Perfect 'Per-Vertex' Collision Algorithms?

So, I am experimenting with physics, and have got a little fun ‘applyForce()’ demo along.
Now I want to know how to detect collision no matter how many vertices there are.

I want to be able to find collision with:
* Convex and concave objects (looking at you, Hyperplane Seperation Thereom)
* Works no matter how many vertices there are

Any bright ideas?