# cube

This hashtag in English

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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

The cube is dual to the octahedron. It has cubical or octahedral symmetry.

The cube is the only convex polyhedron whose faces are all squares.

The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The first and third correspond to the A2 and B2 Coxeter planes.

The cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane.

For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian coordinates of the vertices are

while the interior consists of all points (x0, x1, x2) with −1 < xi < 1 for all i.

In analytic geometry, a cube's surface with center (x0, y0, z0) and edge length of 2a is the locus of all points (x, y, z) such that

A cube can also be considered the limiting case of a 3D superellipsoid as all three exponents approach infinity.

For a cube of edge length ${\displaystyle a}$:

As the volume of a cube is the third power of its sides ${\displaystyle a\times a\times a}$, third powers are called cubes, by analogy with squares and second powers.

A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length+width+height).

For a cube whose circumscribing sphere has radius R, and for a given point in its 3-dimensional space with distances di from the cube's eight vertices, we have:

Doubling the cube, or the Delian problem, was the problem posed by ancient Greek mathematicians of using only a compass and straightedge to start with the length of the edge of a given cube and to construct the length of the edge of a cube with twice the volume of the original cube. They were unable to solve this problem, and in 1837 Pierre Wantzel proved it to be impossible because the cube root of 2 is not a constructible number.

The cube has three uniform colorings, named by the colors of the square faces around each vertex: 111, 112, 123.

The cube has four classes of symmetry, which can be represented by vertex-transitive coloring the faces. The highest octahedral symmetry Oh has all the faces the same color. The dihedral symmetry D4h comes from the cube being a prism, with all four sides being the same color. The prismatic subsets D2d has the same coloring as the previous one and D2h has alternating colors for its sides for a total of three colors, paired by opposite sides. Each symmetry form has a different Wythoff symbol.

A cube has eleven nets (one shown above): that is, there are eleven ways to flatten a hollow cube by cutting seven edges. To color the cube so that no two adjacent faces have the same color, one would need at least three colors.

The cube is the cell of the only regular tiling of three-dimensional Euclidean space. It is also unique among the Platonic solids in having faces with an even number of sides and, consequently, it is the only member of that group that is a zonohedron (every face has point symmetry).

The cube can be cut into six identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces).

The analogue of a cube in four-dimensional Euclidean space has a special name—a tesseract or hypercube. More properly, a hypercube (or n-dimensional cube or simply n-cube) is the analogue of the cube in n-dimensional Euclidean space and a tesseract is the order-4 hypercube. A hypercube is also called a measure polytope.

There are analogues of the cube in lower dimensions too: a point in dimension 0, a line segment in one dimension and a square in two dimensions.

The quotient of the cube by the antipodal map yields a projective polyhedron, the hemicube.

If the original cube has edge length 1, its dual polyhedron (an octahedron) has edge length ${\displaystyle \scriptstyle {\sqrt {2}}/2}$.

The cube is a special case in various classes of general polyhedra:

The vertices of a cube can be grouped into two groups of four, each forming a regular tetrahedron; more generally this is referred to as a demicube. These two together form a regular compound, the stella octangula. The intersection of the two forms a regular octahedron. The symmetries of a regular tetrahedron correspond to those of a cube which map each tetrahedron to itself; the other symmetries of the cube map the two to each other.

One such regular tetrahedron has a volume of 1/3 of that of the cube. The remaining space consists of four equal irregular tetrahedra with a volume of 1/6 of that of the cube, each.

The rectified cube is the cuboctahedron. If smaller corners are cut off we get a polyhedron with six octagonal faces and eight triangular ones. In particular we can get regular octagons (truncated cube). The rhombicuboctahedron is obtained by cutting off both corners and edges to the correct amount.

A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes.

If two opposite corners of a cube are truncated at the depth of the three vertices directly connected to them, an irregular octahedron is obtained. Eight of these irregular octahedra can be attached to the triangular faces of a regular octahedron to obtain the cuboctahedron.

The cube is topologically related to a series of spherical polyhedra and tilings with order-3 vertex figures.

The cuboctahedron is one of a family of uniform polyhedra related to the cube and regular octahedron.

The cube is topologically related as a part of sequence of regular tilings, extending into the hyperbolic plane: {4,p}, p=3,4,5...

With dihedral symmetry, Dih4, the cube is topologically related in a series of uniform polyhedra and tilings 4.2n.2n, extending into the hyperbolic plane:

All these figures have octahedral symmetry.

The cube is a part of a sequence of rhombic polyhedra and tilings with [n,3] Coxeter group symmetry. The cube can be seen as a rhombic hexahedron where the rhombi are squares.

The cube is a square prism:

As a trigonal trapezohedron, the cube is related to the hexagonal dihedral symmetry family.

It is an element of 9 of 28 convex uniform honeycombs:

It is also an element of five four-dimensional uniform polychora:

The skeleton of the cube (the vertices and edges) form a graph, with 8 vertices, and 12 edges. It is a special case of the hypercube graph. It is one of 5 Platonic graphs, each a skeleton of its Platonic solid.

An extension is the three dimensional k-ary Hamming graph, which for k = 2 is the cube graph. Graphs of this sort occur in the theory of parallel processing in computers.

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Y’a beaucoup de passions qui sont pas les miennes mais que je comprends.... mais la passion du Rubik’s cube ??? pour quoi faire
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@bambamsoftbam Il a été dans sm the ballad quand il était trainee ^^ Il a été trainee chez sm pendant 6 ans ensuit…
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Maybe Ice Cube saw that stripper commercial because if so I agree lol
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The cube is once again within our control
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Get 40% OFF the Nike Signal D/MS/X "Ocean Cube" + free shipping Buy Here:
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@domesticmothman The one with Ice Cube?
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Watching Ice Cube get read for filth might be the highlight of my day.
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[#홍석] Did you dream of me? 👀♥️
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RT @croissant_mag: Amazon Fire TV Cubeを1名にプレゼント！ 【応募方法】 １、クロワッサン公式twitter（@croissant_mag）をフォロー。 ２、この投稿をリツイートすればOK ※当選連絡はDMで行います。 【締め切り】 2…
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RT @pentagon_promo: [INFO] SHINE has surpassed 100 Million streams on Spotify!!! @CUBE_PTG #PENTAGON #펜타곤
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RT @NuitGod: Y’all mad at Ice Cube for meeting with Biden on the CBA, when Biden has 50 executive orders and not one is for you? I guess y’…
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the more we edit these the closer to minecraft we become. rackam cube will go global and then it will come full cir…
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RT @Ioveatory: hello kitty ice cube tray
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RT @MagnivGames: I've released the first demo for the game. Please try the game and tell me…
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RT @The_Acumen: I don’t understand why Ice Cube, or any other celebrity would be meeting with any president or elected as “the voice of Bla…
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@CrookedIntriago Mix those together and you get some of the GOATS!!! Public Enemy, Ice Cube and Kxng Crooked I
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Because the only people that people listen to are people they either envy or think are better than them because of…
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who the hell made ICE CUBE the representative of black people in America?
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RT @buitengebieden_: 3D cube illusion..
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RT @GeneralWarPHare: I don’t remember electing Ice Cube to lead the delegation on our behalf.
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RT @sakipon_delion: これ…今のツイデモの給付金の話で「働いた方が早い」って即時に言っちゃう人達にも当てはまる気がする デモしてる人たちのスペックでは働くのが困難な現状なのに自分のスペックでは働くことの方が早いから強気で言うけど相手の背景見えてない。自信があ…
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RT @buitengebieden_: 3D cube illusion..
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RT @doritegrocery: .@icecube is meeting with .@JoeBiden The number is 12 trillion Mr President to close the lineage wealth gap for Black de…
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RT @buitengebieden_: 3D cube illusion..
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RT @katieandmister: My cat woke me up screaming because he wanted an ice cube to play with on my kitchen floor... a habit he apparently dev…
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[#PTGET] 후이는 🐸 동선 정리 중 (Feat. [WE L:VE] Ver.) #펜타곤 #PENTAGON #후이 #HUI
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RT @MAMAMOOTH_: [INFO] 210205 #มุนบยอล ชนะรางวัล Best Female Solo 🎉 ขอบคุณทุกคนที่ร่วมโหวตค่ะ 🙏🏻 ผู้ชนะจะได้รับโฆษณา 🔅ออฟไลน์ ที่ Samsung…
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RT @awhile_korea: ตามรอย #TrueBeauty ค่าา 💖 กับ colorgram multi cube pallet ที่ #จูกยอง ของเราใช้นั่นเองง 💖 มี 2 เฉดสี 💖 570 ส่งฟรีลทบ…
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RT @RadioDuna: 📻 #SantiagoAdicto Carmen Romero y Cube Studies: “Es un espectáculo dirigido y creado por un grupo de circo australiano. Se d…
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RT @CUBEENTGLOBAL: @CUBE_PTG [#PTGET] HUI is organizing the 🐸 blockings (Feat. [WE L:VE] Ver.) #펜타곤 #PENTAGON #후이 #HUI
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RT @XTigerHyperX: fun fact but the cube sounds still exist in the files till this day and i find it kinda amazing and nostalgic also note…
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RT @dingo_official: [#딩고봇] 딩고가 외장하드 털어왔당!!! &lt;썸타는 편의점&gt;주인공들의 실체?! 귀여워...&gt;_&lt;/// 어쩜 다들 이렇게 말랑말랑 순둥순둥한거야,,,💛 @echoglobalgroup @CUBE_PTG @VICTON…
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Seeing that quote made by a cube representative still makes me laugh. "Mature fandom culture is an image of the a…
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RT @XTigerHyperX: fun fact but the cube sounds still exist in the files till this day and i find it kinda amazing and nostalgic also note…
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RT @ptg_uni_jp: [🎬Thanks to #UNIVERSE❤] #5thTTA Prelims Winner in 🇲🇾🎉 From #PENTAGON #펜타곤💌 @CUBE_PTG #TTA 最終ラウンド🗳VOTE 👉
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RT @Gnosis1211: 190728 🌟 😆😆😆 @CUBE_PTG #접근금지 #펜타곤 #PENTAGON #신원 #고신원 #SHINWON
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@jamesj0int that looks like cube surfer
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RT @TTA_tenasia: [🎬Thanks to #UNIVERSE❤] #5thTTA Prelims Winner in 🇲🇾🎉 From #PENTAGON #펜타곤💌 @CUBE_PTG #TTA Final in progress! 결선 투표 많은…
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RT @thehill: Ice Cube says Biden administration has reached out to him
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@XTigerHyperX nah its because of how the cube works in creative (it doesnt attack back at the player on shot or even kill)
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RT @dingo_official: [#딩고봇] 딩고가 외장하드 털어왔당!!! &lt;썸타는 편의점&gt;주인공들의 실체?! 귀여워...&gt;_&lt;/// 어쩜 다들 이렇게 말랑말랑 순둥순둥한거야,,,💛 @echoglobalgroup @CUBE_PTG @VICTON…
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RT @XTigerHyperX: fun fact but the cube sounds still exist in the files till this day and i find it kinda amazing and nostalgic also note…
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Today was a good day - Ice Cube 💎
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Eine kleine Runde in der Dippoldiswalder Heide ☀⛅ . . #spazieren #nature #outdoor #frischeluft #sport #wanderlust #mountainlovers #inliner #wettergenießen #cube #naturelovers #fun #abschalten #sportlicheaktivität #outdoorsports #abtauchen #sunglass😎 #sunglass #glares #men #eyewear #dresden #smile #alwayssmile #lächelnistgesund #fun #menfoto #menphoto #menphotography
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Wieder ein wundervoller Start in den Tag! 🚴‍♀️😎👍 #runningmike #mdrza ID5899 #bike2work #instacycling #radsport #lovecycling #radpower #besserbergauf #triathlon #marathon #berlinhalf #berlin42 #kempten #allgäu #weilerimallgäu #westallgäu #sommer2020 #frischluft #co2neutral #ohneakku #immerimtraining #cubebikes #litening #cube
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10k run with my Padawan biking 🚴‍♀️ and @susanmus (photographer) in Dyrehaven, Nice. #dyrehaven #run #oncloud #cube #visitdenmark #oplevdanmark #visitcopenhagen #dadanddaughter #familytime
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🚲 jobringa.hu 🚲 #cube #cubebikes #cubeebike #ebike #hybrid #stereo #fully
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