Bees and wasps build space‑efficient and strong nests using hexagonal cells.

Introduction

The question of why honey bees adapted to building their nests from hexagonal cells has been debated for centuries. In On the Origin of Species, Darwin theorized that natural selection led to “an economy of wax.” Being frugal with wax is wise work for a honey bee given they need to consume approximately eight pounds of honey to produce one pound of wax.

But it took mathematicians studying the hexagon shape to make a beeline to the truth. Around 36 B.C., a scholar by the name of Marcus Terentius Varro first wrote about this particular math problem, later dubbed the “the honeycomb conjecture,” by stating that, compared to other shapes such as a triangle or a square, a “hexagon inscribed in a circular figure encloses the greatest amount of space.”

Birth of a Bee

Hexagons in beehives aren’t just for aesthetics, and they aren’t just for honey storage. Each cell is a potential cradle and food supply for a larva to develop in as seen here. The way human beekeepers get bee-free cells is to prevent the queen from being able to reach certain areas of the hive.

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The first 21 days of a bees life condensed into 60 seconds. Filmed by Anand Varma at the Harry Laidlaw Honeybee Research Facility at UC Davis with the help of Billy Synk. Music by Rob Moose (@mooseofrob)

The Strategy

In a 2019 interview, Thomas Hales—the mathematician who finally proved the conjecture—said that ultimately, “A hexagonal honeycomb is the way to fit the most area with the least perimeter.” From a bee’s perspective, that means storing more honey in a larger volume while spending less energy building a structure to contain it. In other words, Darwin was right.

And space-efficiency isn’t the only benefit of building with hexagons. Stacked together, hexagons fill spans in an offset arrangement with six short walls around each “tube,” giving structures a high compression strength. Beehives also dissipate heat well, preventing the waxy structure from melting on hot days. Though few species of wasps store honey, they too build nests using hexagonal cells, taking advantage of these same benefits. Efficiency, strength, and controlled heat loss are all important for human structures as well, so it’s no wonder that honeycombs inspire human design.

A hexagon with the same perimeter as a triangle contains more area.

Hexagons are the highest‑sided polygons that tessellate, or fit together. Comparing tessellated triangles and hexagons with the same area illustrates that hexagonal honeycombs minimize the material needed, making them space‑efficient.

He must be a dull man who can examine the exquisite structure of a comb, so beautifully adapted to its end, without enthusiastic admiration. Charles Darwin

The Potential

Scientists and engineers have incorporated hexagonal designs into seemingly endless applications, including light-weight building materials, flexible panels for bridge construction, sound absorption, light diffusion, catalyst design, magnetic shielding, tissue engineering, and even building better surfboards.

“He must be a dull man who can examine the exquisite structure of a comb, so beautifully adapted to its end, without enthusiastic admiration,” wrote Darwin. As we examine these structures more than a century and a half later, we’re still finding new things to admire and .

Honey bees on honeycomb
Image: Meggyn Pomerleau / Public Domain - No restrictions

Now that we know why honeybees build hexagons, how do they engineer such precise shapes? Check out "body heat melts wax" in the related content below to find out. 

Image: portukcan / CC BY NC ND - Creative Commons Attribution + Noncommercial + NoDerivatives

Honeycombs maximize the volume of honey that can be stored with the least amount of construction material.

Hornets in nest
Image: Steve Knight / CC BY NC - Creative Commons Attribution + Noncommercial

Hornets also build nests out of honeycombs.

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Last Updated November 11, 2020