History Main / AlienGeometries

* ''Animation/{{Lamput}}'': The staircase room in "Art Gallery" has weird geometry like the Creator/MCEscher work "Relativity", with Lamput and the docs defying gravity as the walk around it. In one scene, there are two staircases next to each other, one appearing to go up and one going down; Specs Doc and Lamput walk on different staircases and the latter ends up larger after reaching the other side while Specs Doc somehow shrinks. They return to their normal sizes when they walk the other way.

* 'The sci-Fi novel 'Triton' features a description of a fantastically complex [[FictionalBoardGame board game]] (great for long space voyages!) with a single seven-sided die alongside four six-sided die.

** Planes in D&D 3rd edition:
*** 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.
*** 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.
** ''TabletopGame/{{Planescape}}'' created Sigil, a city that exists on its own plane, connected to others only by portals in the forms of doors. The city resembles the inside of a tire; it's a tube that wraps around on itself, so you can look up and see buildings in the sky, walk straight for hours and end up in the same place, and open any door and end up somewhere else. Gravity seems to work for whatever ground you're standing on right now and light is just sort of there. To top it all off, it's floating on the top of an infinitely-tall spire in the middle of a plane that is both infinite and finite. The best part, though, is that, since Sigil exists completely separate from any other plane, there is a chance that it has no outer surface.

The term [[https://en.wikipedia.org/wiki/Non-Euclidean_geometry "Non-Euclidean"]] gets used often to describe shapes and structures that don't make logical sense, though it's not always correct. It was used by Creator/HPLovecraft to describe the impossible angles and shapes found in alien structures in his works, though not all impossible geometries would be counted as "non-Euclidean"; that term refers to certain geometric forms that don't behave like a "flat" surface but still form a consistent and logical geometry, e.g. the spherical geometry of our Planet Earth, where a curved path is likely to be the shortest path if the distance is five digit kilometers. (It's possible to construct a 2-dimensional geometry on a curved Euclidean surface that is non-Euclidean, but a three-dimensional non-Euclidean geometry requires spacial distortion, such as might be induced by a powerful gravitational field.)