Editing Cube (section)

{{Short description|Solid object with six equal square faces}}
{{other uses}}
{{infobox polyhedron
 | name = Cube
 | image = File:Cube-h.svg
 | type = [[Hanner polytope]],<br>[[orthogonal polyhedron]],<br>[[parallelohedron]],<br>[[Platonic solid]],<br>[[plesiohedron]],<br>[[regular polyhedron]],<br>[[zonohedron]]
 | faces = 6
 | edges = 12 
 | vertices = 8
 | vertex_config = <math> 8 \times (4^3) </math>
 | schläfli = <math> \{4,3\} </math>
 | symmetry = [[octahedral symmetry]] <math> \mathrm{O}_\mathrm{h} </math>
 | dual = [[regular octahedron]]
 | angle = 90°
 | properties = [[Convex set|convex]],<br>[[edge-transitive]],<br>[[face-transitive]],<br>[[non-composite polyhedron|non-composite]],<br>[[Orthogonality|orthogonal]] faces,<br>[[vertex-transitive]]
 | surface area = 6 × side<sup>2</sup>
 | volume = side<sup>3</sup>
}}
A '''cube''' or '''regular hexahedron'''{{r|trudeau}} is a [[three-dimensional space|three-dimensional]] solid object in [[geometry]], which is bounded by six congruent [[square (geometry)|square]] faces, a type of [[polyhedron]]. It has twelve congruent edges and eight vertices. It is a type of [[parallelepiped]], with pairs of parallel opposite faces, and more specifically a [[rhombohedron]], with congruent edges, and a [[rectangular cuboid]], with [[right angle]]s between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: [[Platonic solid]], [[regular polyhedron]], [[parallelohedron]], [[zonohedron]], and [[plesiohedron]]. The [[dual polyhedron]] of a cube is the [[regular octahedron]].

The cube can be represented in many ways, one of which is the graph known as the '''cubical graph'''. It can be constructed by using the [[Cartesian product of graphs]]. The cube is the three-dimensional [[hypercube]], a family of [[polytope]]s also including the two-dimensional square and four-dimensional [[tesseract]]. A cube with [[1|unit]] side length is the canonical unit of [[volume]] in three-dimensional space, relative to which other solid objects are measured. Other related figures involve the construction of polyhedra, [[Space-filling polyhedron|space-filling]] and [[Honeycomb (geometry)|honeycomb]]s, [[polycube]]s, as well as cubes in compounds, spherical, and topological space.

The cube was discovered in antiquity, associated with the nature of [[Earth (classical element)|earth]] by [[Plato]], for whom the Platonic solids are named.  It can be derived differently to create more polyhedra, and it has applications to construct a new [[polyhedron]] by attaching others. Other applications include popular culture of toys and games, arts, optical illusions, architectural buildings, as well as natural science and technology.