The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.

Cuboid and Cube

A cuboid (a "box" in everyday parlance) is also known as a rectangular parallelepiped or as a right prism. A special case of the cuboid is the cube, with all sides equal:

a = b = c

A cuboid with sides and face diagonals of integer length is called a Euler brick. Examples for an Euler brick are a=240, b=117, c=44, or a=275, b=252, c=240. If we require the space diagonal to be also of integer length, we get a perfect cuboid. However, the perfect cube has not yet been found, despite an exhaustive search for all "odd sides" up to 1010.

The volume V of the cuboid is defined by

V = abc.

The surface S of a cuboid is given by

S = 2(ab+bc+ac)

The length of the space diagonal ds can be calculated using

Last Update: 2010-12-06