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Cuboid
 
 
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In anatomy, the cuboid bone
Cuboid bone

The cuboid bone is one of seven tarsus bones....
 is a bone in the foot.
In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing and incompatible definitions of a cuboid in the mathematical literature. In the more general definition of a cuboid, the only additional requirement is that these six faces each be a quadrilateral
Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
, and that the undirected graph formed by the vertices and edges of the polyhedron should be isomorphic
Graph isomorphism

In graph theory, an isomorphism of graph s G and H is a bijection between the vertex sets of G and Hsuch that any two vertices u and v of G are adjacent in G if and only if ? and ? are adjacent in H....
 to the graph of a cube
Cube

A cube is a three-dimensional space solid object bounded by six square faces, facets or sides, with three meeting at each wikt:vertex. The cube can also be called a Regular polyhedron hexahedron and is one of the five Platonic solids....
.






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In anatomy, the cuboid bone
Cuboid bone

The cuboid bone is one of seven tarsus bones....
 is a bone in the foot.
In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing and incompatible definitions of a cuboid in the mathematical literature. In the more general definition of a cuboid, the only additional requirement is that these six faces each be a quadrilateral
Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
, and that the undirected graph formed by the vertices and edges of the polyhedron should be isomorphic
Graph isomorphism

In graph theory, an isomorphism of graph s G and H is a bijection between the vertex sets of G and Hsuch that any two vertices u and v of G are adjacent in G if and only if ? and ? are adjacent in H....
 to the graph of a cube
Cube

A cube is a three-dimensional space solid object bounded by six square faces, facets or sides, with three meeting at each wikt:vertex. The cube can also be called a Regular polyhedron hexahedron and is one of the five Platonic solids....
. Alternatively, the word “cuboid” is sometimes used to refer to a shape of this type in which each of the faces is a rectangle
Rectangle

In geometry, a rectangle is a Closed set planar quadrilateral with four right angles. A rectangle with vertices ABCD would be denoted as .A rectangle with adjacent sides of lengths a and b has area ab and diagonals of equal length ....
, and in which each pair of adjacent faces meets in a right angle
Right angle

In geometry and trigonometry, a right angle is an angle of 90 degree s, corresponding to a quarter turn . It can be defined; as the angle such that twice that angle amounts to a half turn, or 180?....
; this more restrictive type of cuboid is also known as a right cuboid, rectangular box
Box

Box describes a variety of containers and receptacles. When no specific shape is described, a typical Rectangle box may be expected. Nevertheless, a box may have a horizontal cross section that is square , elongated, circle or oval; sloped or domed top surfaces, or non-vertical sides....
, rectangular hexahedron
Hexahedron

A hexahedron is a polyhedron with six faces. A Regular polyhedron hexahedron, with all its faces Square , is a cube.There are many kinds of hexahedra, some topologically similar to the cube and some not....
, right rectangular prism, or rectangular parallelepiped
Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. It is to a parallelogram as a cube is to a square : Euclidean geometry supports all four notions but affine geometry admits only parallelograms and parallelepipeds....
.

General cuboids

By Euler's formula
Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent....
 (the number of faces (F), vertices (V), and edges (E) of any convex polyhedron are related by the formula F + V = E + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces
Face (geometry)

In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the square s that bound a cube is a face of the cube....
, 8 vertices
Vertex (geometry)

In geometry, a vertex is a special kind of point which describes the corners or intersections of geometric shapes. Vertices are commonly used in computer graphics to define the corners of surfaces in 3d models, where each such point is given as a vector....
, and 12 edges.

Along with the rectangular cuboids, any parallelepiped
Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. It is to a parallelogram as a cube is to a square : Euclidean geometry supports all four notions but affine geometry admits only parallelograms and parallelepipeds....
 is a cuboid of this type, as is a square frustum
Frustum

A frustum is the portion of a solid?normally a Cone or pyramid ?which lies between two parallel planes cutting the solid. The term is commonly used in computer graphics to describe the 3d area which is visible on the screen ....
 (the shape formed by truncation
Truncation

In mathematics, truncation is the term for limiting the number of numerical digits right of the decimal point, by discarding the least significant ones....
 of the apex of a square pyramid
Square pyramid

In geometry, a square pyramid is a Pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry....
).

Rectangular cuboids

In a rectangular cuboid, all angles are right angle
Right angle

In geometry and trigonometry, a right angle is an angle of 90 degree s, corresponding to a quarter turn . It can be defined; as the angle such that twice that angle amounts to a half turn, or 180?....
s, and opposite faces of a cuboid are equal
Congruence (geometry)

In geometry, two sets of point are called congruent if one can be transformed into the other by an isometry, i.e., a combination of translation s, rotations and reflection s....
. It is also a right rectangular prism
Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
. The term "rectangular or oblong prism" is ambiguous. Also the term rectangular parallelepiped
Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. It is to a parallelogram as a cube is to a square : Euclidean geometry supports all four notions but affine geometry admits only parallelograms and parallelepipeds....
 or orthogonal parallelepiped is used.

The square cuboid, square box ,or right square prism (also ambiguously called square prism) is a special case of the cuboid in which at least two faces are squares. The cube is a special case of the square prism in which all six faces are squares.

If the dimensions of a cuboid are a, b and c, then its volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 is abc and its surface area
Surface area

Surface area is how much exposed area an object has. It is expressed in square units. If an object has flat Face , its surface area can be calculated by adding together the areas of its faces....
 is 2ab + 2bc + 2ac.

The length of the space diagonal
Space diagonal

In a cuboid or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner....
 is

Cuboid shapes are often used for box
Box

Box describes a variety of containers and receptacles. When no specific shape is described, a typical Rectangle box may be expected. Nevertheless, a box may have a horizontal cross section that is square , elongated, circle or oval; sloped or domed top surfaces, or non-vertical sides....
es, cupboard
Cupboard

A cupboard or press is a type of Cabinet , often made of wood, used indoors to store household objects such as food and crockery, and protect them from dust and dirt....
s, rooms, buildings, etc. Cuboids are among those solids that can tessellate 3-dimensional space
Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions....
. The shape is fairly versatile in being able to contain multiple smaller cuboids, e.g. sugar
Sugar

Sugar is a class of edible crystalline substances, mainly sucrose, lactose, and fructose. Human taste buds interpret its flavor as sweet. Sugar as a basic food carbohydrate primarily comes from sugar cane and from sugar beet, but also appears in fruit, honey, sorghum, sugar maple , and in many other sources....
 cubes in a box, small boxes in a large box, a cupboard in a room, and rooms in a building.

A cuboid with integer edges as well as integer face diagonals is called an Euler brick
Euler brick

In mathematics, an Euler brick, named after the famous mathematician Leonhard Euler, is a cuboid with integer edges and also integer face diagonals....
, for example with sides 44, 117 and 240. A perfect cuboid
Euler brick

In mathematics, an Euler brick, named after the famous mathematician Leonhard Euler, is a cuboid with integer edges and also integer face diagonals....
 is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists.

See also

  • Hyperrectangle
    Hyperrectangle

    In geometry, an orthotope is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of interval s....
  • Oblong
    Oblong

    Oblong may refer to:*A rectangle that is not square .*Angus Oblong, American author and actor*Oblong, Illinois, a village in the United States...


External links

  • Paper models and pictures
  • , an Oxford research project
  • from Math Is Fun
    Math Is Fun

    Math Is Fun is an educational website maintained by Rod Pierce devoted to the concept that mathematics is, indeed, fun.There are several aspects to the website:...