          # Cube

• regular hexahedron type platonic solid
elements f = 6, e = 12
v = 8 (χ = 2)
faces by sides 6{4}
conway notation c
schläfli symbols {4,3}
t{2,4} or {4}×{}
tr{2,2} or {}×{}×{}
face configuration v3.3.3.3
wythoff symbol 3 | 2 4
coxeter diagram     symmetry oh, b3, [4,3], (*432)
rotation group o, [4,3]+, (432)
references u06, c18, w3
properties regular, convexzonohedron
dihedral angle 90° 4.4.4
(vertex figure) octahedron
(dual polyhedron) net net of a cube 3d model of a cube

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.

• orthogonal projections
• spherical tiling
• cartesian coordinates
• equation in • formulas
• doubling the cube
• uniform colorings and symmetry
• geometric relations
• other dimensions
• related polyhedra
• cubical graph
## This article is about the 3-dimensional shape. For cubes in any dimension, see Hypercube. For other uses, see Cube (disambiguation). Regular hexahedron (Click here for rotating model) Type Platonic solid Elements F = 6, E = 12V = 8 (χ = 2) Faces by sides 6{4} Conway notation C Schläfli symbols {4,3} t{2,4} or {4}×{}tr{2,2} or {}×{}×{} Face configuration V3.3.3.3 Wythoff symbol 3 | 2 4 Coxeter diagram     Symmetry Oh, B3, [4,3], (*432) Rotation group O, [4,3]+, (432) References U06, C18, W3 Properties regular, convexzonohedron Dihedral angle 90° 4.4.4(Vertex figure) Octahedron(dual polyhedron) Net Net of a cube 3D model of a cube 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. Contents 1 Orthogonal projections 2 Spherical tiling 3 Cartesian coordinates 4 Equation in $\mathbb {R} ^{3}$ 5 Formulas 5.1 Point in space 6 Doubling the cube 7 Uniform colorings and symmetry 8 Geometric relations 9 Other dimensions 10 Related polyhedra 10.1 In uniform honeycombs and polychora 11 Cubical graph 12 See also 13 References 14 External links  