“The universe, which others call the library, is composed of an indefinite, perhaps infinite number of hexagonal galleries”
– Jorge Luis Borges, Labyrinths
Six sides is best
Hexagons are the bestagons. Why? Because of bees. Bees are the best. And they build only the best shape, the hexagon (the bestagon). The humble bumblebee has an engineering problem to solve. She makes two things: honey and wax. The former to eat and the latter to contain the former. To make one unit of wax, she needs eight units of honey. To make a hive that contains the maximum honey, while using the minimum wax, is vital.
Thus, a honeycomb conjecture. Which shape works best? There are many options and lots of polygons to choose from. But pentagons are broken and leave gaps. Same with septagons. The hexagon is the only regular polygon to tile a plane without resorting to self-division.
The circle offers a shape defined by the least perimeter for the most area, but that only works when you need just one. Pack circles together and they also leave wasted space. Bees use hexagons because no shape is better at creating the maximum area for the minimum wall. Hexagons show up everywhere. Hexagons are the bestagons.
Sixth planet from the Sun
Let us travel to Saturn, 1.2 billion kilometres away, and a mass that’s 95 times the Earth’s. At its north pole it has a charismatic hexagon – a wave pattern of gas. It is composed of clouds somehow keeping shape and changing colour. It’s a magnificent solar system mystery.
And from the largest, down to the smallest. Take the snowflake. Guess how many sides they have? Yep. When water molecules join together to make a flake, the sturdy shape they prefer is the hexagon. As more molecules join, they extend the flake fractally up. If there is ice in your drink, give thanks to the hexagon for keeping it cool.
Many atoms use hexagons because – take note – hexagons are the bestagons.
C is for carbon
Your pencil is an elegant thread of graphite – which is, you guessed it, hexagonal carbons. Even more than that, when carbon is in a straight sheet it’s called graphene: which just happens to be the strongest atomic material in the entire universe.
Graphene can take a hundred times more force than steel. This is because when hexagons come together, they form three-sided joints of 120 degrees. This, for the least material, is the most mechanically stable arrangement. Pull on one joint, and the other two equally pull back, push in, and the other two are the most able and stable to resist.
This is another reason hexagons show up everywhere. Hexagons can be flexible while keeping their strength, letting us construct some sublime materials. Print out a grid of hexagons using anything, from aluminium to cardboard, make a little sandwich, and POW! You have honeycomb panelling. A tear-resistant material that is also super light and flexible. It’s used everywhere but especially in aviation. Rockets need to be strong yet light. Same for aircraft wings – they must not tear, but also need to bend. And only the magic of the honeycomb panel can do both equally well.
The ancient Greeks suspected it, Charles Darwin wrote about it, and now mathematics has proven it, with a 1999 paper by Thomas Hales at the University of Michigan: the hexagon honeycomb is a masterpiece of engineering.
Sources: www.cgpgrey.com; NASA Cassini mission; The Symmetrical Universe, Alan Lightman. Pictures: Saturn’s hexagonal pole; the atomic shape of graphene.
James Neophytou