Contact simplex between 2D convex polygons

Question

How do I find the point/line of contact between two convex intersecting 2D polygons?

I have implemented both the Separating-Axis test and the GJK algorithm, but neither of these return the contact simplex between the shapes (although the EPA extension to GJK will give me penetration distance).

edit: This is for a physics engine, so I need 3 pieces of information from the collision:
1. Normal of collision.
2. Penetration distance (for collision resolution)
3. Points of contact (for angular impulse calculations)