Today I suddenly realized that in 4D, one can build a spiral staircase flush against a wall.

In 3D, the central column of a spiral staircase must be set apart from any walls so that there's space to put the spiralling steps around it, since otherwise the steps would collide with the wall(s).

In 4D, however, thanks to the extra dimension, the central column of a spiral staircase can actually be flush against a wall, and the steps can spiral around it while still remaining flush with the wall. Better yet, since the walls of a 4D room are 3D, there is actually no need for any central supporting column; the steps can be attached directly to the wall (a flat wall!) and spiral upwards at the same time. Furthermore, the resulting staircase will only jut out from the wall as far as the width of each step, and no more, so it could be fitted even between two walls only the width of each step apart. In 3D, the opposite walls of a spiral stairwell must be at least two widths of the steps apart. (Of course, this is compensated in 4D by needing the walls to be sufficiently wide in 2 dimensions.)

After so many years speculating on 4D worlds I didn't think I could find anything more that'd impress me, but I just did.