This seems to be a basic questions, but I really don't know a good computer algorithm to do this. I have a set of planes (parameterized by normal direction and distance from a given point), and I want to determine the (convex) polyhedron whose faces are on those planes. In particular, I'd like to obtain the coordinates of the nodes corresponding to each face.
Moreover, I don't know if such a polyhedron is uniquely determined.
The question in 2D seems much easier since we can determine the two adjacent normal directions for each given normal direction.