# Unit cube

Revision as of 22:01, 28 November 2014 by en>Cydebot (Robot - Moving category One to Category:1 (number) per CFD at Wikipedia:Categories for discussion/Log/2014 November 19.)

A **unit cube**, more formally a **cube of side 1**, is a cube whose sides are 1 unit long.^{[1]}^{[2]} The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.^{[3]}

## Unit hypercube

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.^{[1]}^{[2]}

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].^{[1]}

The length of the longest diagonal of a unit hypercube of *n* dimensions is , the square root of *n* and the (Euclidean) length of the vector (1,1,1,....1,1) in *n*-dimensional space.^{[2]}

## See also

- 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