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
- Four space diagonals of same lengths ()
- Surface area of . (6 sides of areas .)
- Volume ()
- A circumscribed sphere of radius
- An inscribed sphere of radius
- A sphere tangent to all of its edges of radius
- A regular tetrahedron can fit in exactly two ways inside a cube
- For any cube whose circumscribing sphere has radius , and for any given point in the its 3D dimensional space with distances from the cube's eight vertices, we have:
See also
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