Cuboid

Cuboid with space diagonal d

Unfolded mesh of a cuboid

A cuboid (also right- sided and sometimes right-sided ) is a body that is bounded by six rectangles .

A cuboid possesses

six side faces that are at right angles to each other,
eight right angled corners and
twelve edges , four of which each have the same length and are parallel to one another .

Opposite surfaces of a cuboid are congruent (congruent).

Formulas for the cuboid
Edge lengths	${\ displaystyle a, b, c}$
volume	${\ displaystyle V = a \ cdot b \ cdot c}$
Surface area	${\ displaystyle A _ {\ mathrm {O}} = 2 \ cdot (a \ cdot b + a \ cdot c + b \ cdot c)}$
Length of the room diagonals	${\ displaystyle d = {\ sqrt {a ^ {2} + b ^ {2} + c ^ {2}}}}$

Special cuboids

In the special case of equal edge lengths , in which all surfaces of the cuboid are squares , a cube results . In the event that exactly two edge lengths are the same, the result is a square straight prism ( ), one speaks occasionally of a square plate ( ) or a square column ( ). ${\ displaystyle a = b = c}$ ${\ displaystyle a = b \ neq c}$ ${\ displaystyle a = b> c}$ ${\ displaystyle a = b <c}$

symmetry

Cuboids are point-symmetrical . The point of symmetry is the intersection of the space diagonals. In contrast to the cube , the room diagonals do not represent (three-fold) axes of rotation.

Generalizations

A three-dimensional body with six pairs of parallel faces is called a parallelepiped , regardless of its perpendicularity. So every cuboid is a right-angled parallelepiped.

Each cuboid is a prism with a rectangular base.

Occasionally the term cuboid is extended to -dimensional spaces, so that especially for a rectangle it can be described as a two-dimensional, an interval or a line as a one-dimensional and a point as a zero-dimensional cuboid. In higher-dimensional polytopes the terms Hyperboxes , Hyperrectangle, -dimensional cuboid or -dimensional interval in use. ${\ displaystyle n}$ ${\ displaystyle n <3}$ ${\ displaystyle n}$ ${\ displaystyle n}$

Web links

Wiktionary: cuboid - explanations of meanings, word origins, synonyms, translations

Commons : Cuboid - collection of images, videos and audio files

Eric W. Weisstein : Cuboid . In: MathWorld (English).