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
Formulae - For a cube of edge length a,
Surface area 6a2
Volume a3
Face diagonal
Space diagonal
Radius of circumscribed sphere
Radius of sphere tangent to edges
Radius of inscribed sphere
Angles between faces
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.
