Hooray For Hexagons!

Next time you’re eye-to-eye with a fly, take a closer look. Thousands of tiny ommatidia (cells that receive light) cover each eye. Like human eyes, each one has a cornea, a lens, and photoreceptor cells that can turn light into information the brain understands. But possibly the most surprising thing about ommatidia is their shape: Each one is a tiny hexagon!

That isn’t the only place in nature where hexagons pop up. When you catch a snowflake or blow bubbles in water, you’re catching and creating hexagons too. Once you start looking for this six-sided shape in nature, it’s impossible to miss!

Have you ever been eye-to-eye with a fly? Next time, take a closer look. Thousands of tiny cells that receive light cover each eye. Each one has parts that are similar to those in a human eye. But possibly the most surprising thing about these cells is their shape. Each one is a tiny hexagon!

That isn’t the only place in nature where hexagons pop up. When you catch a snowflake or blow bubbles in water, you’re seeing hexagons too. Once you start looking for this six-sided shape in nature, it’s impossible to miss! 

One reason hexagons are everywhere is that they’re a very practical shape. “A regular hexagon, where the side lengths and angles are all the same, tiles the plane,” says Marc Chamberland. He’s a professor of mathematics at Grinnell College in Iowa. “You can make copies of the same hexagon and you can use them to cover the plane.” Only three regular shapes can be copied over and over again to fill a flat area with no gaps: equilateral triangles, squares, and regular hexagons.

Honeycombs are an example of hexagons in nature. Each honey-holding cell is made of wax shaped into a regular hexagon. Bees need less wax to build the honeycomb and use less energy to store the most honey by using this shape. It has the smallest perimeter, or distance around the wall, yet creates a shape with the largest area.

“Hexagons are closer to a circle,” explains Chamberland. Of any shape, circles have the largest area relative to their perimeter. Hexagons approximate a circle, but unlike circles, hexagons can cover a plane seamlessly.

One reason hexagons are everywhere is that they’re a very practical shape. A regular hexagon has six sides that are all the same length. It can be copied over and over again to fill a flat plane with no gaps, says Marc Chamberland. He’s a professor of mathematics at Grinnell College in Iowa. Only three regular shapes can cover a plane this way: equilateral triangles, squares, and regular hexagons.

One example of hexagons in nature: honeycombs. Bees build these structures to hold the honey they make. Each cell in a honeycomb is made of wax shaped into a regular hexagon. The shape lets the bees use less wax and less energy to store the most honey. That’s because hexagons have a relatively small perimeter, or distance around the wall, but a relatively large area.

Of any shape, circles have the largest area compared to their perimeter. But circles can’t cover a plane seamlessly. “Hexagons are close to a circle,” explains Chamberland. Bees can pack them together to store as much honey as possible with the least construction work. 

Human builders also put hexagons to work. It’s an easy choice for tiles that will cover walls or floors. But the shape is also used for its strength. Similarly to how hexagons use the smallest perimeter of any polygon to create the most area, they also need the least amount of material to support the most weight.

The Vessel in New York City is a structure made up of staircases. Each part of the Vessel was made of carbon steel pieces called dogbones. They’re horizontal platforms with angled staircases on each side, one going up and one going down. When pieced together, these dogbones create hexagonal shapes.

“We wanted to create something that had a minimal footprint and to ensure that the plaza’s flow was uninterrupted,” says Laurence Dudeney, an architect on the Vessel project. By creating hexagons out of staircases and platforms, the Vessel has large open areas that don’t block views. It also has a small base of strong hexagons to support the wider shape at the top.

Human builders also use hexagons. The shape makes good tiles to cover walls or floors. But hexagons are strong as well. Compared with other polygons, they need the least amount of material to support the most weight.

The Vessel in New York City is a structure made up of staircases. Each part of the Vessel was built with pieces called dogbones. Dogbones are horizontal carbon steel platforms. They have angled staircases on each side, one going up and one going down. The dogbones create hexagonal shapes when they’re pieced together.

“We wanted to create something that had a minimal footprint,” says Laurence Dudeney. He’s an architect on the Vessel project. Staircases and platforms that form hexagons leave the Vessel with large open areas in its sides. That way the structure doesn’t block views. A small base of strong hexagons also supports the wider shape at the top. 

Other factors push natural things into hexagonal shapes. For example, all snowflakes are hexagonal. This is because of how water molecules interact with one another. Each water molecule is made of two hydrogen atoms and one oxygen atom.

These three atoms make an angled shape, with oxygen at the vertex. The most efficient way for three water molecules to join together is by forming a hexagon, with each molecule making up two sides of the shape.

Many hexagons form naturally. For example, snowflakes grow in a hexagonal shape. This is because of how water molecules interact with one another. Each water molecule is made of two hydrogen atoms and one oxygen atom. These three atoms make a wide “V” shape. The oxygen is at the point of the V. The easiest way for three water molecules to join together is by forming a hexagon. Each of the three water molecules makes up two sides of the shape.

Erik Klemetti is a volcanologist who studies how magma is formed and what happens when the molten rock erupts, becomes lava, and cools. One of the most striking lava formations is called columnar jointing. It often results in towers of rock. As the lava cools and shrinks, it cracks—often into hexagonal shapes.

But it isn’t clear why this is the most common shape. “There isn’t a good reason for why hexagons form. It has to do with how that stress is being distributed,” Klemetti says. “A lot of stress is put on cooling magma when it’s turning into rock that causes these cracks to form.”

The reasons hexagons form are as varied as the places they appear. Odds are there are even more surprising hexagons in nature waiting to be discovered!

Erik Klemetti is a volcano scientist. He studies how the lava that flows out of volcanoes cools. One of the most striking lava formations is called columnar jointing. It often results in towers of rock. As the lava cools and shrinks, it cracks. This often creates hexagonal shapes.

It isn’t clear why this shape is so common. “There isn’t a good reason for why hexagons form,” Klemetti says. But he thinks it’s related to the forces in the lava as it cools. “A lot of stress is put on cooling [lava] when it’s turning into rock,” he says. “That causes these cracks to form.”

The reasons that hexagons form are as varied as the places they appear. There may even be more surprising hexagons in nature waiting to be discovered. Keep your eyes peeled!