At this time of year more than any other, the air is full of symmetrical objects. Not just the five-pointed stars that adorn Christmas trees, or the six-armed snowflakes that accompany the increasingly Arctic weather. It's the explosion of symmetrical shapes shot through the air every time someone sneezes that accounts for the surge of seasonal symmetry. The viruses that carry the coughs and influenza that lay us low each winter are invariably constructed with beautiful but sometimes deadly symmetry.

In 1918, the Spanish flu pandemic killed 50 million people, more than the casualties of the First World War. Such devastation concentrated scientists' minds on determining the mechanism of this dangerous disease. They soon realised that bacteria was not the cause, but something that could not be seen under a conven-tional microscope. They called these new agents viruses, after the Latin for poison.

The discovery of the true nature of these viruses had to wait for the development of a new piece of equipment called the electron microscope, which gave scientists a way of penetrating the underlying molecular structure of the organisms that were reaping such havoc. A molecule is a bit like a collection of ping-pong balls connected together with toothpicks. The pictures that you get from the electron microscope are a bit like shining a light on one of these structures and looking at the shadow created by the arrangement of ping-pong balls.

This is where mathematics can become a powerful ally in unravelling the information contained in these shadows. The game is to identify what three-dimensional shapes could give rise to the two-dimensional shadows from the electron microscope. Progress often depends on getting the right angle to reveal the molecule's true character.

When scientists studied the 2-D pictures that these new techniques were revealing they found, rather than a tangled mess of molecules, shapes full of symmetry. The first views revealed dots arranged in triangles, which implied that the three-dimensional shape could be spun by a third of a turn and the shape would realign. When the biologists looked in the mathematicians' cabinet of shapes, the Platonic solids seemed to be the best candidates.

The Platonic solids are the symmetrical shapes that make good dice, such as the cube made up of six square faces. As any Dungeons & Dragons aficionado will know, we can construct four other dice in addition to the cube. The tetrahedron, for example, comprises four equilateral triangles; the first die used in history, it featured in a forerunner of backgammon, played in 2,500BC by the Babylonians.

The trouble was that all five of Plato's dice had axes through which you could spin the shape by a third of a turn such that all the faces would realign. It was when they looked at the shadow from another perspective that they were able to pin down the shapes of these viruses more precisely. Suddenly dots arranged in pentagons appeared. This allowed the scientists to home in on one of the more interesting of Plato's dice, the icosahedron, a shape made up of 20 triangles with five triangles meeting at each point.

Subsequent analysis has revealed that the underlying structure of some of the most deadly viruses are constructed using the shape of an icosahedron. From influenza to herpes, from polio to the Aids virus, symmetry is the key to the mechanism by which these viruses can so easily replicate themselves. The symmetry of the shape provides a simple formula for constructing multiple copies of the virus, which is what makes it so virulent.

Explore Tech & Web

• Personal Tech

• The Web

• Gadgets & Gaming