I know (as almost anyone) how to divide an square in let's say 4 equal parts, a cube in 8 or more, i.e. sub-squares and sub-cubes respectively. But a high dimensional space??? . ..I mean where dimensions are >>3, for example 100 or 1000?. In fact I don't know if the space is "hyper-rectangle" or "hypersphere". Probably this second part (to know or determine the shape of the hyperspace) is another question...

I apologise if this is not the correct forum, then I'll apreciate if you can suggest another forum to post this/these questions

thanks