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World Shapes

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Since the most prominent force in shaping a molten proto-object large enough to later be called a planet is its own gravity, worlds in real life tend to be roughly spherical in shape. This is also why there is a direct relationship between the size of a lump of rock floating through space and its degree of roundness.
However, some Speculative Fiction and Fantasy series, in order to drive home the point that they do not take place anywhere resembling Earth, have their heroes adventuring on a planet with a totally different and often quite impossible shape.
Common world shapes:
Spherical — Typically, a world is assumed to be a sphere unless specified otherwise. However, it is somewhat poorly portrayed in video games, where an effectively toroid world is easier to implement. See below.

Dyson Sphere — A spherical shell built around a star, typically to capture all of a star's energy or to maximize living area. People live on the inside surface.
Flat World — Usually found in fantasy settings, generally as a flat disk carried about by huge animals or pillars or floating in space. Less commonly, examples may spread out infintely or gradually fade into nonexistence at their edges.
Hollow World — A regular planet, but hollow inside; the inside surface is usually inhabited.
Ring World Planet (concave cylinder or ribbon) — Typically artificial and built by advanced civilizations for living space. As in Dyson spheres, people live on the inside surface.

Impossible shapes — Alien Geometries, shapes with dimensions from four on up, hyperfolds, things only mathematicians and madmen can visualize, etc.
A twist on this is Video Game Geography, type 1, where the world doesn't actually have an odd shape, but the way the programmers implemented the world map implies that it does. Most Role Playing Games with a Global Airship would actually end up donut-shaped (keep going north and you end up on the same place on the south edge of the map). Even the torus model does not accurately describe these worlds, or else the time it took to travel on the toroidal axis would depend on your position on the poloidal axis. These worlds are actually shaped as a duocylinder, which is a shape that's impossible to depict in 3D space, so a toroid is often given as a technically wrong but close enough example you can actually have a picture of.
Xianxia and Xuanhuan stories — two genres of Chinese fantasy literature — tend to be set in worlds of varying shapes. The basic forms include flat worlds floating in space surrounded by an also floating ocean, pocket worlds inside bigger worlds that are pocket worlds themselves nested inside an even bigger world, and planets of massive size that can rival our sun, but there are also more creative shapes.
Notably, when "planet" was given a formal definition (thus demoting Pluto), "big enough to be spherical from its own gravity" became one of the requirements, so any non-sphere planet is not a planet (of course, any such body being discovered in the real universe has a solid chance of leading to a change in definition)
Compare Object-Shaped Landmass, for when this is applied to a landmass, and Heavenly Concentric Circles, when heavenly planes or beings are depicted as concentric circles in the sky.
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The Salvation War: Heaven and Hell have bizarre topologies. They are hollow worlds that have an inner surface, but lack an outer one. If you dig down long enough you'd exit somewhere else.
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Cosmic Osmo has everything from a cardboard diorama to a stellated polyhedron.
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Might and Magic: It's stated in the endgame that some of the worlds on which the series takes place are actually giant spaceships. The worlds of the fourth and fifth games are the front and backside of a large flat rectangle; playing both games in sequence gives you an extra endgame that (somehow) lets you combine these into a sphere. Heroes of Might and Magic V and Dark Messiah remove the science fiction elements, but Might & Magic X implies it still takes place in the old setting (just on a world that has forgotten it and lacks any obvious SF elements), and other an astronomer mentions seeing flat worlds during a time when the heavens were unusually clear.
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Glasshouse: Humankind is spread throughout a huge number of space stations and spacecraft in deepspace, all linked together by an even greater number of wormholes. This often results in bafflingly complex geometries and TARDIS-like effects where different rooms and floors of what appear to be a single contiguous building need have no geometric relationship to each other at all, once you enter them. This can make some regions impossible to navigate without computer assistance.
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Darkstalkers: The world map visable during the character select screen appears to be some kind of triangular mobius strip.
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RuneQuest: The world of Glorantha is shaped like an enormous stone cube floating in the ocean. On its upper surface, patterned, weathered and scarred by ages of cataclysms and divine events, are the continents and oceans of the world. At its edges, the ocean drops off into a fathomless abyss and continues until the absolute edges of the universe, which form a perfect sphere around it. A few islands float on the waters just past the edges of the world proper, while the Underworld lies beneath Earth and Water at the bottom of the universe.
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The Silmarillion: Arda was created as flat world floating in a vast ocean like a giant ship, and was made spherical only after the sinking of Númenor.
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MS Paint Adventures:
Homestuck: The Battlefield actually changes shape. It starts as small flat world, then becomes a larger flat world, then a cube, then finally ends up as a sphere.
Problem Sleuth: The Imaginary Universe consists of two seemingly-spherical lands on opposite sides of a typical spatial void containing a way-small sun and moon and at least one Floating Continent, the two worlds connected by a single gigantic 133,331-story cathedral. It is either heavily implied or outrightly stated that the Imaginary Universe is much, much "wider" than it is "tall". If none of that is making sense, there's a picture of it here◊.
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Xeelee Sequence: The short story collection Vacuum Diagrams has two examples. The story "Vacuum Diagrams" itself features a perfect cube large enough to have its own gravity. Standing on the flat surface, it appears to be hyperbolically curved, with the horizon ending in four enormous mountains. The stories "Shell" and "The Eighth Room" feature a planet Earth that is a four-dimensional sphere. Due to this Alien Geometry, each place on the Earth appears to be the interior of a hollow sphere, with the 'other' Earth hovering in the center of it, or a curved surface which is surrounded by a 'sky' which is the surface of the 'other' Earth. In fact 'both' of these 'worlds' are three-dimensional surfaces of the four-dimensional sphere.
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Rice Boy: The world is a typical flat disk world spinning like a coin, with the notable deviation that both sides are inhabited. The majority of the story takes place in Overside, but the eponymous Rice Boy eventually traces his own origins to Underside.
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Robotomy: "Nana's Run": Escargot, the planet of the snail people, is shaped like a giant snail shell.
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Tales of Eternia (Tales of Destiny 2 in the US) has a universe consisting of two flat edge-warping worlds that face one another, so each world is effectively the other's sky. A sun dispensing variable illumination is lodged in an energy barrier that keeps the two worlds apart.
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Problem Sleuth: The Imaginary Universe consists of two seemingly-spherical lands on opposite sides of a typical spatial void containing a way-small sun and moon and at least one Floating Continent, the two worlds connected by a single gigantic 133,331-story cathedral. It is either heavily implied or outrightly stated that the Imaginary Universe is much, much "wider" than it is "tall". If none of that is making sense, there's a picture of it here◊.
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Shadow of the Wool Ball: The titular planet, true to its name, apparently resembles a giant ball of wool (with drooping loose bits of tread) when observed from a distance.
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Fighting Foodons: The ending song of the anime series reveals the planet everyone is on to be shaped like a bowl.
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Majyk by Accident: The world keeps changing its shape, due to being over-saturated with magic. At present it looks like a Moebius strip.
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Humanx Commonwealth: While the planet itself is round, Moth has uniquely-shaped ornamentation: it's a winged world, as it used to sport Saturn-like rings, but these were disrupted by a near-miss from a dwarf planet and split into two sections.
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Flash Gordon (1980): Mingo's moon, Arboria, is bowl-shaped. Everything seems to be on the concave side.
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Qumi-Qumi: Each habitat is patterned after a certain shape: Juma-Qumi is square, Yumi-Qumi is triangular, and Schumi-Qumi is circular. This is highlighted in each of the shapes of the tribes that live on that habitat.
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Well World: The titular world is spherical, but the surface and atmosphere are divided into hexagons, with a hundred-miles-tall band around the equator.
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Discworld:
In The Light Fantastic, the characters get a glimpse of some other worlds, including one based on the Norse conception of the world as a flat disc surrounded by the Midgard serpent, and one where an enormous tree sits at the hub. According to the Creator (the guy who made the universe) most worlds and universes he makes are flat worlds. There was one universe he forgot to put edges on the planets though...
The Science of Discworld, the wizards keep trying to build a giant turtle out of rock so Roundworld can have a "proper" world in it, but it keeps collapsing into an unsatisfactory spherical mass.
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Mortadelo y Filemón: In El Quinto Centenario (written to celebrate the 500th anniversary of Columbus' first journey), Columbus shows several potential forms, including Flat Earth, a tetrahedron and... something that looks like an Eduardo Chillida statue.
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In The Light Fantastic, the characters get a glimpse of some other worlds, including one based on the Norse conception of the world as a flat disc surrounded by the Midgard serpent, and one where an enormous tree sits at the hub. According to the Creator (the guy who made the universe) most worlds and universes he makes are flat worlds. There was one universe he forgot to put edges on the planets though...
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The Transformers
Planets in the first two seasons of the original series were spheres. Come The Movie we are introduced us to Junkion, which is for all intents and purposes, a planet with a surface made of used chewing gum pulled taut over a large area, and Quintessa, which looks like a sphere, but has several large, almost blade like, masses of continent jutting out from the equator.
Cybertron is round in the sense that a massive katamari is round. It's like the skyline of every major city on Earth wadded up into a round chunk of skyscraper.
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Planescape:
While the plane of the Outlands is, presumably, a flat world, its most interesting feature, the planar trade hub of Sigil, is built on the inside of a toroid that floats above the spire at the plane's center. The first books even had special rules for getting disoriented when you look up and see more city instead of sky.
Ysgard (Chaotic Neutral-Chaotic Good) is composed of three layers: Ysgard proper (hovering mountains foth fire on one side), below that is Muspelheim (mountains further apart and fire-side up) and Nidavellir (underground tunnels full of geothermal activity).
Limbo (Chaotic Neutral) is an infinite shifting storm of the four elements.
Pandemonium (Chaotic Neutral-Chaotic Evil)is an endless series of caves that acts as a world-sized out-of-tune woodwind instrument that will drive you insane if you stay there for too long.
The Abyss (Chaotic Evil) is infinite layers of mind-bending horrors. They never go into detail as to what they look like, but it's not a leap to assume that every world shape is eventually accounted for.
Carceri (Chaotic Evil-Neutral Evil) is an infinite series of concentric spheres, each of limited size. Each layer of Carceri is occupied by an infinite number of planets arranged like strings of pearls, and descending to the next layer takes you to a smaller version of the planet you started on (on the first layer the planets are physically connected; each subsequent layer increases the distance between surfaces).
Hades (Neutral Evil) is three flat, blasted wastelands that meet in the City In The Center◊
Gehenna (Lawful Evil-Neutral Evil) is a trio of volcanoes of limited size. In First Edition, it was three infinite flat plains... on which gravity functioned at 45 degrees to horizontal.
Baator (Lawful Evil) is shaped like Dante's Inferno — concentric ledges, each of infinite size.
Acheron (Lawful Neutral-Lawful Evil) is four classic-style dense asteroid belts, each layer with unique asteroid shapes, the best-known of which is just cubes, as far as the eye can see.
Mechanus (Lawful Neutral) is seemingly infinite system of country- to continent-sized gears, interlocking in a vast clockwork mechanism, whose surfaces are habitable and settled.
Arcadia (Lawful Neutral-Lawful Good) is two flat layers connected at their edges, resulting in a gradual downward "slope" as one heads deeper into the plane. On the upper layer there's a mountain where an orb that emits light on one side and darkness on the other spins on its axis, providing night and day.
Celestia (Lawful Good), viewed from afar, is an enormous mountain surrounded by an infinite sea of holy water. Those on the mountain view it as divided into seven layers, each smaller than the last, and each of infinite size.
Bytopia (Lawful Good-Neutral Good) is two layers arranged sandwich-style with a few mountains connecting the two. One layer is domesticated farmland, the other a somewhat harsh wilderness; natives can move from one to the other as they please.
Elysium (Neutral Good) is the opposite number to Hades, but still flat.
The Beastlands (Chaotic Good-Neutral Good) are three planes of wilderness: one of eternal day, one twilight, and the last night.
Arborea (Chaotic Good) is three flat layers: one an exaggerated realm of incredibly huge mountains and forests of giant trees, one infinite shallow ocean, and one dusty desert.
The Far Realm (???), which contains an infinite number of not quite really parallel layers, each of which ranges from inches to miles thick. It's often possible to perceive multiple layers simultaneously. These layers can grow, spawn further layers, breathe and possibly die.
While the Astral Plane doesn't technically have a landscape, it does serve as a sort of elephant's graveyard for dead and forgotten deities, whose gargantuan petrified bodies drift in the void. Some of them have been colonized by githyanki or other Astral residents.
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Monty Python and the Holy Grail: Sir Bedevere, a Know-Nothing Know-It-All, believes the Earth to be banana-shaped.
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Homestuck: The Battlefield actually changes shape. It starts as small flat world, then becomes a larger flat world, then a cube, then finally ends up as a sphere.
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Unicorn Jelly:
Triangular world-plates with triangular lakes in the middle, each orbited by a tiny sun and moon. Jennifer Diane Reitz loves this trope; her sci-fi setting spans multiple universes, and each has its own laws of physics, which manifest mostly in bizarre world shapes.
This illustrates that a sphere can be a bizarre world shape. A scientist from an alien universe, where gravity as we know it doesn't exist but where there is an absolute "down", comes across a fragmented description of our world. He speculates that the spherical shape of our planet must lead to a very stratified society, where the rich all live in the "safe" areas closest to the top of the sphere, and lower classes live further down the slope, where they must deal with the risk of slipping off.
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Guardians of the Galaxy: In one arc, the Guardians encounter the Topographical Man, an inhabited planet-sized humanoid.
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Rolie Polie Olie: Olie's friend Billy Bevel and his family come from the square planet Cubey.
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Pastel Defender Heliotrope: Toroid-shaped worlds are seen, but not visited. Also seen: worlds shaped like endless living strands, worlds shaped like... this, and worlds shaped like scary alien tendrils. The very worlds/continents of Pastel count. They are rectangular sandwich-things, made of two layers of ground around a central layer of... gravity. As in, a strange mineral that causes attraction to itself, but only on a single universal axis; all the rectangles are perpendicular to this axis, so things "stick" to both sides, but things outside of it are in zero-g, even if they are right to the side of one. You can also dig out the central layer, creating zones of zero-g wherever you want them. Furthermore, all the rectangles are always moving in the same direction, towards the edge of the universe where they get ground up to power one of the superweapons sent against the scary alien tendrils above, possibly the title character, which creates constant winds that has caused the life in the worlds to evolve in response: grass is shaped like shark fins aligned with the wind, some plants are tunnels that catch water from the passing wind, etc. And last but not least, the "sun" in this universe is a line of light, paralel to the movement of the continents/worlds, which results in all of them having a bright side and a dark side. Humans generally live in the former and strip-mine the later.
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Xanth: The later books introduce Ida's moon, which contains a complete copy of the world except slightly shifted. Naturally Ida exists on that moon and has a moon and so on. All of the shapes from spheres to discs to toroids to dumbbells to spirals to floating islands show up as one progresses down the chain of moons.
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World Shapes
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Digimon Adventure: In the last story arc, the Digital World is transformed into a huge pyramid with four distinct biome strips — ocean, forest, city and wasteland — twisted in a spiraling shape.
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World Shapes
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Schlock Mercenary: Zoojacks is shaped like a pair of toy jacks. The Enireth-built Tinth, are shaped like giant sandwiches. Yes, the strip linked to refers to the Tinth-Philkra system, but strictly speaking it's the Philkra system, and was renamed by popular mistake as everyone assumed the Tinth-Philkra Dialogues were named for the system, rather than the hypernet node of origin (on Tinth-III, in the Philkra system).
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Last Exile: Prester is hourglass shaped, and rotates around the waist for gravity. The bottom of each 'bell' forms the surface for each half, and the atmosphere is shared through a massive cyclonic structure at the 'waist'. The temperature difference between the two bells is the driving force of the conflict between their respective inhabitants.
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Dungeons & Dragons. The known planes of existence include both finite and infinite flat worlds (including one with two flat, populated surfaces "facing each other"), cubic planets, planets that are giant mountains etc. etc.
Dragon Magazine #160 has an article describing how to model exotic world shapes, including flat worlds (gravity pulls down along a plane, walls or mountains are needed to keep the air in), shards of broken worlds (wedge-shaped where gravity pulls towards the former core, habitable on their top surface is some means is devised to keep in the atmosphere), and cylindrical worlds (very similar to spherical ones in practice, although walking onto the flat surfaces is very disconcerting).
Planescape:
While the plane of the Outlands is, presumably, a flat world, its most interesting feature, the planar trade hub of Sigil, is built on the inside of a toroid that floats above the spire at the plane's center. The first books even had special rules for getting disoriented when you look up and see more city instead of sky.
Ysgard (Chaotic Neutral-Chaotic Good) is composed of three layers: Ysgard proper (hovering mountains foth fire on one side), below that is Muspelheim (mountains further apart and fire-side up) and Nidavellir (underground tunnels full of geothermal activity).
Limbo (Chaotic Neutral) is an infinite shifting storm of the four elements.
Pandemonium (Chaotic Neutral-Chaotic Evil)is an endless series of caves that acts as a world-sized out-of-tune woodwind instrument that will drive you insane if you stay there for too long.
The Abyss (Chaotic Evil) is infinite layers of mind-bending horrors. They never go into detail as to what they look like, but it's not a leap to assume that every world shape is eventually accounted for.
Carceri (Chaotic Evil-Neutral Evil) is an infinite series of concentric spheres, each of limited size. Each layer of Carceri is occupied by an infinite number of planets arranged like strings of pearls, and descending to the next layer takes you to a smaller version of the planet you started on (on the first layer the planets are physically connected; each subsequent layer increases the distance between surfaces).
Hades (Neutral Evil) is three flat, blasted wastelands that meet in the City In The Center◊
Gehenna (Lawful Evil-Neutral Evil) is a trio of volcanoes of limited size. In First Edition, it was three infinite flat plains... on which gravity functioned at 45 degrees to horizontal.
Baator (Lawful Evil) is shaped like Dante's Inferno — concentric ledges, each of infinite size.
Acheron (Lawful Neutral-Lawful Evil) is four classic-style dense asteroid belts, each layer with unique asteroid shapes, the best-known of which is just cubes, as far as the eye can see.
Mechanus (Lawful Neutral) is seemingly infinite system of country- to continent-sized gears, interlocking in a vast clockwork mechanism, whose surfaces are habitable and settled.
Arcadia (Lawful Neutral-Lawful Good) is two flat layers connected at their edges, resulting in a gradual downward "slope" as one heads deeper into the plane. On the upper layer there's a mountain where an orb that emits light on one side and darkness on the other spins on its axis, providing night and day.
Celestia (Lawful Good), viewed from afar, is an enormous mountain surrounded by an infinite sea of holy water. Those on the mountain view it as divided into seven layers, each smaller than the last, and each of infinite size.
Bytopia (Lawful Good-Neutral Good) is two layers arranged sandwich-style with a few mountains connecting the two. One layer is domesticated farmland, the other a somewhat harsh wilderness; natives can move from one to the other as they please.
Elysium (Neutral Good) is the opposite number to Hades, but still flat.
The Beastlands (Chaotic Good-Neutral Good) are three planes of wilderness: one of eternal day, one twilight, and the last night.
Arborea (Chaotic Good) is three flat layers: one an exaggerated realm of incredibly huge mountains and forests of giant trees, one infinite shallow ocean, and one dusty desert.
The Far Realm (???), which contains an infinite number of not quite really parallel layers, each of which ranges from inches to miles thick. It's often possible to perceive multiple layers simultaneously. These layers can grow, spawn further layers, breathe and possibly die.
While the Astral Plane doesn't technically have a landscape, it does serve as a sort of elephant's graveyard for dead and forgotten deities, whose gargantuan petrified bodies drift in the void. Some of them have been colonized by githyanki or other Astral residents.
Ravenloft consists of chunks of landscape adrift in a Mist-filled void. Differs from World in the Sky in that this arrangement is highly unpredictable and tenuous: cross the Misty borders, whether by walking, riding, or even sailing, and it's anyone's guess where (or if!) you'll come out.
The World Builder's Guidebook, a vintage supplement, discusses possible shapes for worlds that DMs can choose among, including spheres, inverted spheres, flat planes, cylinders, toroids, and the shapes of gaming dice.
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The Integral Trees takes place in the Smoke Ring, a "world" which is just a breathable ring of gas around a neutron star.
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World Shapes
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Halo has the Halos (Halo: Combat Evolved and Halo 2), which are ringworlds; the Ark (Halo 3) which is shaped like a flower; and the Shield World (Halo Wars) and Requiem (Halo 4), which are small Dyson Spheres.
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World Shapes
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The Touryst: As revealed in the ending, the game has a cuboid world while retaining visible gradations in terrain upon its Earth-like continents.
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Biomega: The bad guys' schemes eventually result in the creation of a bizarre new world which is shaped like a giant worm, tens of millions of miles long.
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 Biomega (Manga)
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Bloom County: In one arc, Opus is put on trial for teaching "penguin evolution", in a riff on Inherit the Wind. At one point, the prosecution introduces an expert witness on the subject of "penguin creationism". Unfortunately for the prosecution, the witness is a bit of a Cloud Cuckoo Lander:
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World Shapes
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World of Tiers: The titular world takes the form of a world-sized wedding cake, just that the layers (tiers) are way wider than they are tall. And the top layer doesn't have a bride and groom standing on it.
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 World of Tiers
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World Shapes
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Galaxy Quest: the Thermian homeworld resembles an immense apple core. This isn't natural; it's the result of the movie's villain Serras' attempts at genocide.
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 Galaxy Quest
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World Shapes
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Captain N: The Game Master: Some of the worlds in had unusual shapes, some inspired by the games they were based on (such as Mount Icarus being mountains and plains suspended above the clouds and Faxanadu being a floating continent dominated by its World Tree) and others with fuzzier inspirations (such as Hyrule being an Earth-like sphere enclosed in some sort of crown-mountain-floating rock thing).
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Emperor Joker: It's revealed that, due to the Joker gaining 99% of the prankster Mr. Mxyzptlx's power, he now is an Insane Reality Warper, and reshapes the Earth into a cube with the continents shaped in his visage.
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 Emperor Joker (Comic Book)
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Gravity Rush is set on the aptly-named World Pillar. It's an enormous, tree-like structure, floating in endless sky. The pillar itself is hollow, and its insides are an Eldritch Location, in which gravity is warped. The city the game's set in is attached to the World Pillar by seemingly-man-made structures, and there are no other known human settlements. It's later revealed that the World Pillar is being slowly consumed by an enormus Gravity Storm (basically black hole), and thus time flows slower the closer to the bottom of the pillar. Some materials also imply that there may be other World Pillars.
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Mission of Gravity: Mesklin spins so rapidly that it's lens-shaped rather than spherical. However, due to the planet's intense gravity, the density of Mesklin's atmosphere varies so strongly with altitude that refraction makes it look bowl-shaped. The Mesklinites can "see" that the world curves up around them, so they believe that they live in a giant bowl. They are skilled sailors and map-makers and should know better, however when you are measuring distances on a curved surface, there are two different shapes that will make all the math work out (convex and concave). The Mesklinites choose the wrong one for their maps and never notice. (Also the Mesklinites living on the northern hemisphere have apparently never before crossed the equator to the other side and therefore didn't know that they were wrong all along.) The result is perfectly accurate and usable maps based on a fundamentally flawed premise.
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World Shapes
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Kadingir is mostly set on Ki, a planet vaguely shaped like a chestnut. There are two hemispheres, with a ring of mountains separating them: Ishtar on the upper side, a rich land filled with rivers, forests, fields, deserts and a central ocean; and Ereshkigal on the lower side, which is little more than a wasteland with a giant volcano in the middle (hence the chestnut shape) that darkens the skies with its smoke.
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World Shapes
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The Inverted World takes place in an universe where planets and stars are shaped like hyperboloids of rotation while at the same time being the regular old universe and the regular old planet Earth for other people unaffected by the book's Applied Phlebotinum.
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World Shapes
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Lexx:
There's a ringed planet with an unexplained donut hole through its middle.
"Patches in the Sky" features a Manganese mining planet with a humongous chunk literally mined out of its side, like a half-eaten apple.
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 Lexx
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World Shapes
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Xenoblade Chronicles 1: In the first game, the world is entirely made up of the bodies of two Physical Gods who either killed or incapacitated each other in combat. There is nothing beneath them but an infinite plain of shallow, empty ocean, and the stars above them are not actual stars, but "ether" light.
 World Shapes / int_8ec33a86
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 Xenoblade Chronicles 1 (Video Game)
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Xenoblade Chronicles 2: The surface of the world is a deep ocean with permanent opaque fog on the surface called the Cloudsea. Civilization exists on Titans, creatures big enough to support cities or even entire natural biomes on them. Some float with ships or guilds hanging from them, some swim on the surface, and some walk across the Cloudsea floor below — and these even have "tides" as they traverse the uneven seabed. All this means that magnetic north is useless for navigation; local directions are given relative to the Titan itself (such as directing people towards the head), and compasses work using the World Tree as the center and winding to the current date to predict where the biggest Titans will be relative to it.
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Tiny Planets: The Tiny Planet of Stuff is shaped like a Möbius strip.
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World Shapes
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Known Space: Jinx, a planet-sized moon of a gas giant, is pulled into a pronounced oval shape by the gravitational stresses of the larger body. Its equatorial region band is extremely hot and too dense to breathe, while its eastern and western poles project clear out of its atmosphere — from the perspective of someone on the moon's surface, they're partway between geographic poles and impossibly tall mountains. Humans live in the transitional areas between the vacuum and the high-density belt; the equator is inhabited by a species of gigantic sluglike aliens.
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 Known Space
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The Death Gate Cycle: The elemental worlds created by the Patryn take some decidedly shapes:
Arianus, the world of air, is a World in the Sky where people live on floating islands above the eternal storm of the Maelstrom, which fills the lower third or so of its volume. Water is scarce, since the island's spongy substrate doesn't retain it well.
Pryan, the world of fire, is a Hollow World with a much larger surface area than the modern Earth. Its inner surface is covered by jungle of miles-high trees, and humanoid civilizations exist primarily in their canopies and on country-sized mats of epiphytic moss.
Abarrach, the world of stone, is a solid mass of rock honeycombed by tunnels and caverns. Its core is highly volcanic and its outer areas deathly cold; civilization can only exist in a Goldlilocks zone between them, and even there is struggles to survive.
Chelestra, the world of water, is an egg-shaped mass of ice within which a "seasun" orbits, cyclically thawing out and re-freezing floating islands within which people live.
The Labyrinth, a prison-world created for the Sartan, the ancient enemies of the Patryn, is a circular flattened world consisting of an outer, mazelike area divided by a large number of geographic gates and an inner, safe area containing a paradisiacal city.
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The DCU:
In the Bizarro Universe, Bizarro Earth (sometimes called Htrae) is shaped like a cube.
Emperor Joker: It's revealed that, due to the Joker gaining 99% of the prankster Mr. Mxyzptlx's power, he now is an Insane Reality Warper, and reshapes the Earth into a cube with the continents shaped in his visage.
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World Shapes
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Orthogonal: The universe seemingly has the topology of a torus, though the only reason the characters believe this is that it's the only way to make its physics consistent; they haven't actually gone all the way around in any direction.
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World Shapes
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BoBoiBoy: Ata Ta Tiga, the world Adu Du and Probe are from, is shaped like a cube similar to its residents.
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The Bible: "After this I saw four angels standing at the four corners of the earth..." (Revelation 7:1). This is consistent with the Earth being a tetrahedron. However, in the Book of Job there is mention of a "circle of darkness" on the "waters" which could refer to the spherical shape of Earth. This would mean that some Hebrews knew about the true shape of the world around 2-3000 years ago.
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 The Bible
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World Shapes
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Taming Dreams: Alora Fane is usually depicted as a flower with six petals (although this is implied to be an abstraction), with each petal constituting it's own separate world, with the implication that something more than a Global Airship is required to get from one world to the next. That said, Mardek's father Enki managed to travel from Mji Mkuu to the Bronze Archipelago somehow, and the Meek race is spread to each of the six petals.
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Magic: The Gathering: The various planes of The Multiverse vary, sometimes dramatically, in shape and scope:
Dominaria is an Earth-like solid globe, albeit with two and half times the surface area.
Rath was a Flat World — one card shows its edge — which steadily grew outward and "vibrated" on a different frequency than Dominaria. As Rath grew larger, its vibrations slowed until it vibrated in sync with Dominaria and eventually merged with it.
Lorwyn/Shadowmoor is a small flat world, ringed by mountains beyond which is the unformed chaos of the Primal Beyond.
Theros is another flat world, this time of the layered sort. Its middle layer is a flat disk where human civilization, nature, and most monsters live. Above it is Nyx, the night sky, home to the gods, their servants, and mythic monstrosities. Below it, amidst the immense pillars that hold up the mortal world, is the Underworld of the dead.
Ixalan is a Hollow World, at whose core is an immense cavern lit by an internal sun.
Kaldheim consists of several smaller, self-contained realms arranged along the immense World Tree, which periodically shift on its branches and come into collision.
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Triangle and Robert's four-dimensional "hypertaco" Earth is not healthy to visualise.
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Ravenloft consists of chunks of landscape adrift in a Mist-filled void. Differs from World in the Sky in that this arrangement is highly unpredictable and tenuous: cross the Misty borders, whether by walking, riding, or even sailing, and it's anyone's guess where (or if!) you'll come out.
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The Dark Side of the Sun has a planet made entirely of water, and two stars twisted into linked toruses.
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 The Dark Side of the Sun
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World Shapes
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Outlaw Star: One episode features a planet with such a high rate of rotation that it's distorted into an oval spheroid.
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 Outlaw Star (Manga)
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Deadly Rooms of Death: The Eighth, the world of the game, is shaped like an eighth of a pie, which is contained in a wrap-around universe.
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Warhammer 40,000: Daemon Worlds often have impossible shapes, either due to the Immaterium's reality-warping nature, or because a Daemon Prince shaped it to their whims.
Oliensis is a single, impossibly large obese man, curled in a fetal position. The Chaos Marines that live there have built bases inside its skin pores.
Planets in the Screaming Vortex include one shaped like a giant, grinning skull and "the Hollows", a forge world where the Dark Mechanicus ate away at the southern hemisphere with deep-core mining technology until the entire planet consisting of only an upper hemisphere with a thick, gnarled stem of rock jutting from beneath, making the planet look like a rotten, half-eaten fruit.
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Little Big Adventure: In Relentless and its sequel Twinsen's Odyssey, the world in question, Twinsun, is spherical, but exists at the barycenter of a binary system. One that, thankfully, has a rather distant orbit. The result? Tropical poles and a giant frozen "ring" around the equator (and presumably no such thing as night, but that's a different matter.)
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Torin's Passage is set on a series of concentric hollow spheres; the main character starts the game on the outermost and has to work his way to the inside of the innermost, where he is in zero-gravity and has to make his way around by using a bagpipe to expel air in the opposite direction. The basic structure of the world is similar in Septerra Core, with the addition that the planet has a clockwork core. Each layer is actually a set of disconnected islands that rotates on its own axis. So, you can see lower layers in the gaps between islands and through holes, with each layer receiving less and less sunlight through the gaps as you get lower (and thus each layer becomes increasingly dark and hellish as you go down). A major plot point involves the rare occurrence of the layers lining up so that a single beam of sunlight reaches the core.
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Doctor Who: In "Castrovalva", the eponymous world is revealed as such when the pharmacist is asked to draw a map of the city, and marks his pharmacy as being at the top, and the bottom, and to the west, and to the east, although there is only one shop.
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Micronauts: In the Marvel adaptation, the Micronauts originated on Homeworld, a planet shaped like a classroom model of a segment of DNA; a dozen spheres linked by cylinders, arranged in two connected rows like a ladder.
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"Lumbanico, the Cubic Planet": The titular planet is shaped like a cube, with each "side" being bordered by seas and huge mountain ranges called "Aristas" (Spanish for "cube edges").
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Super Mario Galaxy. Pick a shape, any shape. Some worlds are spheres, some are cylinders, and at least one is peanut-shaped. All have gravity perpendicular to the surface. The sequel features a planet shaped like Mario's head that's been fitted with engines and turned into a Faceship.
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ALF: ALF's home world Melmac is pear-shaped.
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Amazing Stories: A 1990s story is set in a world that's spherical, but with more than 360 degrees of rotation. In other words, if you sail 360 degrees eastward you end up somewhere that has the same time zone as your origin, but which isn't the same place.
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Rocheworld, by Robert L. Forward, has two egg-shaped planets orbiting so closely around each other that they share atmosphere, and come to conical points at the ends nearest each other. Oceans can even flow between them under certain circumstances. The oddest thing is that this bizarre world-shape uses real-world physics, and double stars with this configuration have been found.
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Cybertron is round in the sense that a massive katamari is round. It's like the skyline of every major city on Earth wadded up into a round chunk of skyscraper.
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Phantasy Star III: The game's world is made of six roughly round portions joined by tubes. As it turns out, it's really a spaceship.
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The Dark Tower, an unfinished novel by C. S. Lewis, features Othertime, which is presumably spherical, but which the inhabitants believe to be saucer-shaped. (Flat, but you can't get to the edge because gravity drags you back to the center.)
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Kirby is full of oddly shaped planets. These range from vaguely acceptable — chunks of rock orbiting each other, a gigantic drop of water — to downright silly, such as a heart-shaped planet with a smiley face and rings with ribbons on them. Kirby's home planet, Popstar, is shaped like a yellow five-pointed star with a couple of rings orbiting it.
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Spore allows for cube-shaped planets to be randomly generated.
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Meteos pulls off most of the tropes on this page and probably more.
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The Elric Saga: Elric at the End of Time has two landscapes, each hanging in the other's sky. Elric is astounded by the sight, yet to the ultra-powerful yet shallow inhabitants of the End of Time it's as remarkable as a new patio. A Rodney Matthews illustration of the story was designed to be viewed both ways up, giving two illustrations for the price of one.
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The Hitchhiker's Guide to the Galaxy: The Magratheans made a business out of building planets to order until the universe's economy tanked. In the movie, this extended to planets in such shapes as octohedral.
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Blame!: The City/Megastructure is a Dyson Sphere on steroids, cocaine, and whatever stimulants it could find. It's a continuously built up (and spreading) structure that has recently passes Jupiter's orbit in its expansion. The Sun is "somewhere inside".
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The Science of Discworld, the wizards keep trying to build a giant turtle out of rock so Roundworld can have a "proper" world in it, but it keeps collapsing into an unsatisfactory spherical mass.
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Reign: The known world is shaped like two people lying down in a pool of water, with one resting an arm on the other. Rendered in three dimensions. This leads to some unusual properties — for instance, the ocean is at a 90 degree angle to the shore; gravity is relative so sea travel still works, but boarding a ship can be tricky.
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Dragon Ball Z: The Legacy of Goku: When flying from place to place, the planet is properly spherical under you. Flying in any direction but the longitudinal axis results in your character marker moving in a parabola on the rectangle-projection map. This is all the more impressive considering it's on the Game Boy Advance
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The Culture: Matter introduces the Shellworlds, spherical worlds tens of thousands of kilometers across, with fifteen concentric habitable layers, each a separate world of its own.
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Star Trek: Voyager: "Blink of an Eye" includes a donut-shaped planet with a third pole (said pole being Voyager itself).
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Voltron: Legendary Defender: Several planets — such as Olkarion, the mermaid world, and Daibazaal — are oddly-shaped, with massive rock or ice formations jutting well beyond the planet's atmosphere.
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Dark Souls: It's difficult to tell at first, but the entire game world appears to be built into the side of a colossal mountain. Most areas are outdoors or valleys, which makes it less obvious, but much of the game world is stacked on top of each other at considerable elevation. Anor Londo is visible in the distance above the rest of the game world. Undead Berg is a climb up to the Undead Parish (several hundred meters directly above the starting point, Firelink Shrine) or down into the Depths — an ironic name for an area that still above the vertical-in-itself shantytown that leads to the swamps of Blighttown. Entire mossy forests grow in the shadows of the upper areas, and the pitch-black Tomb of Giants buried beneath the human Catacombs is itself still considerably above the Fire and Brimstone Hell Demonic Ruins — and those are still considerably above sea level. The player has to go far out of their way to Ash Lake in order to reach the "floor" of the world — an optional area the player may never see.
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Doctor Who New Adventures: In Sky Pirates!, the pocket dimension known as the System comprises four Single Biome Planets all of extremely unusual shape. Possibly the most normal is Prometheus, a desert planet shaped like a large bowl. The water world Elysium is actually a globe, but it's also a vast blob of water with no actual planet beneath it. Aneas is a jungle planet shaped like a giant tree, and Reklon is an ice planet shaped like a snowman, complete with pipe and silly hat.
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Happy Heroes: Suspicious Planet, which serves a major role in the "God of War Legend" Story Arc from Season 7, is shaped like a heart.
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The following is a list of statements referring to the current page from other pages.

 World Shapes
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Deus Est Machina
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Geometry Tropes
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Otherworld Tropes
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Settings
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Shapes and Symbols Tropes
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Speculative Fiction Tropes
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