Hexagons in Na­ture

‘With­out hexagons, you would be a pud­dle of goo’

Country Life Every Week - - Contents -

E ex­pect Na­ture to be a messy busi­ness, es­chew­ing straight lines and sim­ple ge­ome­tries and con­sist­ing only of or­ganic lumps and bumps, ran­dom ar­range­ments or sim­ple chaos, yet the res­o­lutely Eu­clidean hexagon ap­pears with re­mark­able fre­quency in the nat­u­ral world. From the gar­gan­tuan to the sub-mi­cro­scopic, hexagons are ev­ery­where. One won­ders why.

It’s all down to ef­fi­ciency, util­ity and an oc­ca­sional abil­ity to form al­most in­ad­ver­tently. The hexagon is sym­met­ri­cal, sim­ple and en­joys the rare skill of al­low­ing it­self to tes­sel­late (tile). Fur­ther­more, as tes­sel­lat­ing shapes go, it’s supreme as it can cir­cum­scribe the largest area for a given perime­ter.

The most fa­mil­iar nat­u­ral hexagon is that of the honeycomb. How bees can con­struct so com­plex a stor­age fa­cil­ity has ex­er­cised the minds of nat­u­ral­ists for cen­turies. The En­cy­clopae­dia Bri­tan­nica of 1797 notes that, of the three reg­u­lar tes­sel­lat­ing shapes—equi­lat­eral tri­an­gle, square and hexagon—the ‘hexagon is the most proper, both for con­ve­nience and strength. Bees, as if they knew this, make their cells reg­u­lar hexagons’.

How­ever, bees, as the writer im­plies, are not the ge­o­me­tri­cians they are re­puted to be—rather, the honeycomb is the nat­u­ral re­sult of fol­low­ing

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some sim­ple rules. Con­struct bee­di­am­e­ter tubes of wax, plac­ing them as closely to­gether as pos­si­ble. When com­plete, climb in­side and raise your body tem­per­a­ture. The heat soft­ens the cells, which then re­lax against their neigh­bours into a hexag­o­nal shape. And that’s it, a strong and ef­fi­ciently ca­pa­cious larder-comenurs­ery, made to sim­ple rules.

A sim­i­lar ef­fect is seen the tubal homes of the honeycomb worm,

Sa­bel­laria alve­o­lata. Th­ese truly hideous crea­tures con­struct their abodes from glued-to­gether sand par­ti­cles. In low-den­sity pop­u­la­tions, they form round tubes. How­ever, if real es­tate is at a premium, they be­come tightly packed to form hexagons, cre­at­ing crumbly, sandy reefs seen on the seashore at low tide.

This tiling pat­tern is also some­times found on the skins of fruit. The most strik­ing be­longs to that denizen of ho­tel foy­ers, the Swiss cheese plant (de­light­fully, Mon­stera de­li­ciosa). It’s the shape of a corn cob and cov­ered with dis­tinct green, hexag­o­nal scales. The de­li­ciosa part of its Latin name, by the way, only ap­plies when the fruit ripens and the scales be­gin to fall away, as it's fairly toxic un­til then. Breadfruit shows the same mark­ings.

An­i­mals also have hexag­o­nal struc­tures. The sur­face of the ex­tinct co­ral Cy­atho­phyl­lum hexagonum is made en­tirely of hexagons, as are the skele­tons of many di­atoms. The lat­ter are exquisitely con­structed, some­times form­ing a flat­tened sphere, some­times a tiny tri­an­gle, all seem­ingly made from the finest lace.

We may be just a lit­tle sur­prised to see so many hexagons in liv­ing things, but, in in­or­ganic struc­tures, they are more to be ex­pected. Crys­tals come in many shapes, re­flect­ing those of their con­stituent atoms or mol­e­cules and how they join hands. Crys­tals are mol­e­cules writ large. The most well-known crys­talline sub­stance is quartz. This form of sil­i­con diox­ide takes its shape very se­ri­ously—not only is it hexag­o­nal in cross-sec­tion, the ends form into six-sided pyra­mids.

Then there is the snowflake. No other crys­tal has such flair, such imag­i­na­tion. Fa­mously, no two are ever the same, a piece of ap­par­ent hy­per­bole that is quite true. Nev­er­the­less, they are all, at heart, hexag­o­nal. In­deed, there are more than a dozen ar­range­ments of wa­ter mol­e­cules that form dif­fer­ent ices (in­clud­ing, for read­ers of Kurt Von­negut Jr, the apoc­a­lyp­tic Ice Nine), yet the hexagon dom­i­nates. Wa­ter mol­e­cules have pos­i­tive and neg­a­tive charges ar­ranged at just the right an­gle for six of them to form a hexagon. Left­over charges en­able the hexagons to join to other hexagons edge-on. They can also join face-on, per­fectly aligned, thus form­ing a crys­tal. I’m hugely sim­pli­fy­ing here, but trust me, it’s for the best.

Sin­gle snowflakes are mostly sym­met­ri­cal and al­ways have six cor­ners. They have the same sym­me­try as a hexagon, but a flurry of snow doesn’t de­posit thou­sands of hexagons on your lawn. Small, young snowflakes, are per­fect hexagons, but, soon, the more electrically charged points at­tract wa­ter mol­e­cules to pro­duce the Fabergé or­na­men­ta­tions that give them their full beauty.

The snowflake fas­ci­nates with its del­i­cate beauty; basalt col­umns, such as the Gi­ant’s Cause­way in North­ern Ire­land, in­spire awe. Th­ese have also puz­zled nat­u­ral­ists over the cen­turies —the idea that they are enor­mous crys­tals quickly be­ing dis­missed

‘From the gar­gan­tuan to the sub-mi­cro­scopic, hexagons are ev­ery­where’

‘With­out hexagons, you would be an un­pleas­ant pud­dle of goo ’

be­cause they con­tain small crys­tals of sev­eral min­er­als.

In fact, the an­swer is sim­ple—they form by the shrink­ing of hot basalt as it cools from its molten state, very much like the roughly hexag­o­nal crack­ing that oc­curs on your (once snow-cov­ered) lawn af­ter a sum­mer drought. The mas­sive and ho­moge­nous na­ture of the basalt en­sures that the forces in­volved are evenly distributed and the frac­tures oc­cur with great reg­u­lar­ity and in the most eco­nom­i­cal of forms: the hexagon.

If you think you your­self to be free of hexagons, then I have to tell you that you’re ac­tu­ally largely built of them. With­out hexagons, I’m afraid you would be an un­pleas­ant pud­dle of goo on the car­pet. It’s all down to the ex­traor­di­nar­ily tal­ented car­bon atom.

Six of them join to form hexag­o­nal ‘rings’, some­times with a car­bon atom re­placed by that of an­other el­e­ment. They’re found in many fa­mil­iar bio­chem­i­cals such as vanillin (vanilla), ben­zene, sug­ars, amino acids and even DNA.

Some sug­ars have one ring, some two, and are there­fore called monoand dis­ac­cha­rides re­spec­tively. Some of those in DNA are found in the ‘bases’ that carry the ge­netic in­for­ma­tion.

What th­ese rings have in com­mon is that they act as a holder for so-called ‘func­tional groups’, which are molec­u­lar struc­tures at­tached to the car­bon and other atoms on the ring that do the work of the whole mol­e­cule.

From the small­est hexagon known, we end with the largest. Dis­cov­ered only in 1982 by the

Voy­ager mis­sion, ‘the hexagon’, as it is so sen­si­bly known, is a cloud pat­tern around the north pole of Saturn.

How such a mon­strous and un­mis­take­able hexagon was cre­ated and is sus­tained is a new prob­lem for sci­en­tists to worry about, but what is not in doubt is its size: it’s twice the di­am­e­ter of the Earth.

Bee friendly: the hive’s fa­mil­iar shape is a re­sult of tubes of wax melt­ing in the colony’s body heat

Hexagons are ca­pa­ble of great del­i­cacy as well as strength as snow or in the drag­on­fly eyes

Crys­tal clear: the hexagons of the Gi­ant’s Cause­way in North­ern Ire­land were formed by the shrink­ing of hot basalt as it cooled. Be­low: The shape of the green tur­tle’s ver­te­bral scutes help to give ex­tra pro­tec­tion on its most vul­ner­a­ble part Above:

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