Cube (geometry)

A cube, or regular hexahedron, is a solid composed of six square faces. A cube is dual to the regular octahedron and has octahedral symmetry. A cube is a Platonic solid. All edges of cubes are equal to each other.

The cube is also a square parallelepiped, an equilateral cuboid, and a right rhombohedron a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

Formulas

A cube with edge-length $s$ has:

Four space diagonals of same lengths $s\sqrt{3}$ ( $\sqrt{s^2+s^2+s^2}=\sqrt{3s^2}=s\sqrt{3}$ )
Surface area of $6s^2$ . (6 sides of areas $s \cdot s$ .)
Volume $s^3$ ( $s \cdot s \cdot s$ )
A circumscribed sphere of radius $\frac{s\sqrt{3}}{2}$
An inscribed sphere of radius $\frac{s}{2}$
A sphere tangent to all of its edges of radius $\frac{s\sqrt{2}}{2}$
A regular tetrahedron can fit in exactly two ways inside a cube

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Cube (geometry)

Formulas

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