express a bounded space as a continuous space by "wrapping it around"

Question

Let's say I have an n-dimensional cube (bounds are -1 and 1) in n-dimensional space z. I want to wrap this cube around such that moving outside the cube systematically injects you back in to the other side of the cube. The particular way I want to do this is to have a new space z' that is simply the bounded space (the cube) repeated (tiled) perfectly such all edges of the cubes line up (I say this since drawing this out seems to indicate other ways of doing it that I'm not interested in). I've implemented equivalent behavior in python give those bounds, but how can I write this out in math / think more formally about this?