.
*a honey-comb is a ‘mass’ of ‘hexagonal wax cells’ built by ‘honey bees’ in their ‘nests’ to contain their [‘larvae’ / stores of ‘honey’ / ‘pollen’]*
.
(‘beekeepers’ may remove the entire ‘honeycomb’ to harvest ‘honey’)
(‘honey bees’ consume about ‘8.4 pounds’ (= ‘3.8 kilograms’) of ‘honey’ to secrete ‘1 pound’ (= ‘454 grams’) of wax, so it makes ‘economic sense’ to return the ‘wax’ to the ‘hive’ after ‘harvesting’ the honey, commonly called “pulling honey”or “robbing the bees” by ‘beekeepers’)
(“…by the bees as well?”)
[the ‘structure’ of the ‘comb’ may be left basically ‘intact’ when ‘honey’ is ‘extracted from’ it by ‘uncapping’ + ‘spinning’ in a ‘centrifugal machine’ (called the ‘honey extractor’)]
(if the ‘honeycomb’ is too ‘worn out’, the ‘wax’ can be ‘reused’ in a number of ways, including making ‘sheets’ of ‘comb foundation’ with a ‘hexagonal pattern’)
(such ‘foundation sheets’ allow the ‘bees’ to build the ‘comb’ with less effort, and the ‘hexagonal pattern’ of ‘worker-sized cell bases’ discourages the ‘bees’ from building the larger ‘drone cells’)
.
(‘artificial honeycomb plate’ where ‘bees’ have already completed some ‘cells’…)
.
(‘broodcomb’ becomes ‘dark’ over ‘time’, because of the ‘cocoons’ embedded in the ‘cells’ and the ‘tracking’ of many ‘feet’, called ‘travel stain’ by ‘beekeepers’ when seen on ‘frames’ of ‘comb honey’)
(‘honeycomb in the “supers” that are not allowed to be used for ‘brood’ (e.g. by the ‘placement’ of a ‘queen excluder’) stays ‘light-colored’)
(numerous ‘wasps’ (especially ‘polistinae’ + ‘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’)
.
(‘natural honeycombs’ on a ‘building’) –>
–
–
(‘honeycomb’ with ‘eggs’ and ‘larvae’…)
.
.
(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’)
.
(*’closeup’ of an abandoned apis florea nest in ‘thailand’*…)
(note 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’)
(the ‘axes’ of ‘honeycomb cells’ are always ‘quasi-horizontal’, and the ‘non-angled rows’ of ‘honeycomb cells’ are always ‘horizontally’ (not ‘vertically’) aligned)
(thus, each ‘cell’ has ‘2 vertical walls’, with “floors” and “ceilings” composed of ‘2 angled walls’)
(2 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 conjecture’, this was given by ‘jan brożek’ and ‘proved’ much later by ‘thomas hales’)
(‘proved’ how?)
(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 bubbles’)
(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’ (albeit ‘3-dimensional’ and ‘little-noticed’))
(the ends are ‘trihedral’ (i.e., ‘composed of 3 planes’) sections of ‘rhombic dodecahedra’, with the ‘dihedral angles’ of all ‘adjacent surfaces’ measuring 120° (the ‘angle’ that minimizes ‘surface area’ for a ‘given volume’)
.
(the ‘angle’ formed by the ‘edges’ at the ‘pyramidal apex’ (known as the ‘tetrahedral angle’) is approximately 109° 28′ 16″ (= arccos(−1/3)))
.
.
*👨🔬🕵️♀️🙇♀️*SKETCHES*🙇♂️👩🔬🕵️♂️*
.
.
.
.
.
💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
.
.
*🌈✨ *TABLE OF CONTENTS* ✨🌷*
.
.
🔥🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥🔥