300px, Unit cube
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.. See in particula

p. 671

. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units..

p. 671

. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units..

Unit hypercube

The term ''unit cube'' or unit hypercube is also used forhypercube
In geometry
Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space th ...

s, or "cubes" in ''n''-dimensional spaces, for values of ''n'' other than 3 and edge length 1.
Sometimes the term "unit cube" refers in specific to the set , 1sup>''n'' of all ''n''-tuples of numbers in the interval , 1
The length of the longest diagonal of a unit hypercube of ''n'' dimensions is $\backslash sqrt\; n$, the square root of ''n'' and the (Euclidean) length of the vector (1,1,1,....1,1) in ''n''-dimensional space.
See also

*Doubling the cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume
Volume is the quantity of three-dimensional space ...

* K-cell
* Robbins constant, the average distance between two random points in a unit cube
*Tychonoff cube, an infinite-dimensional analogue of the unit cube
*Unit square
*Unit sphere
References

External links

* {{mathworld , urlname = UnitCube , title = Unit cube Euclidean solid geometry 1 (number) Cubes