# Unit cube

Unit cube

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 ${\displaystyle {\sqrt {n}}}$, the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space.[2]