Unit cube

[1][2] The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.

[3] 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.