The Impossible Hierarchy is the name used to describe a hierarchy were its completely impossible for anything to be beyond first level of the hierarchy, the second level is bigger and its impossible for anything to possible be beyond it, this cycle continues forever.
The Impossible Hierarchy contains all of the lesser versions of The Box. The Box is impossible to understand so all of our views on how The Box work are only lesser versions of The Box contained somewhere in The Impossible Hierarchy.
The Poly Cosmologies are contained in Altraca witch are a part of the Impsible Cosmology
The Barrel is a structure that towers through the Impossible Cosmology conecting one part of it with another
Like everything else, its contained in The Box.