Cube

Cube
Type	Hanner polytope, orthogonal polyhedron, parallelohedron, Platonic solid, plesiohedron, regular polyhedron, zonohedron
Faces	6
Edges	12
Vertices	8
Vertex configuration	${\displaystyle 8\times (4^{3})}$
Schläfli symbol	${\displaystyle \{4,3\}}$
Symmetry group	octahedral symmetry ${\displaystyle \mathrm {O} _{\mathrm {h} }}$
Volume	side3
Dihedral angle (degrees)	90°
Dual polyhedron	regular octahedron
Properties	convex, edge-transitive, face-transitive, non-composite, orthogonal faces, vertex-transitive

A cube or regular hexahedron is a three-dimensional solid object in geometry, which is bounded by six congruent 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 angles 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 polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with 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 and honeycombs, polycubes, as well as cubes in compounds, spherical, and topological space.

The cube was discovered in antiquity, associated with the nature of earth by Plato, the founder of the Platonic solids. It was used as a part of the Solar System, proposed by Johannes Kepler. 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.