The Tesseract Maze or the Hypercube Dungeon

One of my favorite modules as a kid was S3: Expedition to the Barrier Peaks, so I've got a thing for meshing weird sci-fi into my ToY games. The "tesseract maze" is a go-to of mine when I'm running these kinds of adventures. I like to insert them into "dungeons" populated by something alien, like the Priests of Syrinx (p. 318).

 

Tesseracts

A tesseract or hypercube is the 4th dimensional analogue of the cube, a strange Outsider construct. It's usually represented like so:

 

Here's a gif of someone "unfurling" this 4d object:

From a game mechanics point of view, the main difference between a Cubic maze and a Hypercubic maze is essentially the difference between a 6-room dungeon and an 8-room dungeon.  A Cubic maze would looks something like this:

While a Hypercubic maze looks something like this:

 Essentially, you are adding an additional dimension of "up/down" to the Cubic Dungeon.  Rooms G and H exist outside of 3-dimensional space - though they have identical exits out of their space back into the 3-dimensional cube, they exist independently of one another.  If you isolate the midpoint of that gif above, it would model a dungeon that would look something like this in a 3-dimensional sense:

Navigating the Tesseract

Each room is a cube of exactly the same size (30x30x30 or what-have-you), with 6 ways in and out - four doors in the center of the four walls, a door in the center of the floor, and another door in the center of the ceiling.  To reduce your (that is, the Arbiter's) amount of work tracking things, you can make each door look identical - I prefer those cool sci-fi iris doors to give things a suitably alien feel:

From instructables.com

Each room should have something that makes it different from the other rooms (unless you're feeling particularly cruel), otherwise navigating the maze is going to be extremely difficult unless the Band does something like mark walls, etc. I confess that one time I did every room differently except two rooms which were identical, that was a lark. I suppose it depends on how much you want the Band to hate you.

The connections between the rooms should be hallways that exist "outside of TIME AND SPACE."  They may or may not contain ladders. The hallways matter for areas G and H, in that gravity should reorient itself when you get halfway down the hallway.  For instance, if you were in area A and dropped a rope down the door in the floor to area G, you would end up coming in through the north door of G - so Adventurers who were climbing down a rope would suddenly find they are able to walk down the wall.  Going up is much more difficult, particularly without a ladder, but the same effect applies.

Example of this gravitational effect from the movie Arrival

 

Again, I like to use the Priests of Syrinx in this kind of maze, assuming that they can just levitate up or down and have no need of those disgusting human ladders. They put their filthy hands on those.

 

Getting Out

The Band obviously need a way out; they'll be traipsing through the tesseract for eternity until they collapse back to 3 dimensional space. How they're able to  accomplish this is up to you, but a few ideas:

• The Hypercube only exists for as long as the aliens / demons / whatever inside maintain concentration, so they need to be killed / distracted / bribed to end the effect.
• The Hypercube only exists until levers are thrown in the right order / buttons in certain rooms are pressed (right order or no) / a control panel puzzle is figured out, etc.
• The Hypercube only exists until the central brain in destroyed / the insane A.I. is tamed / the gate to Hell is closed, etc.

 Once the technology / magic / etc. of the Hypercube is broken, the Adventurers can just leave through the north door of Area A if you want to maintain a sense of linearity. The Hypercube collapses to a regular Cube that can be navigated using the Cubic maze image above, but the north door of Area A and the south door of Area F don't connect - they just spit you out in the correct direction.

The Final Word

Read the room, obviously (no pun intended). If your Band doesn't like puzzles and mazes, definitely give this one a pass as it can become maddening. But some of the best player creativity I've seen has come out of navigation the Hypercube Dungeon. 

May your Band always stay together.