Alien Geometries: Difference between revisions

{{trope}}

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Alien Geometries are often depicted as being dangerous to the sanity of normal humans; where you have to ''read'' the [[Tome of Eldritch Lore]] for it to drive you crazy, just ''looking'' at this stuff can have an [[Motif of Harmful Sensation|unpleasant effect]] on your mental stability. Or at least really hurt your eyes. <ref> In real life, the mathematical implications of non-Euclidean geometry tend to hurt even math majors' brains.</ref>

[[Eldritch Location|Eldritch Locations]] are a good place to find this. Sometimes it is a single wall or building that is just a little... ''off''. See also [[Hyperspace Is a Scary Place]], an entire alternate universe that just does not make sense. A [[Minus World]] in video games might be considered one due to [[Good Bad Bugs|unintentional programming bugs.]]

== Anime and Manga ==

* ''Casshern'' shows what appears to be a metal bolt of lightning -- or a metal construct -- striking from the sky and staying in place for several days, inciting a transfer of what we are led to believe is superdimensional energy into our dimension. This energy is visible in the form of sparkling mystical runes hovering in the air facing the observer. ''It's awesome''.

== Comic Books ==

* In the JLA storyline ''Rock of Ages'' the Joker nearly drives Superman and the Martian Manhunter mad by trapping them in a maze-like satellite, the structure of which is controlled by his subconscious mind.

** In a another sequence, when Calvin was told to look at things from multiple perspectives he took literally and started seeing things as a Cubist painting, and another time when he used supposed lack of depth perception as an excuse for running into furniture.

* This is generally how much of [[Galactus]]'s technology is portrayed in Marvel comics. An alternate universe version of Reed Richards once spent decades figuring out the technology of a single room in the alien creature's massive home.

== Fanfiction ==

* In ''[[Fuck the Jesus Beam (Fanfic)|Fuck the Jesus Beam]]'', there is a city that literally ''does not exist'', as it is only a lie. Despite this, it is also a physical location. Given the name Αδιβ, when someone who can see in only three dimension looks at it, it appears normal, but in progressively higher dimensions, the architecture becomes more and more bizarre.

== Films -- Live-Action ==

** Even more impressive when you consider that they were created in the pre-digital era using 28 precisely-timed exposures.

== Literature ==

** In the film, the proportions are a sexier 1:9:25 (1^2:3^2:5^2), or maybe 1:8:27 (1^3:2^3:3^3). In comparison, 1:4:9 looked like a brick.

* The House of the Maker from ''[[The First Law]]'' trilogy by Joe Abercrombie. The protagonists enter about halfway up, walk around a bit inside but never ascend or descend, then exit on the roof. Most of the characters can't wait to get out of the place, even if it does involve crossing the narrow, rail-less, hundred-foot-high bridge. And there's always the possibility of leaving the place ''before'' entering it.

** In [[Dan Abnett]]'s ''[[Eisenhorn]]'' novel ''Xenos'', the saruthi "tetrascapes" include regular octagons that nevertheless tessalate. Eisenhorn rescues some [[New Meat|green soldiers]] from such a tetrascape, and later chooses them over experienced soldiers to go into one. Wise of him: the green soldiers had actually seen a tetrascape before, and the experienced ones hadn't. As a result, the "greens" manage to shoot and kill dozens of enemies, but the elite Deathwatch Space Marine attached to Eisenhower's squad can't hit ''anything'' thanks to the effect the twisted geometries have on ballistics.

** In [[Ben Counter]]'s ''[[Horus Heresy]]'' novel ''Galaxy In Flames'', Death's Tomb is bigger on the inside than the outside — as well as other repulsive features.

** Lampshaded by the Red Queen, when Alice found herself unable to run quickly. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" The Queen was able to travel much faster, since she was a Queen, [[Chess Motif|and can cross the width and breadth of the chessboard in a single move.]]

* ''[[Thursday Next]]'''s Uncle Mycroft, among his other [[Mad Science]] projects, developed "Nextian Geometry" with his wife, said to be based on how a cylinder looks like a rectangle from the side, which allows one to use a circular cutter on dough without any left over: it makes circles tesselate.

* [[Robert A. Heinlein]]'s short story ''[[And He Built a Crooked House]]'' involves an architect who, inspired by higher-dimensional geometry and high real-estate prices, builds a house in the shape of an unfolded hypercube. Then an earthquake makes it fold in on itself into a hypercube, so to the architect's delight it's eight times roomier on the inside than on the outside. Just one small problem: the house's new topology makes it a bit difficult to leave once you're inside. When you do get outside, you may have a whole new problem.<br /><br />A math-nerd resident of ''[[Second Life]]'' actually went and reproduced the Crooked House in 3d, and if it's still rezed somewhere public you can actually walk through it. Not a real hypercube of course but some excellent special effects. [http://nwn.blogs.com/nwn/2006/06/_and_he_rezzed_.html Here's the story with video.]

* ''[[The Magids|Deep Secret]]'' - the [[Place of Power|Hotel Babylon]] has halls where you can go around more than four right angles before coming back where you started thanks to the building being on top of a bunch of [[Ley Line|ley lines]].

* ''[[The Wheel of Time]]'' - The Aelfinn and Eelfinn ("the Finn") inhabit one or more separate dimensions described by the author as having radically different natural laws. Successive windows do not show what one might expect. That the magic system in the series is heavily geometric likely has a great deal to do with why its use is explicitly forbidden there. The doorways into their realm also resemble this in the "real world", and are described as "twisted".<br /><br />Though it's less apparent, the same is true of the Ways, an artificially-constructed dimension meant for quick travel. Except in one dream sequence (which, for complicated reasons, probably reflects the reality of the Ways), the realm is extremely dark, but travelers there have noted that by the arc of the bridges they're walking on, the platform they've just arrived at should be directly beneath the last. During the dream sequence, it becomes apparent that the platform-islands extend infinitely downward—and unless you follow the bridges with your eyes, appear to be on the same plane. The doorways seem to be a description of a three-dimensional Möbius strip.

* ''[[Night Shift]]'' - Inverted in Stephen King's short story ''I Am the Doorway''. An alien lifeform [[Humans Through Alien Eyes|sees]] a boy walking with a sieve under his arm: "an abominated creature that moved and respired and carried a device of wood and wire under its arm, a device constructed of geometrically impossible right angles."

* In Stephen King's novel ''[[From a Buick 8]],'' the titular car is actually an interdimensional portal/device that only looks like a car. It's noted that the human eye perceives it as a car because that's the only image the mind can supply for the actual shape of the device.

** He also appeared to use this in ''[[Out of the Silent Planet]]'', but the room turns out be normal human geometry, just a very unusual sort.

** The sunken city of R'lyeh

** The Antarctic city in ''At The Mountains Of Madness''.

* ''The Hounds of Tindalos'', by Lovecraft's friend Frank Belknap Long, features ravenous creatures of weird geometry who travel trough time and space, and the only way to avoid them once they're on your trail is to completely avoid sharp angles (such as in a completely circular room).

* ''[[The Way Series|Eon]]'', by Greg Bear, features an asteroid hollowed out by people from ..elsewhere, with seven chambers running along its internal axis. The first six contain cities, parks, a spaceport and loading area, and power generators. The seventh chamber {{spoiler|goes on forever, contains objects made from redistributing probability over space, and a mathematical singularity running along its centre.}} And ''then'' things start to get weird.

** Bloody Stupid Johnson, architect, [[Bungling Inventor]], and general anti-genius regularly does this kind of stuff ''entirely by accident''.<br /><br />He once designed a letter-sorting machine whose central component was a wheel that had pi equal to ''exactly'' three. This causes it to sort out letters it hasn't had put in yet, among other oddities.<br /><br />Empirical Crescent, a row of terraced houses where every door and window leads somewhere other than where you'd expect it to lead. At least it makes it easier to get rid of rubbish—just toss it into the garden. After all, it might not be your garden.<br /><br />The reason for this corruption of dimensions occurs because the row of houses is crescent shaped on the outside only. Inside, it's supposedly laid out like a straight row. Presumably the two configurations conflict. Occupants had a tendency to leave in the middle of the night, often without stopping to pack...

*** The first chapter mentions one of the gods using a 7-sided (but still cube-shaped) die to cheat.

** The buildings of the Unseen University, which have been rather strongly influenced by the vast amount of magic that has flowed through its halls over the centuries, have floors and rooms where logic says they simply could not exist. Magic is as much a part of the architecture as cement.

*** In reality, however, power is equal to dW/dt, or energy acting as work divided by time, and energy is equal to m*c^2, or mass multiplied by the speed of light in a vacuum squared. However, the lack of correct physical defintions is overlooked due to the [[Rule of Funny]].

** Death's house is bigger on the inside than on the outside, being the size of a cottage on the outside, but the size of a small castle on the inside. This is not so much intentional, but is rather the result of a slight blindness to ordinary architecture on Death's part. Many of the rooms have the peculiar effect of being enormous at the same time as being regularly sized. Death's room in particular is stated to be about a mile wide, but most can be crossed in only a few steps.

** The Tooth Fairy's house in ''Hogfather'' is another example of this trope.

** The Gnarly Ground in Lancre is a seriously bizarre landscape of crags and valleys "scrunched up" into a small area, overlapping in space; what geographical features you see there and have to deal with depend largely on your mindset. It makes a good hiding place.

* The Starfish structures in ''[[Blind Lake]]'' have disturbing interior geometry. Robot probes (and people) who go in too far don't come back. The deep interior seems to be entirely exempt from the usual rules of time and space.

* In the eighth book of the ''[[Everworld]]'' series, the main characters are cast into an inverted realm where the ground they stand on is ''above'' their heads, and gravity pulls them ''up'', with the colors of everything reversed for good measure. This naturally strongly bothers David, April, Jalil, and Christopher. [[Hot Witch|Senna]], however, ''likes'' it, and compares the reversed plane to fine art.

** Many sequels have been written. ''Flatterland'' has even ''more'' bizarre geometry, including a hyperbolic world, a fractal world, a grid world, and so on.

* ''Threshold'' by Caitlin Kieran contains a fossil in a shape that cannot exist, causing the heroine to [[Go Mad From the Revelation|black out when she looks at it too long.]] What is this sinister shape? [[Writers Cannot Do Math|A regular heptagon.]]

** Even weirder, {{spoiler|In the novel version, it turns out that the Inverted World is actually EARTH - the inhabitants of the City only perceive it the way they do because their perceptions (and possibly their physical reality) have been altered.}}

* The protagonist of ''[[Return From the Stars]]'' comes back to Earth after over a hundred years of absence. In the meanwhile, architecture has changed/evolved so much and [[Bizarrchitecture|so confusingly]] that when he first steps out into a spaceship depot, everything around looks to him like an abstract, shapeless muddle of pathways.

* In the [[Star Trek Shatnerverse]] novel ''The Return'', The Borg have built a hypercube base inside a subspace tunnel.

* ''[[The Last Battle]]'', the final volune of ''[[The Chronicles of Narnia]]'', ends in a world that's essentially the opposite of reality, in that the closer you get to the center, the more there is.

{{quote| ''After the man had fallen through every place and every time that ever he had even imagined, he began to fall through the places that his mind could not conceive. He passed into structures that did not follow geometry, saw shapes that had no edges or sides, that extended into themselves and into all directions. He saw triangles with one hundred eighty one degrees. He saw minds that had no reason or morality. He saw colors indescribable to others. He saw the true shapes of his dreams, and the ten dimensions of the earth and sky. He saw what no one saw, felt what no one felt. He heard sounds with his finger tips, and tasted with his ears. He had secrets whispered to him in a language that can't be translated.''}}

* In [[Larry Niven]]'s ''Protector'' the Brennan Monster amuses himself by creating full scale replicas of some of Escher's art, using things like artificial gravity to make them work.

== Live Action TV ==

* The ''[[Doctor Who]]'' [[Expanded Universe]] speculates that this is the default setting for the interior of a TARDIS, and that the Doctor's TARDIS projects a more easily comprehended interior so as not to [[Brown Note|freak out]] the Doctor's human companions. [[Genius Loci|She is just a sweet old thing.]]<br /><br />In "The Lodger" the Doctor uncovers an alien time-distortion device similar to the TARDIS in the upstairs flat of a British apartment building. Amy, poring over the building plans for the address, discovered that the building didn't even have an upstairs, it was a one-story building. Perception filters kept people from noticing anything out of the ordinary.

** Not to mention how a triangular-pyramid shaped spacecraft can land on a square-pyramid.

* ''[[Neverwhere]]'' does a very nice demonstration of this in passing. The protagonist is led down into the London Underground, then through a door, and down a stair case. This continues, always going down, until they reach a small door and step out on to the roof of a building.

* The ''[[Hitch Hikers Guide to The Galaxy]]'' series has a few examples:

== Paintings ==

* In [[Mortasheen]], this is where the [http://www.bogleech.com/mortasheen/xenogog.htm Xenogog] lives naturally, only coming into ours with a screw up in a time travel experiment.

* The near-universal hallmark of things made in the name of Chaos in ''[[Warhammer 40000]]''. For example the [[Always Chaotic Evil|Dark]] [[Our Elves Are Better|Eldar]] capital Commoragh has spatial anomalies, "wandering shadows that tear apart the unwary" and many other dire things. It lies deep within a nest of extra-dimensional tunnels.

** The Classic ''Dungeons & Dragons'' system delved deep into this trope with its boxed set for PC Immortals, redefining game-reality in terms of five spatial dimensions. Mortal creatures exist in three, Immortals in four, and Old Ones in five. ''Which'' three a mortal creature occupies can vary: Nightmare-reality creatures share only one spatial dimension with Normal-reality beings such as humans, and "nippers" from the Astral Plane overlap with dimensions of both Nightmare and Normal reality. As for how all this applies to the geometry of the planes themselves, thinking about it could make [[Your Head Asplode]].

** The Planes in D&D 3rd edition got like this at times, such as an infinite plane having an edge. Seasoned Planeswalkers tended to give the advice "Try not to think about it."

*** In the ''Queen of the Demonweb Pits'' module, the players ventured into The Abyss to confront Lolth, the demon queen of the spiders. Lolth's domain consisted mainly of long, open passageways hanging in space. Even though these passages pass over and below each other, they never ascend or descend in any way.

*** Less heady are the Githzerai monasteries on Limbo, which take advantage of the fact that "down" is whichever direction you want it to be, giving us some extremely Escher-esque architecture.

* ''[[GURPS|GURPS: Illuminati University]]'' describes a campus which teaches human students and everything else capable of paying the exorbitant university fees how to function as [[Mad Scientist|Mad Scientists]], World-Conquering Dictators, Marketing Specialists, and other strange jobs.<br /><br />The campus is a stereotypical university: the campus has an open area or "Quad" in which students and staff may pause for reflection, study, impromptu lectures and other activities from which [[Hilarity Ensues|adventures may spring]]. Illuminated University has ''The Pent'', which has five sides for [[Rule of Cool|no particular reason]]; students who happen to have a protractor handy will discover that all five of the corners have 90-degree angles. One of the dorms is stated as having rather similar angles.

* The Terminal in ''[[Over the Edge]]''. It's Al Amarja's massive airport, nine-storeys high and built like a maze. Navigating it is so difficult, people need to hire guides. Of course, the best part is when you leave the airport and see that it's built like a step-pyramid. An ''upside-down'' step-pyramid.

** As you might imagine, this makes travel around Malfeas... interesting. Once you enter the dimension proper, you must cross Cecelyne, the Endless Desert, for five days to actually get to the Demon City. No, it doesn't matter if you're walking on foot, riding on horseback, and piloting a First Age airship. The trip ''always'' takes five days. Then you get to the Demon City, which is layers upon layers stacked on top of one another - but each layer has Ligier, the Green Sun, shining above it, no matter how deep down it is.

== Video Games ==

** Several third party [[Game Mod|Game Mods]] do this, for example one level of "Keep the Home Fires Burning" has a 720-degree circular hallway with two overlapping hallways going down the middle. And "Schmackle" in ''Marathon EVIL'' has a part where you go through a portal into an alternate version of the level occupying the same space. Sort of like the "Tier Drops" example below.

*** The level "Lunatic Fringe" is a 720-degree circular hallway around a central hub, so you have to walk around the hub twice before actually returning to where you started.

*** The level "Tier Drops" has four overlapping areas connected by a hallway around them and drop tubes inside. The guys at 3D Realms beat the level in just ''ten seconds''.

*** A few of the game's levels actually use these quirks transparently and a number of user-made levels deliberately work to show them off or to fake architecture that's not truly possible with the game engine.

** ''[[Descent]]'' can use similar techniques with user-made levels. One example was appropriately titled "4D".

** The Source engine as of 2011 has a feature that allows for something like this; they [[Mundane Utility|mainly just used it for]] testing unfinished level designs. It can produce some [http://www.youtube.com/watch?v=_xFbRecjKQA crazy stuff] if you know how to use it right. Unfortunately, the version of the engine it's in can really only make ''Portal 2'' add-on content for now.

** The Unreal engine is also capable of things like torus-shaped levels and endless corridors with creative application of warpzones, right from the earliest version of the engine. It's far from perfect, though: non-projectile or "hitscan" weapons can't shoot through, stacking more than four warpzones results in the engine glitching and drawing the portal surface's texture, warpzones must have the exact same dimensions at both ends or the game will crash, etc.. The level DM-Fractal even has a relatively simple "anyone falling into the floor trap falls out of a hole in the ceiling" trick.

* A little-known 2.5D sci-fi (considering it was made in Russia, nostalgical sci-fi) first person shooter ''[[Madspace]]'' embodies this trope, complete with this feature actually being [[All There in the Manual|mentioned in the manual]]. If you decided to dig the game out, there's one thing you should consider... never ''ever'' use the ghost cheatcode.

* Games like ''[[Asteroids]]'', 'and the like, use an unwrapped toroidal universe—the environments have the same geometry as the surface of a donut. [[Super Mario War]] does the same thing by default, but because all the levels are custom-designed, you can modify it to take place in an enclosed space, or add kill zones at the sides of the game window [[Super Smash Bros]]-style.

** Which is at least easy to wrap one's head around, it seems. For the truly mind-bending type, see the above example about the Source engine.

* The Polyhedron in the Russian art-house game ''[[Pathologic]]''. Hooooo boy. From the outside, the building simply appears to be impossible. {{spoiler|The inside is implied to more or less be another ''dimension'', inhabited by hundreds of children suspended in some kind of weird dream world.}} Yes, the game is a total [[Mind Screw]].

* In ''[[Diablo II]]'', the Arcane Sanctuary area contains some quite Escher-esque geometry: platforms are supported by pillars that stand on other platforms which ought to be at the same height. The game gives the option of displaying in perspective (parallel lines converge at the horizon) or isometric (parallel lines remain parallel). In Arcane Sanctuary, the perspective option is disabled, due to it being impossible to draw.

** The Canyon of the Magi doesn't let you use perspective either for no obvious reason. Maybe an anomaly left behind from the magical battle that happened here? Or maybe I'm overthinking this and it's just a bug.

* ''Echochrome'' is a puzzle game based on the works of M. C. Escher. The geometries are as weird as you might expect.

** To elaborate, in the game, you are allowed to "cheat" the laws of perspective because only the camera angle's perspective counts as "real". If there is a beam covering up a hole, the hole [[Logic Bomb|then ceases to exist.]] This is a necessary skill to guide the main character<ref>You control the camera, not the player character</ref> to safety.

** There's also the Lost Cave in [[Fire Red]] and [[Leaf Green]], in which it is possible to walk through a door, turn around, and find yourself in a completely different room than you started in.

** The Psychic move Trick Room...well, look at the description. "The user creates a bizarre area in which slower Pokémon get to move first for five turns." The user warps space so that going slower makes them move faster. That's pretty alien.

* According to the characters, the Primeval Thaig in [[Dragon Age II]], although we have to [[Take Our Word for It|take their word for it]], cuz that's kind of hard to program.

* Certain areas in the ''[[Silent Hill]]'' series, usually paired with [[Chaos Architecture]]; examples include but are not limited to: the girls' bathroom in [[Silent Hill 1|the alternate school]] which leads you to the second floor when you exit it, the door between the first and second floors in Nowhere, and the convoluted space-time of the alternate Lakeview Hotel in ''[[Silent Hill 2]]'', where the doors now teleport you around the building, and you have to find the correct one that will warp you to the otherwise inaccessible east wing. And going back in the same door leads to a different door than the one you entered. Not to mention the Historical Society, where you jump down several extremely deep holes, then take an elevator even further down, but when you come out of it on the lakefront, you're only about 20 feet below where you started. It also has Escher-esque architecture at points, e.g. the room with the hole leading to the prison (doors on the floor and walls), and the rotating room in the Labyrinth.

** Of course, rather disappointingly, there's nothing physically impossible about it—it's just a web of extremely convoluted tunnels.

* In ''[[Guild Wars]]'', there is no in-game map showing the entirety of the Realm of Torment. There is a very good reason for this- direction and distance are coherent within regions of the Torment, but not between them.

** Not so much a geometrical issue, don't think it fits here. Sigil is alive. The streets move because they'd rather be somewhere else. Or they're making space for newborn streets. Also, the city is a Portal Nexus. If you enter a house and find yourself in a larger-than-seems-likely space, you might not technically be in Sigil anymore, whether you just entered heaven or hell is pretty much a matter of luck.

** Sigil also happens to be at the top of an infinitely-tall spire; something that certainly can't be done in regular geometry.

**** ''And'' manages to be infinitely tall while having both a bottom and a top, both of which can be visited.

** However, one character talks about being transported by a hidden portal that consists of the archway that appears when approaching two trees from the right angle.

* A wonderful example in text adventure ''Trinity'', which contains a Klein Bottle that you can walk through. After you do, east and west are reversed everywhere else in the game. This is useful for {{spoiler|turning a clockwise screw into a counterclockwise screw}}.

* ''[[Visions and Voices]]'' has the mirror worlds. While they aren't that extreme, they can be pretty freaky—numerous characters are evidently freaked out upon seeing them.

* ''[[Prey]]'' is based aboard a cybernetic moon size space ship where things like gravity and even space-time are not consistent. The player character occasionally remarks on this.

* A particular player-made map for ''[[Far Cry|Far Cry 2]]'' is shaped like a cube with two sides removed and tilted on its axis. Due to the inclines that a player is able to move on without sliding off or falling, the players can run on all four of the inner faces, even though they appear to be perpendicular without close examination. This leads to strange cases of a player standing on the wall of a building and firing at someone on the street ahead of them, which is going into the sky.

** The Fairies' Woods in ''[[Oracle of Ages]]'', in which moving from one screen to the next and back again winds up placing you in a completely different spot than before.

** ''[[Majoras Mask]]'' - The Stone Tower in involves reversing gravity so you can run around in the ceilings of rooms. This is made even more [[Mind Screw|mind-twisting]] by the fact that the horizontal orientation of the temple is preserved after it is flipped over -- i.e. a room on the right of the entrance normally would stay on the right of the entrance when flipped -- meaning the dungeon somehow ''inverted itself''. Even the Perfect Guide writers were confused by the whole thing.

* There's a game in development, called ''Miegakure'', in which the puzzle aspect involves a 4th spatial dimension. Just trying to visualize a textual description of the game mechanics is enough to cause a headache. A three-dimensional environment can be represented by multiple two-dimensional images. Imagine taking an object, and tracing its outline on a flat surface from each side. You can get a good idea of the actual shape of the object in three dimensions by putting those images together in your head. What Miegakure does is present a four-dimensional environment in a similar fashion, in a series of three-dimensional models. You can switch the "angle" from which you view the four-dimensional environment by hiding one dimension and causing another one to become visible, similar to how a flat picture of a three-dimensional object "hides" the depth dimension.

* The Bizarre Room in the Wonderland level of ''[[Kingdom Hearts]]''. Entering from different points of the world -- including the room itself -- leads to you stand on different dimensions of the room, i.e. the walls and roof. However, the dimensions of the areas you are entering ''from'' don't change at all.

* Two areas in ''[[Sub Machine|SubMachine: Subnet Exploration Project]]'' have rooms that connect in ways they should not. Appropriately, one of them houses a fan theory that the [[Sub Machine]] is looped through the fourth dimension, and the other is a series of padded cells. Another area is, for no apparent reason, sideways.

* In ''[[The Dig]]'', the architecture of the Cocytans shows a lot of reverence to the 5 Platonic solids, including shapes with strange symmetries; and there also the in-universe example of space-time six -- a 6 dimensional realm.

* Entering the main room of the Tremere chantry in ''[[Vampire: The Masquerade Bloodlines]]'' is easy: just walk in the front door, go straight, take a left, a right, then another left. But try to reverse those directions to leave, and you end up back at the same place you started. Any wrong turn on the way out sends you back to the main hall, and the path out is not the same as the path in.

* Invoked in one of the epilogues in the game ''[[Primal Rage]]''. When you play as Vertigo, the epilogue says she forced enslaved humans to build a palace whose alien gemoetries drove the human workers insane. There's a illustration with it.

* There's an old russian [[Game Mod|mod]] of the 1990 ''[[Prince of Persia]]'' game, called 4D Prince of Persia. It takes advantage of the way room connections are programmed and creates levels where normal directions don't apply: Levels that loop and wrap around, corridors where running back doesn't take you where you came from, [[Bottomless Pits|infinite pits]]... The mod [[Downplayed Trope|doesn't do it that much actually]] however; it only does it on palace levels, and leaves many levels unchanged. Then there are further mods ad level packs inspired by 4D, and they take the idea [[Up to Eleven|much further]].

== Webcomics ==

* In ''[[8-Bit Theater (Webcomic)|Eight Bit Theater]]'', Black Mage's face is apparently so hideous as to be non-Euclidean—the hat keeping his features in shadow prevents people from [[Go Mad From the Revelation|being driven insane just by looking at it]], as seen [http://www.nuklearpower.com/2001/06/18/episode-044-what-the-hell-just-happened-in-survivor-8-bit-style-part-9/ here]. A more recent strip implied that revealing himself would ''[http://www.nuklearpower.com/2008/01/05/episode-939-total-protonic-reversal/ destroy the universe]'', but this was just an idle daydream.<br /><br />When the Light Warriors enter the [[The Very Definitely Final Dungeon|new-and-improved Temple of Fiends]], Black Mage criticizes it's infantile sense of twisted geometry (The room is merely upside-down for no reason), claiming that to "draw out ancient and malevolent forces of the underverse" you need to "[http://www.nuklearpower.com/2008/06/12/episode-1004-fun-house/ start with parallel lines that intersect]".

* According to ''[[Questionable Content]]'', [http://questionablecontent.net/view.php?comic=1380 dildos] can have alien geometries too.

* The polygons in ''[[Triangle and Robert]]'' tend to have their own style of geometry, leading to strips like [http://tr.froup.com/tr.pl?412 this] or [http://tr.froup.com/tr.pl?2327 this].

* From ''[[Tales of the Questor]]'', we have the ''[http://www.rhjunior.com/totq/00513.html Unseleigh castle...]''

** [http://www.mspaintadventures.com/?s=6&p=004942 The final form that Skaia takes as well.]

* ''[[Chainsawsuit]]'': [http://chainsawsuit.com/2010/05/12/cthulhu-cheats/ Cthulhu gets caught using non-Euclidian dice during a game of] [[Dungeons and Dragons|Humans and Habitats]].

* A few arcs in ''[[Fans]]'' (notably the whole of Book 5) centered around a power-object called the 23-Sider, an RPG die with 23 identical sides. When the 23-Sider was formed in Book 5 it warped reality.

== Web Original ==

* Doctor Ka's mansion in the ''[[Global Guardians PBEM Universe]]'' is effectively a [[wikipedia:Tesseract|tesseract]], and is definitely [[Bag of Holding|bigger on the inside]] than on the out. If its layout was drawn on a set of blueprints it would feature rooms that overlapped spatially, rooms that seemed to have no exits or entrances, spherical rooms that nonetheless had corners, and rooms where the plane of gravity depending on which way you were looking.

{{quote| '''Prof. █████████:''' We know that after 2 comes 3 and after 3 comes 4. What this formula proves is that we missed a number somewhere. Imagine if all our technology was based on the belief that after 4 came 6. We simply didn't know or conceive of 5. That is in essence what this formula proves. We missed a number. ... I don't think it "destroys" anything. I think it tries integrating itself into our system and our system can't hold it.}}

* The [[PPC|PPC Headquarters]]: It is unclear whether it is just a confusing maze of a building or whether it can actually move around, but thanks to the Laws of Comedy, one of the only ways to find the place you are trying to go is to distract yourself and not think about it. However, it "was" built by alien plants, and they seem to be able to navigate it just fine. Also, poorly-constructed descriptions in the Word Worlds cause some rather eye-breaking visuals for the agents when the worlds try to put them into practice.

** In one mission, Agents [[Tempting Fate|tempted fate]] by saying "It's a wonder we're still in three dimensions."

** The [[Hell Hotel]] in the [[Halloween Episode]] of ''[[Tribe Twelve]]''.

** ''[[One Hundred Yard Stare]]'': When Avery, Macy, and Ellie first run from Slenderman there is a good dosing of this, with them starting in a yard of some sort and ending up, after a jaunt in a building, next to a moving train.

* ''[[The Dionaea House]]''. All of them. The one in Boise, for example, has a second floor that is not visible from the outside. It says something that [[People Puppets|this is]] [[Genius Loci|not the]] [[I'm a Humanitarian|strangest thing about it.]]

* There is no geometry but [[Time Cube]]. You are educated stupid. Time Cube is so obviously true that knowing anything except Time Cube will drive you crazy when compared to Time Cube.

* [[The Fear Mythos|The Empty City]], also known as the City of Empty Shadows or [[Names to Run Away From Really Fast|DEVOURER]]. It's a [[Genius Loci|living city]] which intentionally makes itself into [[Alien Geometries]] in order to make sure its victims stay within it until they die. [[And I Must Scream|Or worse.]]

== Western Animation ==

* The ''Foghorn Leghorn'' cartoon "Little Boy Boo" plays this for laughs. Foghorn is playing hide and seek with a child genius and hides in the coal bin. The kid performs a few calculations and then ''digs Foghorn out of the lawn''. A very befuddled Foghorn protests that he was in the coal bin, but the kid just shakes his head and holds up the calculations. Foghorn then goes to look inside the coal bin, but decides "No, I'd better not look. I just ''might'' be in there."

* Presumably alien geometries are how [[Scooby Doo]] and his gang perform their [[Scooby-Dooby Doors|strange chase routines]]. Perhaps something much more sinister than anyone suspected was going on the whole time.

* There are multiple projections used on pictures, most commonly the gnomonic projection. The fisheye projection is also well-known. The reason these are necessary is that people see in elliptic geometry. As a simple example, imagine that you are standing on a railroad track, facing along the track. If you look straight down, the rails will look parallel, but if you look straight forward, they will intersect. If you look halfway between, you should be able to see where they're parallel and where they intersect, despite being perfectly straight.

* Relativistic physics border that territory at times. e.g length contraction says when moving at a high enough speed there is a visible decrease in lengths (the length decrease is always there, just you can not see the difference caused by sqrt(1-(v/c)^2)). That is still believable if you have some fantasy. The trouble is, from the other point of view the not moving system is the one shortened. Better not try it yourself.<br /><br />To clear the confusion (as much as possible, anyway), if things are moving, they are shortened in the direction of their motion by a numerical factor dependent on their velocity. If you measure the length of an object at rest you will always find it is greater than the length of the same object moving at a finite speed with respect to you. Of course, in said object's reference frame, it is by definition at rest, and it is ''you'' who is moving, and therefore, shortened.<br /><br />The distance that the distance one through spacetime, the spaectime interval, is of a constant length, and is determined by the formula s = sqrt(x^2 + y^2 + z^2 - (c*t)^2). That is to say, although space contracts by a factor of sqrt(1-(v/c)^2)), time expands by an equal factor, so the spacetime interval that you cross remains constant. This means that the velocity of the thing that travels along the interval is already determined for any given observer. For the layman, this means that objects do not really shrink when you travel at velocity; they are actually just rotating in four dimensions, and just appear to shrink because we can only see in three dimenions.

* The Bermuda Triangle, according to many theories and reports. In addition to vehicles vanishing without trace (no wreckage left), reappearing after disappearing from radar, etc. some people have reported experiencing "time warping" or "missing time" while traveling through here.<br /><br />In reality, while several accidents have taken place there, they're not statistically more common than in any other area of sea with the same density of traffic. Which, in spite of the stories, is considerable.

* The Mandelbrot Set is a two-dimensional slice of a four-dimensional object that represents the eventual fate of iterating the assignment z <- z* z + c, where z and c are complex numbers (two dimensions each). Start with z=0 and try different values of c, and you get the usual two-dimensional view of the Mandelbrot set (which is, properly, only the ''boundary'' of the usually-black region representing points that do not escape to infinity). Fix a value for c and try different starting points for z, and you get a Julia set. The complete four-dimensional object stacks all the two-dimensional Julia sets along a complex dimension for a total of four real-valued dimensions.

[[Category:Alien Geometries]]

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