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Non-Euclidean geometry can be inspirational in constructing adventure scenarios and places for PCs to explore. A simple method is to have a bunch of locations and then connect them at random. Instead of drawing them on a conventional map, you can draw each separate "room" as its own self-contained section which is internally self-consistent. But when you transition through a threshold to another "room" you just connect them with numbered labels or arbitrarily drawn lines.
So for example, you walk in the hallway on the grond floor. It has four exit doors. Passing through one takes you directly to the main bedroom on level 2, without going up any stairs. Another door in the bedroom takes you to the basement. The connections can be impossible in three dimensions, but that's not really a problem!
And each "room" doesn't need to be a literal single room. You can make them cover multiple connected rooms that map normally. It's only when you transition to another "room" section that the weirdness happens.
There are many pre-written adventures that use this or similar mapping tricks to effectively present a non-Euclidean environment for players to explore. Including:
- Dungeon Module Q1 Queen of the Demonweb Pits (1980), by TSR.
- The Dancing Hut (1984), by Roger Moore, published in Dragon magazine #83.
- The Dancing Hut of Baba Yaga (1995), by TSR. A Second Edition D&D adventure based on the above.
- The Sky-Blind Spire (2016), by Trilemma Adventures. (Highly recommended! We played this and had a blast.)
Commentary by memnarch (who has not seen the movie)
Hah, this place was meant to be super confusing and it's not just the time juice! Or at least, that was the original idea. I'm almost surprised that the GM didn't add in a Peter Pan reference of some kind.
It does feel that the blacksmith idea isn't going to work though. Perhaps what's actually going to happen is that in the search, the group stumbles into the First Order group with the knife/key and it gets stolen back. Then we have the whole cat-and-mouse chase thing happen again but this time we're on the planet with the end goal.
Transcript
Poe: Hey, stranger! Is there a blacksmith around here?
Stranger 1: East two blocks, then left twenty minutes ago.
Stranger 2: 360° past the shop that doesn’t exist yet.
{Poe returns to the others}
Finn: Any luck?
Poe: I got directions!
GM: Kijimi’s crooked streets seem to twist and fold back on themselves in multiple dimensions.
GM: You’re no longer sure where they were pointing. Or when.
BB-8: I think that’s a hint that looking for a blacksmith is fruitless.
Rey: Or! The liquefied space-time I’m carrying is distorting causality and we need to survey the city block by block to reconstruct the true topology!
GM: Oh god, I forgot about—
GM: Yeah. What Corey said.