Quite a few years back, I wrote a program that generates mazes. It wasn't a very practical program, but what I enjoyed about it was that I could use it to create a maze of anywhere up to 10 dimensions, although in practise it was limited to four or five.
It isn't too hard to conceive of a maze in more than three dimensions. Imagine that you are in a labyrinth. From where you are standing, you can see exits to the north, south, east or west. That's two dimensions. Now imagine that there are ladders going up and down. That's the third dimension.
To get to the fourth dimension, let's just assume that there are exits in two more directions. I typically think of those directions as "in" and "out". It's not too important to visualize just exactly where these go, except that going "in" or "out" brings you to a different place than all of the other directions.
To get to the fifth dimension, add two more directions - I usually think of them as "hot" and "cold". You could just as easily think of them as "red" and "blue" - the important thing is that going "red" and then "blue" should bring you back to your starting point, and that the place visited in between should have been different from all of the other places connected to the other exits.
Other properties hold for "rectilinear" mazes. In particular, traveling in a square should bring you back to your starting point. For example, going north, east, south, then west, or going up, "in", down, then "out" are both instances of square paths. In general, traveling along opposite edges of an n-dimensional "square" should bring you back to your starting point. For instance, going north, east, up, "in", "hot", and then south, down, "out", west, and "cold" moves along opposite edges of a 5-square (or 5-cube, or hypertesseract), and would return you to the starting point (assuming that there were no walls in the way along your journey.)
Sadly, I have never been able to get anyone interested enough in a higher order maze to attempt to solve it. Anyone that has tried to solve even a three dimensional ball-in-a-cube puzzle knows that they can be fiendishly difficult, and adding more dimensions makes it harder yet. It might be interesting to try to adapt the output of the maze program to generate web pages, though. Perhaps in my copious free time.
You can respond to my ranting here.
In for a penny, in for a rant.