Disease causing agents are parts of the natural world just like the animals and plants you see around you every day, and like animals and plants their shapes are distinctive and characteristic. But, while evolution has modified them to be the shapes that are best suited to their way of life, it is often hard to see how the geometry comes in because they are so complex -- for example, while a bird is a recognisable shape and has wings, legs, beak and so on of the right shapes and sizes to do the job best the shape looks organic, rather than being a cube or a pyramid.
In the same way the larger disease causing organisms like the protozoa which cause malaria and the bacteria that give you strep throat are shapes which have evolved to be easy to produce and reproduce in an organic way, while conforming to the needs of the species. The geometry is there, but it is partially concealed by its complexity.
But viruses are very small, simple disease causing agents, and in their case evolution has given them such a simple geometry that it is easy to see. Their shapes tend to be icosohedrons (type the word into
www.google.com for links showing you this shape); this means that the outer coat can be made of a few very simple subunits which assemble themselves into a capsule which can contain the other parts of the virus. Other viruses may be other shapes, such as rods.
URL of pictures to follow in a later post.
