h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

In this document, it is said that our typical view of a cube is the way in which a 2D creature would see it, however, this is incorrect. A 2D creature has 2D vision (1D with depth), and thus all one could ever see is an infinitely thin sliver, thus they could not see our version of a cube, because they would not be able to see in width and depth. Our view lets us see all that lies on a 2D plain, as a 4D ceature would see all parts of a 3D space at once without overlap, when we merely see a 2D view with depth. This is the same reason we can't ever properly view a tesseract, only a small portion of it at a time.

I agree, but you can look for strange behaviour. If you rotate a cube resting on a plane in one direction, the two dimensional being should be able to detect a change, if only to a line segment.
I haven't constructed the symmetry group for a tesseract, but if I did I would be looking for strange behaviour.
How to determine what is strange I don't know. But we can look at permutations with knowledge of what rotations and reflections look like.