Unit cube
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A unit cube is a cube all of 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.
[edit] Unit Hypercube
The term unit cube or unit hypercube is also used to refer to hypercubes, or "cubes" in n-dimensional spaces, for other values of n than 3. Very often it means the specific unit cube which is the set [0, 1]n of all n-tuples of numbers in the interval [0, 1]. A Hypercube - when related to a square - has a minimum value of three sides.
The length of the longest diagonal of a unit hypercube of n dimensions is the square root of n.
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