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A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of 3-sided trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). A cube is the three-dimensional case of the more general concept of a hypercube, which exists in any dimension. Image File history File links Hexahedron. ...
Spinning hexahedron, made by me using POV-Ray, see image:poly. ...
In geometry, a Platonic solid is a convex regular polyhedron. ...
It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ...
In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ...
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wijthoff, is a method for constructing a uniform polyhedron or plane tiling. ...
Coxeter groups in the plane with equivalent diagrams. ...
Image File history File links CDW_ring. ...
Image File history File links CDW_4. ...
Image File history File links CDW_dot. ...
Image File history File links CDW_3. ...
Image File history File links CDW_dot. ...
// List of symmetry groups on the sphere Spherical symmetry groups are also called point groups (in 3D). ...
The octahedral rotation group O with fundamental domain Chiral and achiral octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. ...
A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...
A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...
H.S.M. Coxeter. ...
This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus J. Wenninger. ...
In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ...
Look up Convex set in Wiktionary, the free dictionary. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
In Aerospace engineering, the dihedral is the angle that the two wings make with each other. ...
Image File history File links Cube_vertfig. ...
In geometry, a vertex figure is most easily thought of as the cut surface exposed when a corner of a polytope is cut off in a certain way. ...
Image File history File links Download high-resolution version (1000x1000, 201 KB)See: Stella (software) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
Image File history File links Hexahedron_flat. ...
Categories: Polyhedra | Stub ...
The space we live in is three-dimensional space. ...
For other uses, see Square. ...
A hexahedron is a polyhedron with six faces. ...
In geometry, a Platonic solid is a convex regular polyhedron. ...
In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. ...
In geometry, a parallelepiped (now usually pronounced , traditionally[1] in accordance with its etymology in Greek παÏαλληλ-επίπεδον, a body having parallel planes) is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ...
The trapezohedron is the dual polyhedron of the corresponding antiprism. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
The octahedral rotation group O with fundamental domain Chiral and achiral octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. ...
A square A projection of a cube (into a two-dimensional image) A projection of a hypercube (into a two-dimensional image) In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). ...
Cartesian coordinates
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 Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
- (±1,±1,±1)
while the interior consists of all points (x0, x1, x2) with -1 < xi < 1.
Formulas For a cube of edge length a, | surface area | 6a2 | | volume | a3 | | radius of circumscribed sphere |  | | radius of sphere tangent to edges |  | | radius of inscribed sphere |  | As the volume of a cube is the third power of its sides a×a×a, third powers are called cubes, by analogy with squares and second powers. Area is a quantity expressing the size of a figure in the Euclidean plane or on a 2-dimensional surface. ...
The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ...
y=x³, for integer values of 1≤x≤25. ...
y=x³, for integer values of 1≤x≤25. ...
In algebra, the square of a number is that number multiplied by itself. ...
A cube construction has the largest volume among cuboids (rectangular boxes) with a given surface area (e.g., paper, cardboard, sheet metal, etc.). Also, a cube has the largest volume among cuboids with the same total linear size (length + width + height). In anatomy, the cuboid bone is a bone in the foot. ...
Area is the measure of how much exposed area any two dimensional object has. ...
Symmetry The cube has 3 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 lowest symmetry D2h is also a prismatic symmetry, with sides alternating colors, so there are three colors, paired by opposite sides. Each symmetry form has a different Wythoff symbol. In mathematics, a vertex-transitive graph is a graph G such that, given any two vertices v1 and v2 of G, there is some automorphism f : G → G such that f ( v1 ) = v2. ...
The octahedral rotation group O with fundamental domain Chiral and achiral octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. ...
This article deals with three infinite series of point groups in three dimensions which have a symmetry group which as abstract group is a dihedral group Dihn ( n ≥ 2 ). See also point groups in two dimensions. ...
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wijthoff, is a method for constructing a uniform polyhedron or plane tiling. ...
(3 colors)
| 2 2 2
D2h |
(2 colors)
4 2 | 2
D4h |
(1 color)
3 | 4 2
Oh | Image File history File links Size of this preview: 600 × 600 pixels Full resolution (1000 × 1000 pixel, file size: 205 KB, MIME type: image/png) Cube, D2h symmetry See: Stella (software) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old...
Image File history File links Download high-resolution version (1000x1000, 201 KB)Image of Cube, colored with dihedral symmetry Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Hexahedron (sometimes called cube), rendered by Java applet I wrote. ...
Geometric relations
 The familiar six-sided dice are cube shaped The cube is unique among the Platonic solids for being able to tile space regularly. 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). Image File history File links Stone_Dice_17. ...
Image File history File links Stone_Dice_17. ...
Dice (the plural of die, from Old French de, from Latin datum something given or played [1]) are small polyhedral objects, usually cubical, used for generating random numbers or other symbols. ...
A zonohedron is a convex polyhedron where every face is a polygon with point symmetry, or equivalently, symmetry under rotations through 180°. The regular polygons with such symmetry are those with an even number of sides, so the zonohedra with regular polygons for sides are easily enumerated: Of the Platonic...
Other dimensions The analogue of a cube in four-dimensional Euclidean space has a special name — a tesseract or (rarely) hypercube. Expo 67, cubes in a room Interior of Man the Producer Pavilion, Restrictions on access: Nil File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Expo 67, cubes in a room Interior of Man the Producer Pavilion, Restrictions on access: Nil File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
The 1967 International and Universal Exposition, or simply Expo 67 was the General Exhibition Category 1 Worlds Fair held in Montreal, Quebec, Canada from April 27 to October 29, 1967. ...
Around 300 BC, the Greek mathematician Euclid laid down the rules of what has now come to be called Euclidean geometry, which is the study of the relationships between angles and distances in space. ...
For other uses, see Tesseract (disambiguation). ...
A square A projection of a cube (into a two-dimensional image) A projection of a hypercube (into a two-dimensional image) In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). ...
The analog of the cube in n-dimensional Euclidean space is called a hypercube or n-dimensional cube or simply n-cube. It is also called a measure polytope. A square A projection of a cube (into a two-dimensional image) A projection of a hypercube (into a two-dimensional image) In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). ...
In math theory you can also have lower dimensional cube. A 0th dimensional cube is simply a point. A 1st dimensional cube is a line. A 2nd dimensional cube is a square. A spatial point is an entity with a location in space but no extent (volume, area or length). ...
“Line†redirects here. ...
For other uses, see Square. ...
Related polyhedra The vertices of a cube can be grouped into two groups of four, each forming a regular tetrahedron. 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. A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ...
A polyhedral compound is a polyhedron which is itself composed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compounds such as the hexagram. ...
Stella octangula The stella octangula (eight-pointed star), also known as the stellated octahedron, is the polyhedral compound of two tetrahedra. ...
An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
One such regular tetrahedron has a volume of ⅓ of that of the cube. The remaining space consists of four equal irregular polyhedra 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 6 octagonal faces and 8 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. In Euclidean geometry, rectification is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points. ...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
For other uses, see Octagon (disambiguation). ...
The truncated cube, or truncated hexahedron, is an Archimedean solid. ...
The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. ...
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. A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ...
A polyhedral compound is a polyhedron which is itself composed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compounds such as the hexagram. ...
The tetrahedra in the cube (stella octangula) Image File history File links Stella_octangula. ...
Stella octangula The stella octangula (eight-pointed star), also known as the stellated octahedron, is the polyhedral compound of two tetrahedra. ...
| The rectified cube (cuboctahedron) Image File history File links This is a lossless scalable vector image. ...
In Euclidean geometry, rectification is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points. ...
A cuboctahedron is a polyhedron with eight triangular faces and six square faces. ...
| Truncated cube Download high resolution version (819x855, 67 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ...
The truncated cube, or truncated hexahedron, is an Archimedean solid. ...
| Rhombicuboctahedron Download high resolution version (823x836, 83 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ...
The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. ...
| The figures shown have the same symmetries as the cube (see octahedral symmetry). The octahedral rotation group O with fundamental domain Chiral and achiral octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. ...
Combinatorial cubes A different kind of cube is the cube graph, which is the graph of vertices and edges of the geometrical cube. It is a special case of the hypercube graph. The hypercube graph Q4. ...
An extension is the 3-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. A Hamming graph is a graph (mathematics) used in several branches of mathematics and computer science. ...
Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain results faster. ...
See also A unit cube is a 3-dimensional geometric figure that consists of a cube in which all of its dimensions are 1 unit long. ...
For other uses, see Tesseract (disambiguation). ...
The Kaaba (Arabic: ; IPA: ) , also known as (), ( The Primordial House), or ( The Sacred House), is a large cuboidal building located inside the mosque known as al-Masjid al-Haram in Mecca, Saudi Arabia. ...
References - ^ English cube from Old French < Latin cubus < Greek kubos, "a cube, a die, vertebra". In turn from PIE *keu(b)-, "to bend, turn".
This article is about the baked good, for other uses see Pie (disambiguation). ...
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