Honeycomb (geometry)

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In geometry, a honeycomb is a space filling or
close packing of polyhedral or higher-dimensional cells,
so that there are no gaps.

It is an example of the more general mathematical tiling
or tessellation in any number of dimensions.
Its dimension can be clarified as n-honeycomb for
a honeycomb of n-dimensional space.

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“The geometry of this shape uses the least amount of material to hold the most weight,”
Sue Cobey, a bee researcher at Washington State University, said.

Materials made with hexagon shapes can also handle a lot of force,
even if they are made out of a lighter material.

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The hexagonal shape of the honey bee cells has attracted the attention of humans for centuries.

It is now accepted that bees build cylindrical cells that later transform into hexagonal prisms through a process that it is still debated.

The early explanations involving the geometers’ skills of bees have been abandoned in favor of new hypotheses involving the action of physical forces,
but recent data suggest that mechanical shaping by bees plays a role.

However, the observed geometry can arise only if isodiametric cells are previously arranged in a way that each one is surrounded by six other similar cells;

here I suggest that this is a consequence of the building program adopted by bees and propose a possible behavioral rule ultimately accounting for the hexagonal shape of bee cells.

Scientific Reports

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The hexagonal shape of the cells of the bees’ honeycomb has intrigued
laypeople and scientists for ages.

Why do bees build this kind of cells?
How can they achieve such a spectacular structure?

Early natural philosophers, like Marcus Terentius Varro,
based on the observation that
hexagons possess the highest surface/perimeter ratio,
compared to other polygons that can be used for tiling the plane,
suggested that honey bees build their hexagonal cells in order to achieve
the best economy of material.

Scientific Reports