[dedward]

It's naturally confusing, because a 4th spatial dimension isn't something we naturally experience. We can't really say what it represents because it's not real... it's not a model of reality.

We see in 2 dimensions and we infer the third from various cues. (The quote that we are "dimly aware of a fourth", which you may have heard, refers to time and is a different issue than a fourth spatial dimension.)

We have three dimensions, all orthogonal to each other. We can translate, rotate, and project things in between them.

So all we can do is apply those same principles and see what comes out - we shouldn't expect it to match anything recognizeable though.