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A
unit cube, sometimes called a
cube of side 1, is a
cubeIn 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
hypercubeIn 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 2
n 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.