A unit cube, sometimes called a cube of side 1, is a cube

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

 whose sides are 1 unit long. 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 to refer to hypercube

Hypercube

In geometry, a hypercube is an n-dimensional analogue of a square and a cube . It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.An...

s, or "cubes" in n-dimensional spaces, for values of n other than 3. In all dimensions, the unit cube has 2ⁿ corners.

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]. The length of the longest diagonal of a unit hypercube of n dimensions is the square root of n.