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..

Unit hypercube

The term ''unit cube'' or unit hypercube is also used for
hypercube 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 \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 ...

Doubling the cube
* 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


External links

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