useful for many decades.

Parting Words

I would like to conclude with the words of Anna Comstock – who in 1908 became the first female assistant professor at Cornell University – from her “Handbook of Nature-study:”

Some have tried to detract from bee skill, by stating that the six-sided cell is simply the result of crowding cells together. Perhaps this was the remote origin of the hexagonal cell but if we watch a bee build her comb, we find that she begins with a base laid out in triangular pyramids, on either side of which she builds out six-sided cells. A cell just begun, is as distinctly six-sided as when completed (Comstock, 1918).

Works Cited

Bauer, D., & Bienefeld, K. 2013 Hexagonal comb cells of honeybees are not produced via a liquid equilibrium process. Naturwissenschaften, 100(1), 45-49.

Biggs, F.W. 1922 The Value of Aluminum Combs. The Bee-keepers’ Review, Volume 35.

Browne, Thomas. 1736 The garden of Cyrus. London.

Comstock, A.B. 1918 Handbook of nature-study for teachers and parents: Based on the Cornell nature-study leaflets, with much additional material and many new illustrations. Comstock Publishing Company.

Davis, S. 2004 Darwin, Tegetmeier and the bees. Studies in History and Philosophy of Biological and Biomedical Sciences, 35(1), 65-92.

Gaulmin, G., & Harris, J. 1818 The Fables of Pilpay. Baldwin Cradock, and Joy,. London.

Huber, F. 1821 New observations on the natural history of bees. W. & C. Tait, and Longman, Hurst, Rees, Orme, and Brown, London.

Kirby. 1836 On Wasps and Bees. The Saturday Magazine. Volumes 9-10 – Page 238.


ELI5: How do honeycombs and beeswax form nearly perfect hexagons?

The hexagon is a very spatially efficient shape which uses less material. Try this experiment: wash your hands with soap, and spread the lather out on a flat surface. The bubbles will spontaneously acquire hexagon-like shapes and arrange themselves neatly. You see the same patterns in basalt columns and mudcracks because it fills the space using little energy.

Or think of it this way: if you try to pack balls of the same size into a flat tray, they’ll naturally pack into a “honeycomb” pattern. The bees just pack it in as best they can, and this is the best they can because geometry. They usually include defects (where a bee created a cell out of the pattern), but most of them do it right.

Actually, they sort of don't. The bees actually make circles, but as they build the hive the pressure of the circles on each other presses the sides flat against one another.

If you get a circle and surround it with other circles, then press them inward, they will flatten the edges where they contact. This happens to the whole hive wall as it is built and produces hexagons, which are fortunately an incredibly strong shape so the bees kept making the hive the same way.


Not just for the bees, honeycomb designs are incredibly versatile when it comes to the construction of different items.

The perfectly symmetrical shape of the hexagonal pattern works to create a strong structural skeleton that is both sturdy and lightweight, a unique combination that is practical for architectural designs as well as furniture and accessories. Without even bothering to conceal this skeletal frame, designers know that the playful honeycomb pattern is appealing to most people, with its crystallized yet organic appearance. People who are attracted to the imagery of sweet sensuous honey and happily buzzing nature will be drawn towards things with a honeycomb design.

Both functional and attractive, structural honeycomb designs and pretty honeycomb prints are being seen in jewelry, home decor, furniture, buildings and artwork.


How honey bees make hexagons

F or as long as mankind has pursued honey bees, he has been fascinated by the shape of comb cells. Since that first discovery, many types of intelligence have been ascribed to honey bees that might result in their extraordinary ability to build perfect hexagons. If you ever tried to draw a regular hexagon, one with equal sides and equal angles, you know how difficult it can be.

But the most plausible theory is that honey bees do not actually build hexagons. Instead, they build wax cylinders that conform to the shape of their bodies. They take the secreted wax flakes, soften them with their mandibles, and assemble them in a tube around themselves. For worker cells, they build a size that just fits: small bees build small cells, and larger bees build larger cells.

The flattened areas result where two cells touch each other. The most obvious example can be seen in soap bubbles. Wherever two bubbles touch, a flat wall is formed. Imagine building row after row of tightly packed cylinders. If you warmed them up so the walls flowed like liquid, they would develop flat sides wherever they touched, just like soap bubbles.

Researchers now believe that as the cells are constructed they are warmed by the bees’ bodies which causes the common sides to flow together and form a flat wall. Because they are closely packed, the rows form a series of hexagons that we recognize as honeycomb.

In their paper, “Honeybee combs: how the circular cells transform into rounded hexagons” (2013), B. L. Karihaloo, K. Zhang, J. Wang report that the transition from round sides to flat can happen in just seconds, depending on the temperature of the wax.

Some of the most compelling evidence for this theory can be found not in the perfectly-shaped cells but in the imperfect ones. For example, wherever the cells are not so tightly packed, such as at the intersection of worker cells and drone cells, you can see many other shapes. Four- or five-sided cells are not uncommon in this area as are cells with random shapes and cells stretched in odd ways in order to meet another cell.

Also telling are the shapes of supersedure cells and swarm cells. Since queen cells are built separately and do not touch other cells, they remain cylindrical. Even queen cells that are started on hexagonal foundation soon depart from the embossed shape and become cylindrical.

In nature, honey bees are not the only insect to build hexagonal nests. Some of their kin, including various wasps, also build hexagonal cells—proof that the hex shape is not exclusively a honey bee thing.

Where soap bubbles stick together, the intersection is flat. Pixabay photo.

Many of the social wasps also build hexagonal cells, such as these aerial yellowjackets. © Rusty Burlew.