The object I’m thinking about is an $n$-dimensional Orthotope (generalization of a rectangle), which is sectioned into $2^n$ orthants (generalization of quadrant). A couple of questions…
What’s the proper name for this object (if such a name exists)? That will help me find literature about it…
Are there any problems where such a structure would be useful?
Are there general properties about this object that are known?
Thanks in advance!