Unit cube
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.<ref name="pcm">Template:Citation. See in particular p. 671.</ref><ref name="cbm">Template:Citation.</ref> The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.<ref>Template:Citation.</ref>
Unit hypercubeEdit
The term unit cube or unit hypercube is also used for hypercubes, or "cubes" in n-dimensional spaces, for values of n other than 3 and edge length 1.<ref name="pcm"/><ref name="cbm"/>
Sometimes the term "unit cube" refers in specific to the set [0, 1]n of all n-tuples of numbers in the interval [0, 1].<ref name="pcm"/>
The length of the longest diagonal of a unit hypercube of n dimensions is <math>\sqrt n</math>, the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space.<ref name="cbm"/>
See alsoEdit
- 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