Topology type question

I has a question for you math folks.

If you have two copies of the same object that are irregular in nature (globular proteins for example) is there always a way to make them contact one another so the region of contact on both identical objects are also identical (i.e., can they always dimerize)?

yes

wait no

Can they fold into each other?

State it like a topology-type question and maybe someone could help you