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Large geometric artifacts are unnerving. They are unfamiliar and inhumanly perfect. Visual artists use these common reactions to convey a sense of the unknown and the sinister.
Humans do not build perfect spherical vehicles or any other large mathematically perfect geometrically shaped device. Such devices seem more than foreign: they seem not of this world.
The lack of visual cues is another source of fear. A giant cube in space does not look like a spaceship; it could be anything. It could be a massive bomb, or a toy, or a probe. Consider the monolith from 2001: A Space Odyssey: it is the ultimate unknown.
This feeds into the reputation for evil that accompanies aliens that have geometric bodies, large or small.
There are exceptions. Very large Ring World style objects are geometric for merely physical reasons. The same is generally true of recognisable space stations and large regular spaces such as hollowed asteroids.
Summary: if your aliens are cute as Care Bears, omens be fair. Picometer perfect polyhedrons? Beware.
See also: Alien Geometries.
Anime and Manga
- Neon Genesis Evangelion: Ramiel, the fifth Angel, is a translucent octahedron, and its sinister nature is infinitely greater in Rebuild of Evangelion. Leliel is a mobile, circular hole with a spherical "shadow" hovering above it. Leliel is also infinitely thin. And it leads into higher-dimensional space. Or something. Other candidates include Arael (the angel of, well, angles) and Armisael (a double helix in a perfect circle).
- In Rebuild of Evangelion Ramiel can now change into all kinds of new alien shapes and does so in ways that, while renderable on a computer, are virtually impossible in reality.
- Just about all the Angels in Evangelion 2.22 are like this; complicated pieces of geometry with off-putting human or animal traits somewhere along the line..
- Digimon Adventure's final Big Bad, Apocalymon, consisted mostly of a giant gold dodecahedron from which claws and a demonic body emerged.
- In Heroman, the Skrugg are big fans, what with their saucer-shaped mothership, conical landing craft, and gigantic, spherical weapons of mass destruction. For bonus points, as with Ramiel above, Conspicuous CG is liberally applied to emphasise their otherworldliness.
- Gurren Lagann's third arc features enemies that look vaguely like tripods with halos. When destroyed, they break into small, multicoloured spheres, cubes and pyramids (which explode on contact with any solid matter).
- Bonus points for excellent use of Conspicuous CGI: the Mugann are completely computer-animated, unlike most of the rest of the show, which is more traditional. This just serves to emphasize their "alienness".
- In The Authority, the Cosmic Horror that created the solar system is a pyramid the size of the moon.
- The spaceship used by Galactus is a similarly massive sphere, though the effect is somewhat mitigated by its Kirby-esque mechanical complexity.
- According to some versions of Marvel canon, the 2001 Monoliths are tools used by the Celestials. This is because Machine Man first appeared in Jack Kirby's 2001 tie-in comic, and later stories retconned the Monolith in that story to have been a Celestial gizmo. Whether this makes all the Monoliths' other appearances in the 2001 comic part of official Marvel canon (which would mean the Celestials are the never-seen 2001 aliens) is up for fan speculation.
- Sort of averted in Lucifer in that cherubim take the forms of oscillating golden spheres because spheres are "perfect Platonic solids". They're actually rather pretty. Cherubs that took Lucifer's side have become diminutive ugly humanoids, for some reason.
- Texas. A wavy landscape which spits out purple blocky spheres.
- Untraceable. Fractals everywhere with an appropriate background music.
- In the end of Time Masters, the planet shown by the mysterious evil aliens known as the Masters of Time is made of two perfect half-spheres and a large glowing cube.
- The "demonic spheres" of Thirty Hs.
- Star Wars: The Death Star. The brutal wedge-shaped Star Destroyers and hexagonal/spherical TIE fighters are classic examples. As part of the same trope the rebels are more human: the X-wing is closer to a fighter jet, the rebel battleships have curved, organic lines. Kaminoan architecture: circular platforms and hemispherical buildings connected by perfectly linear causeways.
- The cylindrical alien probe from Star Trek IV. Borg cubes. However Gene Roddenberry originally intended for the Borg to use spheres, since the Borg were supposed to be the most efficient species and it can be mathematically proven that a sphere is the most efficient shape (in the sense that no other shape with the same surface area will have as great an interior volume). However, spheres were too hard for the special effects people to produce so he was forced to use cubes instead. They do launch a sphere in First Contact.
- The ships of the Vogon Constructor Fleet from the movie of The Hitchhikers Guide to The Galaxy were rectilinear. It helped showcase the Vogon's utter lack of imagination.
- The MCP from Tron
- The monolith(s) from 2001: A Space Odyssey: sinister in appearance, and utterly unknown. And exactly 1:4:9 ad infinitum.
- The Stargate sequence includes the Mindbender shot, depicting seven octohedral shapes made of light which float above an infinite moving plane.
- THE CUBE (the capitals indicate you speak with reverence while reading it) from Transformers (2007).
- The Zevo Toy Factory in Toys is made of platonic solids, painted in flat colors. It is filled with them; it is also clearly the home of the protagonists from the beginning. But there's a very definite strangeness to the place, and that's played up for all it's worth in the movie.
- The 1997 psychological horror film Cube. The protagonists are trapped in a grid of cubic rooms filled with deathtraps.
- In the sequel Hypercube, the hypercube is the deathtrap. And has this weird tesselation thing at one point that does strange things to reality... as well as dicing up one of the characters.
- The 1969 Jim Henson film The Cube. A protagonist is trapped in a mysterious cube and experiences a series of puzzling and frustrating encounters with people who enter. Especially if you take into account that when the protagonist wounds himself, he bleeds, of all things, strawberry jam, implying that even suicide isn't an option in the Cube.
- The titular building from AJ Annila's Surreal Horror indie-film Sauna is a small, white rectangular building with a black rectangular doorway. Through creative use of atmosphere it's given an incredibly sinister aura - many reviewers have been reminded of 2001's Monolith, while it also resembles an eyeless face with a gaping mouth.
- The titular sphere from the film Sphere.
- The spaceship used by the Egyptian Pantheon in Enki Bilal's Immortal is naturally a flying pyramid.
- Hellbound Hellraiser II, introduces us to Leviathan, the Satan-alike ruler of the Hell dimension. It is portrayed as a giant geometric shape resembling a three-dimensional lozenge that sits at the center of the hell-labyrinth, rotating and emitting a lighthouse beam of pain and evil visions.
- The alien spacecraft at the end of Starman was a perfectly reflective sphere. Not malevolent, but incomprehensible and spooky.
- Pulp age killer robots were often just a box for a head and body, and sometimes feet. Bars for arms and legs.
- The fourth Magic Kingdom of Landover novel, "The Tangle Box", uses this as one of the three coinciding plotlines, in which the characters inside are stripped of their memories and magical powers.
- The titular sphere from Michael Crichton's Sphere.
- The shining trapezohedron from H.P. Lovecraft's story Haunter in the Dark. Gazing into this alien artefact will grant you visions from beyond our world, but also summons the titular monster, an avatar of the Crawling Chaos Nyarlathotep, to kill or possess you. 
- The Sphere in Flatland probably counts as this, being of perfect geometry even when viewed in 2d space. And the 4-sphere in Flatterland. Indeed, any Flatland or its knockoffs counts.
- The Phages in Charles Sheffield's Heritage Universe series of novels, found swarming around hundreds of Big Dumb Objects left behind all over the galaxy by a mysterious and long-vanished race known only as the Builders. Phages resemble dull grey dodecahedrons 48 metres to a side and can open a maw on any of their faces to consume anything (or anyone) that gets in their way. It is eventually revealed during the course of the novels that the Phages may be the degenerate remnants of the Builders themselves.
- The Inhibitors of Revelation Space are race of Sufficiently Advanced Aliens that manifest as conglomerations of black cubes that operate on unknown principles. They've also been exterminating sentient life for millions of years.
- The Excession in Iain M Banks' Culture novel Excession: a perfect black body sphere impervious to anything, connected to the hyperspace energy grids "above" and "below" the plane of the universe, and enough of an "Outside Context Problem" to freak out even the Deus Est Machina Minds.
Live Action TV
- Star Trek: Borg cubes and other spaceships. The enormous First Federation ship, which is a sphere made of spheres each larger than the Enterprise.
- The Void Ship in Doctor Who is not only a scary perfect sphere, it also has no detectable mass or radiation, which instinctively upsets anyone who looks at it. And it's full of Daleks.
- On that note, consider the Daleks: Cone-shaped, no visible head or normal extremities.
- In ABC Family's made-for-TV miniseries version of Fallen, hell includes an endless staircase. The simplest M. C. Escher staircase illusion.
- The murderous dividing sphere from Tool's video for their song Parabol/Parabola.
- Gary Numan is awfully distrustful of the glowing pyramid on the cover of The Pleasure Principle.
- In Bionicle, Pohatu is bothered by the fact that some of the underground tunnels on Mata Nui are smooth and geometrically perfect, and therefore could not have been dug by Matoran. This was an early piece of foreshadowing on how the the entire island was an artificial construct.
- She Who Lives in Her Name from Exalted is a solid example. Manifested as 100 998 (originally 100 101 - one sphere, surrounded by a hundred, themselves surrounded by a hundred thousand) perfect spheres of fire-containing crystal, she is an utterly brilliant, alien being of unbelievable magical might who despises free will and wants to strip it from everyone.
- Magic: The Gathering gives us the hedrons of Zendikar. They actually keep the Eldrazi in Zendikar and make it so the Eldrazi can't escape and then eat the plane. The Eldrazi themselves are a case of Alien Geometries.
- The Monoliths and the general architectures of Necrons from Warhammer 40000. All stern geometric forms in black and glowing green shades. And they are immortal and implacable omnicidal androids, by the way.
- X-COM Enforcer features this, and HOW.
- CPU from Final Fantasy IV
- Ozma from Final Fantasy IX
- The structures on the Aparoid homeworld from Star Fox Assault were symmetrical. The Aparoids are bent on assimilation.
- Kirby 64 The Crystal Shards: The Crystal Shards had a boss shaped like a giant 20 sided die. It was Miracle Matter, a giant white icosahedron with each side graced with a red eye. Also, the boss of that game's second world was a trio of octohedra called 'Pix.'
- The entire point of Geometry Wars. While the player-controlled ships are strangely shaped, many of the enemies are perfect circles or regular polygons.
- Silent Hill's Pyramid Head.
- Halo: The giant, circular structure beneath New Mombasa. At first, its roundness isn't too bad... until you read supplemental materials and learn that it's perfectly circular to the subatomic level.
- Fable II has the Shards, magical war machines, which are just black, metal, floating, upended pyramids that spit lightning. They have strange markings, but are otherwise eerie in their simplicity - especially when they change their forms and mass with casual disregard for physics.
- The boss of level 10 in Space Harrier II, Bins Been, is an animated icosahedron.
- And don't forget the original Binzbeans from Space Harrier, prevalent in levels 4, 9, 14 (Ceiciel, Revi and Asute - the ones with the ceilings) and sporadically appearing in 17 (Nark).
- The hollow, cylindrical Rama, from Rama.
- The Stone-Like, from Radiant Silvergun. It's a giant octahedron that destroys all life on Earth. And then things get worse.
- The final boss, Yami in Okami has several "big scary sphere" forms.
- In Myst III: Exile, the Amateria Age is an island consisting of an extensive Giant's Causeway-like basalt column formation... combined with its iridescent mineral springs and glowing crystals it has a very unique otherworldly flavour even for a Myst level.
- Intelligent Qube pits you against an endless stream of giant, stomping, unstoppable, perfect cubes, and only cubes.
- The artifact of The white chamber is an imposing black shape, best described as a triangle on a trapezoid. Scarier than it sounds.
- The Fighting Polygon Team from Super Smash Bros Melee: They're not regular shapes, but they are polyhedra, and true polyhedra are generally unnatural.
- Spore. Chances are your exploration across the galaxy will have you stumbling across planets where much of their geography consists of terrain resembling chocolate bars, gears, crystals, or the skin of a pineapple; but nothing is more unsettling than discovering a cube planet, which vaguely resembles a Portal weighted storage cube.
- The aliens from The Dig, are shown to have a lot of reverence to the five Platonic solids. In fact, the probe that takes the astronauts to their planet looks like a crystal dodecahedron in space.
- The octahedral Cranassian Power Crystals in the Raiden series, which power the final bosses of most of the games. The Loop 1 Final Boss of IV is an icosadodecahedron.
- In Shin Megami Tensei Nocturne, after the apocalypse, there's suddenly a number of bizarre structures sprouting out of the ground everywhere. They don't seem to be built by human hands at all; there's no furniture in them, they're too smooth and blocky, and have Tron Lines prominently throughout them.
- The Shivering Isles expansion pack for Oblivion featured a weird, crowded world full of giant multi-coloured mushrooms, bizarre plants, dizzyingly bright skies, strange beings and similar people. Every now and then, you also come across silver obelisks coming up from the ground. They have no markings, make no sound, and cause (as far as you can tell) no harm - but their stark, steely simplicity within the garish realm of madness is both jarring and sinister. They're an effect of the Graymarch, the encroachment of Jyggalag's Order on the Shivering Isles.
- God of War 3 featured prominently Pandora's Box, a giant puzzle prison made of cubic rooms interlocking into a shifting giant cubic puzzle. Reassembling this puzzle into a coherent whole is a major plot point of the game.
- Sword and Sworcery EP: The Trigon Trifecta, a triplet of upside-down triangles which must be fought and tamed. Almost everything else in the game is done in a retro pixellated style, but the trigons are perfect triangles, which adds to the sense of their otherworldliness.
- Most of Earthbound's late-game alien enemies are rendered on the overworld as floating grey octahedrons. Unlike most enemies, their actual forms in battles look nothing like these overworld sprites; an octhedron could be anything from an alien bounty hunter to a mysterious robot, and you won't know until you're in battle with it.
- Sinister-looking polyhedrons occasionally pop up in A Beginner's Guide to the End of the Universe, invariably bringing trouble. For example, the Stone Cube sprouts into a Mook Maker tree, while a Stone Tetrahedron transforms into a troublesome Enigmatic Minion. By the time a Stone Dodecahedron pops up, the protagonist has had enough and lasers the heck out of it before it can do something nasty.
- The Second Renaissance in The Animatrix series features massive octahedral warbots, floating over the shattered battlefield.
- The Omnidroid from The Incredibles.
- In one episode of The Real Adventures of Jonny Quest, the team visits Easter Island and uncover a circular pod. They are amazed by how perfect its dimensions are. This leads to them finding the information the pod's former owners had on genetic engineering, which causes Surd to hack in, which leads to stuff going very badly for Dr. Quest and Race. Very badly.
- The U.S. government recently commissioned an academic study to recommend architectural designs for nuclear waste storage sites that could be seen as unambiguously dangerous and menacing. The message needed to be universal, so that humans thousands of years in the future would be discouraged from disturbing the radioactive sludge buried there even if language had evolved or if there had been a severe loss of scientific knowledge. Suggested site designs included a grid of huge, closely-spaced black cubes and a field of massive angular metal "thorns" jutting out of the desert floor.
- The F-117 Nighthawk and B-2 Spirit stealth bombers. The edgy triangular black Nighthawk covered with triangular facets, and the large black flying-wing B-2 have been often mistaken as UFO's. More modern stealth aircraft, like the F-22 Raptor, are rather less sinister..
- The hexagon of Saturn. While not entirely sinister, it's still rather confusing.
- The Giant's Causeway off the coast of Ireland, made of many nigh-perfectly formed hexagons, all naturally formed. There are others.
- While not on the same scale of a plane, the NASA experiment Gravity Probe B uses ~1 inch quartz spheres for gyroscopes that are spherical to within forty atoms. If scaled to the size of the earth, the tallest mountains would be 2.4 m (8 ft) high.