Non-Euclidean Dungeon Puzzle Ideas

[Jay R]

Back in the 1970s, I started designing the tower of the Mathemagician.

Five of the dungeon levels were the sides of the five platonic solids (dice). The first one would be the cube. You drop into the middle of the room from a hole in the ceiling, and you're in a 10x10 room with a door in each wall. Going through it would put you in a similar room, but you didn't notice the 90 degree change in direction. Going straight through four rooms would get you back to the first one. So would going to the right three times, or to the left. Going straight for two rooms would get you to the opposite side of the die. What feels "up" is really down. There is a hole in the ceiling. Back up to the higher level? No, down to the next lower level. The only time you would feel the change in gravity is going through this hole (or others like it) and suddenly you're looking (and probably falling) down into the next room -- triangular room on the next level.

One level was a torus. The doors at one end took you to the other end.

One long corridor was a mobius strip. Walk all the way down, and everything looks mirror-reversed. If you went back up at this stage, you would discover that right-handed characters were now left-handed, and vice versa.

I never finished it.