Name for generalized quadtree or octree?

I posted this thread here because I didn't really know in which room to post it. Anyway, is there some name for a generalized quadtree or octree, i.e. a spatial data structure which is made out of hypercubes, where each hypercube can be divided into $\displaystyle 2^n$ smaller hyper cubes (n = number of dimensions) with half the side by dividing it on the midle once for each dimension? What about hyperoctree? I need a name for this data structure since I have just written one in C++!