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Geometry Formula for Cube

A cube in geometry is a three-dimensional solid object bounded by six square faces, facets or sides that all meet each vertex. The cube is also called a regular hexahedron and is one of the five Platonic solids.

The cube is a special kind of square prism, of rectangular parallelepiped and of trigonal 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. It has 11 nets. If one were to color the cube so that no two adjacent faces had the same color, one would need 3 colors. If the original cube has edge length 1, its dual octahedron has edge length \sqrt{2}

Formulae - For a cube of edge length a,

Surface area   6a2

Volume            a3
Face diagonal  \sqrt 2a

Space diagonal            \sqrt 3a

Radius of circumscribed sphere         \frac{\sqrt 3}{2} a

Radius of sphere tangent to edges     \frac{a}{\sqrt 2}

Radius of inscribed sphere     \frac{a}{2}

Angles between faces \frac{\pi}{2}

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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