> We don't have special words for the voluminous versions of other 3D shapes, so why do spheres need one?
Topologists don't need them because they already have ball and sphere.
In analysis, I can imagine them calling full hyperrectangles "brick", and empty hyperrectangles "box", but both words start with "b", so there is no shorthand for them on paper. I^n and ∂I^n are just fine.