Tell your friends about the mighty hexagon, and how!

Getting in shape? Try the hexagon. It’s only the finest shape in existence. Just take a gander at this glorious structure:

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Ok, these hexagons aren't planar, so they're not perfect, but let's just allow some leeway for non-Euclidean geometry or just assume these are differentiable manifolds, mmk?

Magnificent, aren’t they? Those, dear reader, are matryoshkanated carbon nanotubes (ok, they’re actually quadruple-walled carbon nanotubes, but the chemistry community really needs to hit up some fun descriptors like “matryoshkanated”). And why are carbon nanotubes magnificent? Why, because they’re made of hexagons!

Hexagons occur all over nature. At the most miniscule, 6 carbon atoms will sometimes bond at 120 degree angles thus forming a benzene ring. Unlike non-aromatic 6-carbon rings in chair or boat formation, benzene is a near-perfect, planar hexagon due to resonance, a phenomenon in which electrons are associated with more than one atom or bond. Resonance structures tend to afford molecules unusual thermodynamic stability; in the case of benzene (or its functional group form, -phenyl), electrons are delocalized cyclically, and conservative forces mold the molecule to a stable, planar conformation (a perfect hexagon). These 6-carbon rings can be conjugated in arrays to form giant masses of hexagons, as is the case with graphite. So now you know why pencils are great; they use hexagons to enable writing in zero gravity.

Snowflakes get the esteemed honor of being the standard similes for uniqueness. What you didn’t know, however, is that at their tiniest, snowflakes are pristinely hexagonal, as reflected in their more macroscopic six-spoked morphology. The following micrograph illustrates this hexagonality quite aptly:

Snowflakes exhibit six-fold radial symmetry derivative of the six-fold crystalline structure of ice, which effectively lies in hexagonal sheets (much like the graphite mentioned earlier, though a more accurate analogy would be graphene). As such, a single ice crystal will incorporate water droplets in the atmosphere around its six prism facets (which can be seen in the picture above), thus promoting proliferation of “arms” in a six-fold array. Hence, six-armed snowflakes are born as more and more water droplets are incorporated into the structure. An important distinction to make between snow and sleet: snowflakes are not frozen water droplets– sleet is. Simply put, snowflakes are amalgamations of water vapor and ice crystals.

Let’s move on to hexagons in biology. The hippocampus contains cells known as grid cells, which fire according to where a hippocampus-possessing animal is in allocentric space. The grid formed by their firing patterns occurs in tessellated triangles (effectively equilateral depending on how fast a given organism is moving), which, of course, create hexagonal patterns. Evolution has determined that hexagons and their constituent parts are ideal for mapping space. How’s that for hexagonal excellence?

In a recent post, I expounded on the various merits of the star-nosed mole. One of these merits included its possession of highly specialized sensory organs known as Eimer’s organs, which lend star-nosed moles their unparalleled tactile sensitivity. Of course, they’re arranged hexagonally:

The cause of this hexagonality is probably a result of space-saving tessellative arrangements of circular cells, but let’s use the next example to explore this idea  a little more thoroughly.

Perhaps the most familiar example of hexagons in nature is brought to us by bees. It’s amazing they haven’t gotten patents on hexagons; they bloody live by the mantra of hexagon excellence. Just take a look at the honeycomb below:

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Honeycombs probably appear as tessellated hexagons for the following reason. If you arrange circles tangent to one another in the most space-saving manner, gaps of space with three vertices inevitably result. If you have seven such circles arranged in a radially symmetric manner, drawing lines tangent to exterior six circles produces a hexagon. Resolving the gaps between the circles results in the following:

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Christaller's Central Place Theory's idealised distribution of settlements.

In the case of honeycomb, the molding of individual cells probably proceeds towards a space-saving arrangement of congruent circles. Circles are easy. However, arranging the circles in a space-saving manner produces the “gaps” mentioned earlier in the form of wax boundaries. These gaps waste space, so they are carved out from the cells inward, thus forming a tessellation of hexagons. Now, bearing in mind the notion that if bees die, the world dies–hexagons are truly masters of us all.

Let’s get even larger-scale. About 50 million years ago, a volcano erupted in what is now Northern Ireland. The molten basalt this volcano spewed forth cooled and then contracted, a process which forced fractures to occur, resulting in a vast number of hexagonal basal columns now called Giant’s Causeway. Unsurprisingly, this spot is a hot tourist location as well as one of the “greatest natural wonders in the United Kingdom” according to whomever is responsible for making such lists. At any rate, that person understands the astounding wonder that is the hexagon.

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The hexagonal basalt columns of Giant’s Causeway are certainly large, but you can’t see them from space. A literally astronomically-proportioned hexagon swirled into existence atop the north pole of Saturn eons ago in a proud salute to the baffling science of fluid dynamics. A circular storm makes sense intuitively. Take Jupiter’s Great Red Spot, for instance; like a hurricane, it spins. In spinning, conserving distance traveled dictates that objects travel in a circular fashion. A hexagonal one, however, is slightly baffling.

It turns out that the ratio of the planet’s angular velocity to that of jet streams surrounding its north pole may be responsible for the peculiar hexagonal maelstrom. Physicists at Oxford simulated Saturn’s odd north pole by spinning a fluid at a particular rate relative to the spinning speed of the container it was in. Depending on the ratio used, apparently ellipses, squares, and triangles could be formed in addition to hexagons. Of course, the “most beautiful” planet in our solar system elected the hexagon because it knows what’s what.

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Even pseudoscience has realized the penultimate power of the hexagon; so-called hexagonal water is marketed as a “perfect substance” that can reverse the effects of aging. It’s probably what the invisible pink unicorn drinks.

It would seem, as such, that the prevailing Christian assumption that the number 6 is evil must be decidedly wrong. Hexagons are good. Oxygen is evil.


7 responses to “Tell your friends about the mighty hexagon, and how!

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