The main symmetries of viruses are:
1. Polyhedral (Icosahedral) symmetry: Spherical in shape
These include:
Naked Capsids: Example: Poliovirus, Adenovirus
Enveloped Capsids: Example: Herpes simplex virus
2. Helical (Cylindrical) symmetry:
These also include:
Naked Capsids: Example: Bacteriophage M13, Tobacco Mosaic virus (TMV)
Enveloped Capsids: Example: Influenza virus
3. Complex symmetry:
There is no clear identifiable capsid. Example: Vaccinia virus