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# Cuboid

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The cuboid is also a right prism, a special case of the parallelepiped, and corresponds to what in everyday parlance is known as a (rectangular) "box." Cuboids are implemented in the Wolfram Language as Cuboid[xmin, ymin, zmin, xmax, ymax, zmax] by giving the coordinates of opposite corners. The monolith with side lengths 1, 4, and 9 in the book and film version 2001: A Space Odyssey is an example of a cuboid.

Let the lengths of the sides be denoted , , and . A cuboid with all sides equal () is called a cube, and a cuboid with integer edge lengths and face diagonals is called an Euler brick. If the space diagonal is also an integer, the cuboid is called a perfect cuboid.

The volume of a cuboid is given by

 (1)

and the total surface area is

 (2)

The lengths of the face diagonals are

 (3) (4) (5)

and the length of the space diagonal is

 (6)

Cube, Euler Brick, Parallelepiped, Prism, Spider and Fly Problem

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## References

Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 127, 1987.Harris, J. W. and Stocker, H. "Cuboid." §4.2.3 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 97, 1998.Kern, W. F. and Bland, J. R. "Rectangular Parallelepiped." §10 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 21-25, 1948.

## Cite this as:

Weisstein, Eric W. "Cuboid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cuboid.html