One Forum, Two Domains, Two Styles

[amagab]

Is it possible to have one forum/database, using two domains and each domain has a separate style?

Let's say this setup:

Category A
Forum A
Forum B
Forum C

Category B
Forum D
Forum E
Forum F

I'd like when people go to myDomainA.com that they are only shown Category A and it's subforums in specific style and when they go to myDomainB.com that they are only shown Category B and it's specific style.

Possible? How?

Thanks!