Cube
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| Regular Hexahedron | |
|---|---|
 (Click here for rotating model) | |
| Type | Platonic solid |
| Elements | F = 6, E = 12 V = 8 (χ = 2) |
| Faces by sides | 6{4} |
| Schläfli symbol | {4,3} |
| Wythoff symbol | 3 | 2 4 2 4 | 2 2 2 2 | |
| Coxeter-Dynkin |      |
| Symmetry | Oh or (*432) |
| References | U06, C18, W3 |
| Properties | Regular convex zonohedron |
| Dihedral angle | 90° |
 4.4.4 (Vertex figure) |  Octahedron (dual polyhedron) |
 Net | |
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.
Formulae
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.
A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length + width + height).
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