Say we have a 3D cloud of dots. An oriented bounding box (OBB) can be constructed around them. It usually has a longest edge. Let's call a line parallel to the longest edge and passing through the center of OBB - axis of OBB.
On the other hand, there exists an enclosing cylinder with minimal diameter. It will roughly have a shape and orientation that of OBB.
The question is: is there a proof, that axes of OBB and the enclosing cylinder are always parallel?