What are the three main symmetries of viruses?

Viruses exhibit three main types of symmetry in their structures:

Icosahedral Symmetry:

Many viruses adopt an icosahedral shape, which is a polyhedral shape with 20 triangular faces. This symmetry allows the virus to enclose its genetic material efficiently using a minimal number of proteins. The icosahedral structure is common among many animal and plant viruses. Examples include the poliovirus and the adenovirus.
Helical Symmetry:

Viruses with helical symmetry have a rod-like structure. Their capsid proteins wind around the nucleic acid in a helical or spiral arrangement, forming a cylindrical shape. This type of symmetry is often seen in RNA viruses. Examples include the tobacco mosaic virus and the influenza virus.
Complex Symmetry:

Some viruses, especially bacteriophages (viruses that infect bacteria), exhibit complex symmetry, where the structure is more elaborate and does not fit into the simple icosahedral or helical categories. These viruses may have a combination of both symmetries or additional features such as tails or complex outer walls. An example of a virus with complex symmetry is the T4 bacteriophage, which has an icosahedral head and a helical tail.
These symmetries reflect the different strategies viruses use to encapsulate and protect their genetic material while maintaining a shape that facilitates their ability to infect host cells.