# Piratecat's dungeon design: fun with tesseracts!



## Piratecat (Feb 29, 2004)

Regdar bashed open the partially ajar door and peered into the room. "Twenty feet square. Empty. Four doors," he grunted back to Mialee. "Nothing special. Regdar finds it boring."

"Let's go, then." Lidda slipped past the burly fighter and headed into the room, and her companions followed. As the door swung shut behind Jozan, though, everything _changed._ Doors shifted to the center of walls, trapdoors appeared on ceiling and floor, and piles of dry bones that hadn't previously been there suddenly appeared. Worse, some of those bones lay stuck to the walls and ceiling. . . and the massive two-headed troll that was obviously responsible for them also appeared, standing easily on the ceiling.

"We've just teleported!" shouted Mialee in a fluting voice. "Or plane shifted. I'm not sure."

"Later," growled Regdar as he looked up at the troll just out of his reach. "We have other problems."​
In the recent "what are your favorite classic Dragon articles?" thread started by Erik Mona, I mentioned that I got a tremendous amount of mileage out of the tesseract articles back in Best of Dragon 1. It occurred to me that most folks nowadays don't remember or haven't read these, so I thought I'd explain the idea behind them.  The last time I used them, it made for an amazingly fun session.

Tesseracts and hypercubes have all kinds of cool mathematical ramifications that don't matter a darn to your D&D game.  Don't worry about them.  In the D&D sense, a tesseract is effectively a closed dungeon set as a demiplane. Until it is sealed or the trap triggered, it's just one room.  Once the demiplane is sealed, however, the room becomes a sealed plane of eight rooms. Each leads into the next in a never-ending loop, and there is no obvious way out. Even better, each wall and ceiling has its own gravity, making for some fun battles. 

So what is it? Picture a square cardboard box. Unfold it, and you have six different 2-D panels that look like this:







Now, what if those panels were 3d instead of 2d? If that were the case, then you'd be looking at a top-down dungeon map instead of an unfolded box.  Each "panel" of the unfolded box would be a regular room. In addition, there would be a 7th and an 8th "panel" that would sit above and below panel A. We'll call those G and H, set those aside for a moment, and come back to them in a bit.

A dungeon tesseract is typically entered through a trapped room that _seems_ normal while its entry door is opened. It can be placed into any dungeon, and is typically 10' x 10', 15' x 15', or 20' x 20' (depending on the type of tactical combat you want to have occur; more on this in a minute.)  Once all four doors of the room are sealed, however, everyone within it is thrust with no saving throw or SR into the closed demiplane of the tesseract.


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## Piratecat (Feb 29, 2004)

[h4]The Simple Version[/h4]



Mialee sighed. "Every room looks just like the next," she complained. This maze is endless!" The elf rolled her eyes.

"No it isn't," countered Lidda as she looked around her. "We're repeating rooms, Mialee. You can tell by the stuff stuck to the walls. I think there's only six rooms. I just can't figure out how they match up, or how to get out of here."​
The tesseract is an "unfolded" 3d box where each door links back to itself. Space doesn't work linearly; you can go out a door to the north and come back through a door from the west.  A top-down view would look like this.






The entry room is A, and the rest of the rooms spring into existence when the trap is triggered. If the group went back into B and kept heading west, they would run from B to D, from D to C, and from C back into A where they started. If they then headed north into E and then east, they'd come through the north door into C. Better hope someone has a good direction sense.

The only way out of such a place is through _plane shift_, similar spells, or a secific item hidden in the dungeon that is designed to allow exit. A typical example might be a special doorknob, a special key, or even a ring that turns a door back into a portal to the real world. 

In a simple tesseract, there is normal gravity and the top and bottom rooms G & H (remember them?) are simply ignored. It is best used as a six room closed dungeon that is near-impossible to escape. This can be great fun, because it's possible for an ecosystem to develop in these if there is some source of water (an endless fountain or decanter of endless water) and a food source (frequent new arrivals, fungus, or the like.) In such a setting, the strong will have triumphed over the weak, and any unwary adventurers will have to be careful not to be overmatched by the local predator.  Alternatively, perhaps only undead or constructs will exist in such a place, or maybe it is being used as a combination treasure vault and trap.


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## Piratecat (Feb 29, 2004)

[h4]The Complex Version[/h4]

Add in rooms G and H, and things get a lot more interesting. Here's a 3d picture of what the tesseract looks like in such a case. The red dots are doors (or trapdoors) leading from one room into the next. The arrows show which doorways connect to which room.







Mialee glared over at Regdar, who was trying to pick up a coin whose subjective gravity adhered it to the side wall. He seemed utterly fascinated. Then she glanced up from where Lidda danced on the ceiling 15' above her head. "Lidda! Come down here!"

"I'd love to," said Lidda shamelessly, "but I'm not sure how to get on the same relative gravity as you have. I ran through a couple of rooms and climbed a few poles, and look at me!" She threw a stone down at Mialee, but it hung in the air for a second right above the elf's head before tumbling back up towards Lidda. The halfling caught it effortlessly. "To me it looks like _you're_ standing on the ceiling. Weird."

Mialee rubbed her temples with two graceful fingers. She felt a migraine coming on.​
in a complex dungeon tesseract, each door is in the exact center of its wall.  You'd need some way to reach the entrances that are not easily accessible. In a tesseract with 10' square rooms, you can boost one another. In a larger tesseract, you may have  climbing poles in the center of each room.






The red lines are climbing poles; each one ends by a door (six doors in each room.) In such a structure, gravity is completely dependent of how you entered a room.

When you exit through a door, it is ALWAYS as if you climbed up a trapdoor. Thus, in the above diagram, if you were on the floor (normal gravity) of room F and decided to go down	through the door in the floor (F6), you would emerge in room H standing on the near wall (H1). Relative	gravity would have shifted.	

If you were on the "floor" of room C and wanted to get to the ceiling of room C, you would go:	
	Exit by C4, entering A2
	Exit by A5, entering G6
	Exit G2, entering C5
Voila! You're on the ceiling of C!	

Alternatively, you could simply climb up the pole to G2, turn around and climb back down again.  Much easier.	

If you didn't want to muck around with variable gravity, you could also decide that gravity was consistent throughout, and didn't vary when going through portals.	

I find the complex version fascinating, because 3d combat where some people are standing on the wall and some people are on the ceiling can be a lot of fun. in such a tesseract, room size is very important; for instance, if each wall is 40' square, you can only have ranged combat with people on the ceiling. If it is 10' square, things are a lot more intimate.


[h4]Using tesseracts in a game[/h4]
I originally used one as an "unescapable" trap designed to lure in and trap a NPC's enemies who tried the "scry and teleport" trick. The tesseract had its own ecosystem and series of powerful inhabitants, including a cannibalistic drow and his skeleton "family", a wraith who demanded life-energy in exchange for water and fungus, an insane priest with three followers who used "create food and water" to demand total loyalty, and one room that was commonly agreed to be neutral territory so that the different power factions could meet and talk with one another.

They make good jail cells as well. Powerful churches or wizards may use such things to contain their enemies, one of whom the PCs might be trying to find and save.

I think these are most useful for catching jaded players off guard, and unsettling them with something that isn't immediately intuitive. 

Anyways, I think tesseracts are interesting and fun; lord knows that they've sat around in my subconscious for over twenty years. Hope this is of some interest or use to folks.  Questions, comments, mistakes?

- Kevin Kulp, Piratecat


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## pogre (Feb 29, 2004)

I remember that!

Thanks for bringing it back to the surface for me!  

Is there a way you could edit the pics to get them working? or perhaps that is just something on my end?


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## Mordane76 (Feb 29, 2004)

I remember the idea of a tesseract from "A Wrinkle In Time" by Madeline L'Engle; they used it as a means to conduct dimensional and temporal travel by describing time and space as a tesseract... pretty trippy stuff, but cool nonetheless.


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## Allanon (Feb 29, 2004)

Great this is just the thing I needed to make them really hate the BBEG (and me), now to just come up with an interesting ecology. Thanks Piratecat!


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## BSF (Feb 29, 2004)

Heh!  I remember those from Dragon too.  Nicely done Piratecat.  I might actually have an application somewhere in my game for those this time around.


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## Piratecat (Feb 29, 2004)

Are the images visible now?  That'll teach me to link my pictures from a closed forum.

All pictures were done in Excel. I love that program.  

Here's an interesting page on mathematical tesseracts and other 4d shapes.


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## Painfully (Feb 29, 2004)

I remember seeing a movie called Hypercube.  It wasn't that great a movie, but it might be worth a look for those that are interested in some of the ways it can be used.


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## Gez (Feb 29, 2004)

I haven't seen these movies, but wasn't it the point of Cube and Hypercube?


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## Mordane76 (Feb 29, 2004)

Cube never specifically stated that it was a tesseract, but it might as well have been.  In Cube, each room was more or less a death trap; the rooms where all part of a gigantic cube that cycled where each individual room was in relation to the true exit from the total cube.  The cube had an astronomical number of rooms (by the participants' calculations), and one needed a degree in advanced algorithms (or had to a be numbers savant) to figure out the cycling time and pattern of the Cube to escape it.

Hypercube... no idea, though.


Cube could make an interesting one-shot dungeon, particularly for a d20 Modern game, as long as the people playing it hadn't seen or heard about the movie.  Such a module would mostly be a meat-grinder, though... but it might be fun to DM if all the players knew up front that they were going to die in the most special-effectsy sort of ways possible.


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## Allanon (Feb 29, 2004)

Piratecat said:
			
		

> Are the iimages now visible?
> 
> Here's an interesting page on mathematical tesseracts and other 4d shapes.




Yes the images are now visible, and they make visualising it all a lot easier


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## Matafuego (Feb 29, 2004)

Thanks a lot!!
I think I'll find some use for this pretty soon


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## DonAdam (Feb 29, 2004)

I'm going to be running a puzzle-heavy, magic-heavy dungeon soon; this will see use.

Many thanks.


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## alsih2o (Feb 29, 2004)

it dudn't get any better than this.


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## tarchon (Feb 29, 2004)

They work great as long as you don't have any 4-dwarves in the party always going "Do I detect a hyper-sloping tunnel?"

Salvador Dali does hypercubes.


_Changed your image to a link, Tarchon.  ~ PCat_


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## Kesh (Feb 29, 2004)

_Cube_ was a great movie. Haven't seen _Hypercube_ though.

Though I'm sure PKitty could use it to take this tesseract dungeon to whole new levels.


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## RingXero (Feb 29, 2004)

The movie 'Cube' didn't have a tesseract, it had just a large collection of cube rooms that mechanically moved around, the whole thing formed a cube itself that was within a larger cube, the larger cube was just large enough for a room cube to exist and move around the cube of rooms.  There was one extra cube that acted as the bridge between the cube of rooms and the exit door that was on the side of the larger cube, it was only there at the start and end of the cycle of movement, once every few days.  a lot of the rooms were trapped.

Cube 2: Hypercube, was a form of a tesseract, and as portrayed in the movie, had an almost infinite number of rooms, the group gets placed within one room and then that room 'unfolds' into an almost infinite number, then it starts to collapse into itself again.  Traps were present as well, no numbers to help out though.

I liked Cube, not as much Hypercube.


RX


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## Psionicist (Feb 29, 2004)

I have seen both Cube and Hypercube, and although the sequel isn't as good as the the original I can recommend it if you liked the first movie because of the cubes and not because it was different. 

Anyhow, nice cubes!


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## SpuneDagr (Feb 29, 2004)

Dude. My friends and I take turns DMing a dungeon-crawl. I'm totally doing the complex tesseract for my next level.


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## Zappo (Feb 29, 2004)

Eh, the hypercube is easy, do a hyperdodecahedron if you want to impress me.


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## Ferret (Feb 29, 2004)

Ow my head hurts.

Looks cool, but I'd rather not DM that game though.


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## Alcareru (Feb 29, 2004)

Ferret said:
			
		

> Ow my head hurts.
> 
> Looks cool, but I'd rather not DM that game though.



My head exploded. My liberal education suffered greatly from weak mathmatics (damn you Pythagoras!!)

Thanks P-cat.


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## Saeviomagy (Feb 29, 2004)

Of course there's no real reason to treat the thing as a tesseract.

Any random connection of rooms to other rooms for any number of rooms and doors will tend to confuse the hell out of players. The key is to make sure that there are loops, and once you've done that, you've created an impossible space that will (naturally) confuse the hell out of your players.


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## Psion (Feb 29, 2004)

I never read the dragon articles, but I wrote my own article on using tesseracts in gaming when I was in college. Spelling and grammar may not be at its brightest, but you might want to check it out:

http://members.tripod.com/~hawk_wind/worlds/Tess.html


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## tarchon (Feb 29, 2004)

> Salvador Dali does hypercubes.
> 
> 
> _Changed your image to a link, Tarchon.  ~ PCat_




The odd thing is the HTML image worked in the preview and when I viewed it right afterward.


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## Liolel (Feb 29, 2004)

head spinning, failed my knowledge check so badly that I don't even know what knowledge type check I failed.

Some things I guess I just can not grasp.


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## Piratecat (Mar 1, 2004)

I'm psyched that this is useful to some folks.

It's actually pretty simple once you stare at it for a few minutes. Just figure out the simple version - all doors connect to one another - and think of some cool encounters. Then imagine there's a top and bottom cube, and every time you go through a door the graviy shifts so that it feels like you're coming up out of a trapdoor. Once you've got that fixed in your head, it makes a lot more sense.


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## Crothian (Mar 1, 2004)

Thanks Kevin, but I have the feeling you're going to get a bit of hate mail from many, many PCs.


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## Abraxas (Mar 1, 2004)

You have to be careful and really know your group when you use these.  My DM a few years back actually used one of these on us + a bunch of math puzzles.

I had a sketch of the place after 1 loop (looking at a room from a different direction really didn't disorient me because of all the papare models I used to make as a kid)  and then it became a tedious exersize in finding the way out. 

A group I used one on later couldn't figure out the connectivity and got pretty frustrated with the endless loops.

I enjoy the larger hypercubes - rooms in the 100 x 100 x 100 size


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## reiella (Mar 1, 2004)

Quick, mostly off topic, question/comment about Tesseracts/Hypercubes.

Does anyone here know who formalized the theory/definition for them?


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## Squire James (Mar 1, 2004)

The module "Baba Yaga's Hut" (a variation of the 1e artifact with chicken legs that still belonged to its original owner) had a something like a tesseract as the interior of the hut.  I think it stuck to the Simple Version to save everyone's sanity.

I even remember a "choose your path" book that involved that same Hut, though I don't recall if it retained the same properties.


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## Thomas Hobbes (Mar 1, 2004)

To say this tickles my fancy is a grave understatement.  I don't know how I'm going to fit this into my game, but I am, gosh darn it....

Edit: Also thanks to Psion for an extremely interesting article.


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## Gez (Mar 1, 2004)

Without using fancy mathematics, I made a confusing dungeon once.

It was a little demiplane. It consisted of rooms, with several doors, all floating in limboplasmic stuff. Well, the "doors" were in fact transportation devices. Each time you opened one, it created a corridor with a random length, and another door at its end. This door at the end would connect to a random room.

It confused the players, until one figured it out. Then they stayed in a corridor, and opened/closed the door until they arrived in the place they were looking for.

Fortunately, the previous levels of the dungeon were more conventionals. Maze, caverns, insane labs, etc.


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## dpdx (Mar 1, 2004)

As a player, I would demand higher-than-normal (like, double) XP for functioning within this headache of a system.

Killing monster: 200 XP
Killing monster while in a tesseract: 400 XP

And treats at the table. Krispy Kremes, strong coffee and Advil, minimum.


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## Dark Jezter (Mar 1, 2004)

Every now and then, I see an idea on these forums that I just have to steal and use in my own campaign.  Thanks for posting this, Piratecat!

I just hope that I don't make my players' heads explode when I unleash this on them.


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## DMScott (Mar 1, 2004)

reiella said:
			
		

> Quick, mostly off topic, question/comment about Tesseracts/Hypercubes.
> 
> Does anyone here know who formalized the theory/definition for them?




Geometrically, it's merely the answer to the question "what is the analogue of a cube in 4-space", which was considered in ancient times. I don't know if it can be credited to any particular person.

For characteristics of tesseracts in fiction, I think they might have started with Robert Heinlein (_And he Built a Crooked House_, 1940).


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## Robbert Raets (Mar 1, 2004)

Hated the movie. It had it's science wrong, and most of the 'mysteries' were just to confuse the wonky writing.

That said, Piratecat's 8-cube dungeonroom is only the _border_ of the tesseract. Y'know, just like six squares are the border of a cube. (Not bad for someone who hates math, eh? )


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## Greybar (Mar 1, 2004)

Hmm... consider a simple hypercube, where each "room" is a stretch of cave football-sized (or rugby-sized, as you might prefer) in near darkness.  You cannot see the relative ceiling very well at any one point, so you don't have the obvious feeling of something being wrong.

This would let the local-ecology thing work pretty well.  Parties that hack at everything would take a while to realize what's wrong, whereas ones that stop to talk to the inhabitants might merely thing they are deranged cultists at first.

This also gives you more room to hide the McGuffin at allows exit from the trap.

hmmm

john
p.s. thanks Piratecat.


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## Castellan (Mar 1, 2004)

DMScott said:
			
		

> For characteristics of tesseracts in fiction, I think they might have started with Robert Heinlein (_And he Built a Crooked House_, 1940).




This is one of my favorite science fiction short stories. If you haven't read it, you should. And I even have a link for you:

http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html

It's not too long, and a *very* good read.

Enjoy!


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## MerakSpielman (Mar 1, 2004)

Nice, PC. I might use this sometime. Only problem is, my new group is somewhat math/spacial-deficient, though, so I might have to stick with the simple version.


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## Davelozzi (Mar 1, 2004)

The simple version works great for running _King's Quest d20_.


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## Sialia (Mar 1, 2004)

Abraxas said:
			
		

> You have to be careful and really know your group when you use these. My DM a few years back actually used one of these on us + a bunch of math puzzles.
> 
> I had a sketch of the place after 1 loop (looking at a room from a different direction really didn't disorient me because of all the papare models I used to make as a kid) and then it became a tedious exersize in finding the way out.



Ahh yes. My first thought when I saw Piratecat's post was "AAAAAaaaah! So that's where that really awful dungeon from that old college campaign came from. "

The GM in that case felt that the puzzle solving was interesting enough that there shouldn't be anything else around to distract us from it, and we should be left to work on it until we solved it, forever if need be. 

It was AWFUL. 

We were bored out of our minds--we never did find our way out and gave up on the campaign altogether rather than mess with the wretched thing anymore. There are rare times when you would actually rather abandon your characters than spend any more real time experiencing being them. Bored frustrated characters = bored frustrated players with better things to do with their lives.

Not one of us was close to understanding what the thing was, and now that I see it, I still have no idea how playing "guess what shape the GM is thinking of" would have helped us. He insisted that the solution to the trap was geometrical, but I still don't see how there is a "solution" inherent to the trap that doesn't still boil down to "find the right doohickey to frob," which is what we were stumbling around trying to do anyway.

I can't begin to describe how awful an experience this was.
A bad taste left in my mouth that over a decade of decent gaming have not washed away.


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## Aristotle (Mar 1, 2004)

Neat...

I had seen the movies Cube and Hypercube, and always wanted to run something based on them but never knew where to start. I'll use this article as a jumping off point.

I also like the hypercube idea where there is additional unfolding. Perhaps the "end cube" unfolds into an adjoining set of cubes every so many hours or days. And after so many cubes have formed they begind to fold back up. This might allow for a larger ecology that has been somewhat stable for a while, but is now in conflict as groups are forced to move into the territory of other groups to avoid the folding. Such an environment might make for an extended dungeon delve as the characters are placed in the dungeon and then forced to defen themselves as they attempt to find a way out before the whole place ceases to exist.


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## Pyrex (Mar 1, 2004)

I used the 8-room version once and my players nearly killed me.  

Of course, not only did I use 8 rooms, I made them figure out how to use the subjective gravity in order to acqueduct Magic Substance A (TM) into Receptacle B two rooms and four gravity-shifts away...


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## Piratecat (Mar 1, 2004)

Interestingly enough, when I used this the group interacted much more with the creatures around than with the space itself. They had been caught horribly off guard because they had teleported in expecting to find an injured enemy; instead, they found an illusion just as the trap triggered. Their primary goal was to get the heck out of there.

If I remember correctly they explored about five rooms and got valuable information from the inhabitants. I hadn't put a key into the space, since it was supposed to be a prison and trap.  Eventually they (correctly) decided that when the owner came to check on things there must be some way for him to get out, and they learned that one room (A) tended to be the entrance place. They centered their search there, and by careful use of _detect magic_ they discovered an invisible keyhole floating in the exact center of the room. Opening that refolded the hypercube and released them.

If they couldn't figure out a solution, I was prepared to fast forward time several months until another prisoner arrived; the players would have to tell me what they had done to change the local balance of power. Luckily, the need never occurred.

Sialia's and Abraxas' advice is superb. Nothing sucks more than being stuck in a boring space with no one to interact with, and facing a DM that's so pleased with the trap that it's not still fun. If you use this, make the creatures and space itself (for instance, through permanent illusions or veils in some rooms) exciting, and use the trap as a cool background.


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## Pielorinho (Mar 1, 2004)

I used it in a game once, thanks to Piratecat. It was pretty fun, although I discovered that Find the Path is a terrible spell .  I really had to work to make sure the players got what they needed out of the prison, after the cleric pulled that spell out.

My setup involved an extradimensional prison used for big nasties; due to a fluke, the PCs and the enemies they were fighting were sucked into the prison into separate rooms.  Each door was guarded by a symbol of weakness, to which the guardians were attuned; the doors could only be opened by the keys that the guardians carried.  

The guardians were heavily modified chain-demons with powers similar to the scary prison guards in Harry Potter:  they could shake you with fear from a gaze attack, they would gesture with their keys to make magical chains wrap around you (a hold person-ish spell with a reflex save instead of will), and they could animate chains that hung on each wall to attack.  They themselves were constructed entirely of coiled chains and locks.

There was a central control room with a gate leading out to the Ur-Prison:  an open immense cavern in which thousands of these guardians floated and from which there were hundreds of gates to similar tesseract prisons.  The gate was the only place from which a _plane shift_ could work successfully.

The prison-dimension did have some advantages:  prisoners couldn't die while there (all wounds regenerated at a rate of 1 hp/hour until the prisoner reached 0 hp), and all checks to escape were at a penalty (whether you were trying to escape a grapple, escape from chains, or escape by running away).

But as I said, the PCs short-circuited the whole thing by casting _Find the Path_.  My advice?  Run the adventure before they hit 11th level.

Daniel


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## Destil (Mar 1, 2004)

*Fun with gravity...*

Take two objects of equal mass through the hypercube in such a way that they get relative gravities in opposed directions, then place them against one and other and weld ‘em together. You’d have a ‘weightless’ object. Unfortunately I don’t see this as a way to support any weight since it would upset the equilibrium of forces needed to keep such objects in place if you apply any force to them. Still may have some applications for the creative, however.

     You could simply place them one underneath the other. As long as they stay in place they would support each others weight, but tip them a little and they’ll slide out of place. Maybe some sort of locking mechanism that could be triggered to whatever you want it to be so the two halves slip apart.

     Since even when an object has no effective weight it still has mass this could make for some nasty traps. With something strong enough to set a truly massive object into motion ‘horizontally’ (a heavy spring mechanism or some counterweights… this could also be used to produce clever systems of balancing counterweights) and no friction to worry about aside from air resistance sliding wall traps could suddenly take on a whole new dimension (pardon the pun). Combining some of these weights with an immovable rod or three could also produce some interesting works, like a pendulum that swings in full circles… make one of the chambers a vacuum (I’ll post a custom spell I designed for just such creative applications in house rules if I get around to it, ‘Airless Barrier’) you could have a perpetual motion machine setup inside of it.

     Bring two bars of iron through the hypercube so they have opposite specific gravities, melt them down and mix them. You could create alloys with a wide variety of relative gravities. Most likely going through a portal again would reset the relative gravities, though. For a truly large hypercube (say where each cell is a demiplane several miles across) this could have some very interesting applications as well. Weightless throwing weapons and ammunition comes to mind (unlimited range increments, going by the weightlessness rules in the MotP). Or axes where the half is made of material with a relative gravity that pulls it upwards, giving it a very different balance (and allowing some nasty downward chops, I’d wager). With a very heavy material like adamant you could create a free-standing tower shield for instance. It would be a bit of a pain to lug around but would most likely barely get knocked around at all by blows from missile weapons, almost like having it on an immovable rod (and since you’re not holding it you wouldn’t be subject to targeted spells while standing behind it), mobile cover.


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## MerakSpielman (Mar 1, 2004)

Let me get this straight... if you mixed a 50-50 specific gravity-ratio chunk of metal to make it weightless, it would weigh nothing but still have mass. So it would float on its own in midair, but you have to work against its mass in order to move it? If it's truly weightless, does that mean you can pick it up, toss it in the air, and it would float upwards forever? I'm trying to understand this...


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## Joshua Randall (Mar 1, 2004)

Piratecat said:
			
		

> Then imagine there's a top and bottom cube, and every time you go through a door the graviy shifts so that it feels like you're coming up out of a trapdoor. Once you've got that fixed in your head, it makes a lot more sense.



Just remember: in 3-space, the direction to the enemy is always *down*. (Thanks, _Ender's Game_!)

Random musing...
PC: "I cast _reverse gravity_."
DM: "Uh oh."


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## MerakSpielman (Mar 1, 2004)

It must be a disconcerting feeling if you jump into the trapdoor on the floor. As your feet enter, they start trying to "fall" up towards your head, but of course the rest of your body out masses them, so your legs would go through and start trying to "fall up," eventually you'd be floating in mid-air with your center of gravity poised on the border between the two opposing gravity areas. But it wouldn't feel weightless... since gravity is affecting each half of your body, just in different directions.


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## drnuncheon (Mar 2, 2004)

The changing of subjective gravity by making every trapdoor be in the floor when it's exited isn't a twist I've run into before.  At the time when I was using it, I left their subjective gravity the same (two people from different sides could climb through the door at the same time, and their gravity would still be different.)

In a way, that was even more evil, because a person's subjective gravity never changes - down was always down to them.  But their relative gravity can and did change - walk through the right sequence of doors and you're suddenly at right angles to the rest of your party.  In the Pcat way, it's a lot easier to get back together (everyone use the same door)...

Since I don't have the Cat's Excel skills (or Excel for that matter) we're going to have to do this without pictures, but you can get some six-siders to help visualize.  Arrange six of them in a cross shape, one on top of the cross, and one other off to the side to be the 'bottom' room.  If each die is a room, it's easy to see how they interconnect.

Now realize that since this is a tesseract, you can move those dice on the 'cross'.  Just keep one of the edges in place, and 'flop' the die over.  All those connections work, too.  You can flop all the way up and down the center 'post', and you can flop side to side on the cross as well.

So, imagine the PCs are at the top of the cross.  They go down a level - now they're in the center of the crossbars.  The rogue, scouting ahead, heads into one of the crossbars (still with the same gravity as the party), and then goes up.  Since there's no die there, you 'flop' the room she was in up, to see where she winds up - and she undergoes a change of gravity relative to her teammates.  Now she's back in the starting room - but she's on the "wall".  It seemed to her like she climbed through a trapdoor in the ceiling.  If she goes through the correct door, she'll be in the same room as her companions...just on a different wall.
A full tesseract has 48 rooms and 288 doors, enough to drive most party catrographers mad.


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## Piratecat (Mar 2, 2004)

Embarrassing confession: Dr Nuncheon, I think that's how it worked in the original Dragon articles. When I was trying to figure this out myself I didn't have access to the original articles, so I took the cheap way out and just decided to make gravity keep shifting when you went through a door. It allowed me to have a relatively easy way of having bad guys on walls and ceilings, but it was simple to keep track of. Anything that slowed down the game as I tried to keep gravity straight was more trouble than it was worth at the time.


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## Psion (Mar 2, 2004)

DMScott said:
			
		

> Geometrically, it's merely the answer to the question "what is the analogue of a cube in 4-space", which was considered in ancient times. I don't know if it can be credited to any particular person.




IIRC reading various books on polygotes, the book _Flatlander_ (late 1800s IIRC) is credited with being the impetus for a lot of thought on extra-dimensions.


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## GuardianLurker (Mar 2, 2004)

MerakSpielman said:
			
		

> Let me get this straight... if you mixed a 50-50 specific gravity-ratio chunk of metal to make it weightless, it would weigh nothing but still have mass. So it would float on its own in midair, but you have to work against its mass in order to move it? If it's truly weightless, does that mean you can pick it up, toss it in the air, and it would float upwards forever? I'm trying to understand this...




Nit-pick: the "specific gravity" of an object has a meaning (density related I believe) in chemisty. Its confusing to me to see it used for "subjective gravity", which is really what we're talking about here.

The mixed subjective gravity alloy he's talking isn't really weightless. Remember, weight is really a function of mass in an acceleration field. I.e. weight is the Force part of good ol' F=M*A from high school physics. What he's done is ensure that he has two opposing accelerations operating on the same object. You can think of these accelerations as great big huge springs.

When the item is in the exact middle of the room, and the forces are balance (springs of equal length), the object will appear to have no weight along that axis (up/down). Moving it from side-to-side (left/right, forward/backward), it will still weigh the same, and still take as much work to move.

Now, the item will want to stay and return to its balanced state in the up/down direction. If you pull it down (or push it up), the object will start to oscillate around the balance point, becoming a pendulum. Over time, the object will move less and less distance with each oscillation, coming to rest in the middle.

Make the object a 4-gravity alloy, and it will travel a circular path (instead of a straight one). Make it a 6-gravity alloy, and it will orbit the balance point. 

If you want real fun, mix the alloys in ratios other than 50/50.


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## Olive (Mar 2, 2004)

Isn't this really just a 8 room dungeon with a twist? And if so, how can you really put much int here? Won't the PCs kill everything in each of the 8 rooms and then just get bored looking around it?


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## Gutboy Barrelhouse (Mar 2, 2004)

Ahhh, Piratecat, thanks for bringing back fond memories.
Read both of the Tesseract pieces in Best of Dragon and the idea captivated me for a long time.
Stuck a few in my dungeons through the years.
Went totally mad and *mapped the inner planes on one, linked to the outer planes mapped on another.* Yep, I stuck the whole dang multiverse on a couple of tesseracts.
Let's not forget Heinlein's _He Built A Crooked House_. Great story.
Favorite memory of tesseract in my dungeon: PCs had opened all the doors and so, could see their own backs four rooms away. Mistook that for bad guys, shot arrows which hit themselves in the back! Priceless.


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## The Goblin King (Mar 2, 2004)

In the movie Hypercube the rooms had different Time traits!  I only watched the end but I know a time loop of some kind was created.  A room where time slowed to a crawl would be an incredibily nasty thing to do.


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## MerakSpielman (Mar 3, 2004)

Hypercube was a poorly done movie, IMHO. It had its moments, though. Like when the heroine character stabs the crazy dude in the eye - leaving the knife there - and slams a door on him, then hears a noise behind her and sees the crazy dude holding the knife to the neck of her friend, except he's clearly 20-30 years older, with a big scar over one eye, saying, "I've been waiting a long time for this moment" or something.


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