How many faces can have at most the intersection of two rectangular frustums?

Question

In a 3D context, I want to evaluate the intersection of two rectangular frustums.
The intersection of those two frustums will be a convex polytope, I think.
What will be the maximum number of faces (and optionally, of vertices and edges) that can have this intersection ?

Answer 1

My experiments have shown that the maximum number of faces of the intersection of those two frustums is 11. I observed it programmatically by computing in a 3d software the intersection of two frustums which dimensions I could change at will.
However I do not have a theoretical proof for that number (neither know if it really is the maximum).