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)
|