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Cuboid


RectangularParallelepiped
Cuboid1Cuboid2Cuboid3Cuboid4

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 a, b, and c. A cuboid with all sides equal (a=b=c) is called a cube, and a cuboid with integer edge lengths a>b>c 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

 V=abc
(1)

and the total surface area is

 S=2(ab+bc+ca).
(2)

The lengths of the face diagonals are

d_(ab)=sqrt(a^2+b^2)
(3)
d_(ac)=sqrt(a^2+c^2)
(4)
d_(bc)=sqrt(b^2+c^2),
(5)

and the length of the space diagonal is

 d_(abc)=sqrt(a^2+b^2+c^2).
(6)

See also

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

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