system
Given the following post, respond as if you're commenting on Reddit:
human
Why do viruses have such complex antigen structures which follow distinct geometrical patterns?
gpt
There are many ways to answer your question.  Here are a few of them:

1. Viruses that don't evade the immune system do not produce more of themselves, so their genetic line dies off.

2. Some viruses do indeed have very complex antigen structures.  This is especially true of enveloped viruses, like HIV, where the key proteins are covered in sugars (glycoproteins).  These sugars don't adopt one specific structure, so there isn't one antigen for the immune system to recognize.

3. Some viruses have antigenic sites that don't vary much, which is why we have vaccines.  Sometimes these sites can't change because their structure is required for a specific function (receptor recognition, pore formation, etc) 

4. Not all viruses have capsids that adopt distinct geometrical patterns.  HIV, for instance, can assemble in many different ways, although it does follow some rules of assembly.  Capsids enclose and protect the genome of the virus until conditions are met for genome delivery and replication.  

But there's a problem.  The virus has to encode the information for a shell that will enclose it.  This becomes a surface area/volume issue. The genome requires 3 bases to encode 1 amino acid, so you can easily guess that it would be excessive for a virus to encode one giant protein to encase the whole virus, since it would inflate the amount of genetic material.  The solution (a handful of proteins that snap together, usually by self-assembly, into a defined shape) allows the virus to encode a small number of proteins, let the cell produce them in large number so that there is a sufficient amount to enclose the genetic information and form another infectious virus.

So, to summarize: 
- geometrical shapes because you need to enclose the genome that encodes the things making the shapes.
- complex antigens propagate because the simple ones are, as a rule, more easily recognized and terminated by the immune system.