Bees and Their Hives

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Honeybees are well known for their busy lives.

But to make the most of their hard work, their homes are designed with efficiency in mind.

An Efficient Hive

Inside a beehive is a densely packed honeycomb structure.

It is made of beeswax, which is secreted by the bees themselves.

The cells are used to store honey, which the bees' larvae feed on.

Together, the cells form a tessellated pattern.

Tessellation:
A repeating geometric pattern
Leaves no gaps between shapes

Regular Tessellation and Prisms

Regular tessellation is created using identical polygons.

It is only possible with three shapes: equilateral hexagons, squares or equilateral triangles.

These are the only regular shapes that fit together without wasting space.

So, there are three possible shapes for the creation of honeycomb cells.

But which shape makes for the most efficient cell, allowing bees to store the most honey for the same outlay of wax?

Each cell is a three-dimensional prism.

Prism:
Three-dimensional shape
Two identical and opposite faces
Side faces are parallelograms

Assuming that each cell is made with one square centimetre of wax, it is possible to compare the volume of honey each would store.

With a triangular prism, the maths reveals that for every square centimetre of wax produced, this amount of honey can be stored.

0.112cm³

With a square prism, the ratio of its surface area to its volume results in a higher capacity, with even more space for honey.

0.167cm³

But with the bees' traditional hexagonal honeycomb, the maximum amount of honey can be stored for the same outlay of wax.

0.232cm³

So hives provide the optimum design for bees' industry, by granting them the most economical use of space.