What is the maximum volume a box can have?

In many applications the bounding box is aligned with the axes of the co-ordinate system, and it is then known as an axis-aligned bounding box (AABB). To distinguish the general case from an AABB, an arbitrary bounding box is sometimes called an oriented bounding box (OBB). AABBs are much simpler to test for intersection than OBBs, but have the disadvantage that when the model is rotated they cannot be simply rotated with it, but need to be recomputed.