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)
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and the total surface area is
(2)
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The lengths of the face diagonals are
(3)
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(4)
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(5)
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and the length of the space diagonal is
(6)
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