The hexagon is a shape (technically a polygon) with six equal sides. That gives it a certain symmetrical beauty. But more than visual beauty, the hexagon has a special place in both mathematics and nature. In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. Thus 6 is a perfect number because it has divisors 1, 2 and 3 which sum up to 6, making the hexagon a shape that embodies the first perfect number.

Nature also delights in hexagons. The shape is visible on bubble rafts, bee hives, snowflakes and graphite, among others. This has to do with packing efficiency. If you want to pack together cells which are identical in shape and size so that they fill all of a flat plane, only three polygons will work – the triangle, square and the hexagon. Of these, hexagonal cells require the least overall length of wall compared to triangles or squares with the same area. Bees know that long before we walked on the earth. Instinctively they know that circles would leave gaps in the honeycomb. Squares and triangles wouldn’t leave gaps, but the hexagon works even better as it uses the least amount of wax to hold the most weight.

Nature also delights in hexagons. The shape is visible on bubble rafts, bee hives, snowflakes and graphite, among others. This has to do with packing efficiency. If you want to pack together cells which are identical in shape and size so that they fill all of a flat plane, only three polygons will work – the triangle, square and the hexagon. Of these, hexagonal cells require the least overall length of wall compared to triangles or squares with the same area. Bees know that long before we walked on the earth. Instinctively they know that circles would leave gaps in the honeycomb. Squares and triangles wouldn’t leave gaps, but the hexagon works even better as it uses the least amount of wax to hold the most weight.

Hexagons are also the building blocks of some of the most amazing physical structures known to man such as carbon nanotubes (CNTs): carbon molecules arranged in a hexagonal cylindrical mesh.

The hexagonal architecture of CNTs account for their extreme strength; a multi-walled carbon nanotube can exhibit a tensile strength of about 9 million psi. This translates into the ability to endure tension of a weight equivalent to 6,422 kilograms-force on a cable with cross-section of just 1 square mm or 0.0016 square inch, making them hundreds of times stronger than steel but six times lighter. Due to their extreme strength and their efficiency as heat conductors, CNTS have played a starring role in a wide variety of scientific applications, from nanotechnology to electronics, optics, bone tissue engineering, fabrication of biomedical devices and implants, and other fields of materials science.

Then we have graphene, an atom-thick sheet of carbon atoms arranged in a honeycomb lattice. When hundreds of graphene layers build up, they are called graphite. The layers are held together by weak van der Waals forces, allowing them to slide easily, making them soft, slippery, and conductive along layers, while within each layer, the carbon atoms are held together by very strong hexagonal ring bonds. This arrangement gives graphite its softness and lubricating properties while at the same time allows for good electrical conductivity parallel to the layers.

Graphite’s unique properties— its electrical conductivity and flexibility – make it a wonder material in science and engineering, with applications ranging from energy storage to lubricants, metallurgy, electronics (conductive additives), water purification and nuclear reactors. This list is growing.