- Source: Unit cube
A unit cube, more formally a cube of side 1, is a cube 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 for hypercubes, or "cubes" in n-dimensional spaces, for values of n other than 3 and edge length 1.
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
n
{\displaystyle {\sqrt {n}}}
, the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space.
See also
Doubling the cube
k-cell
Robbins constant, the average distance between two random points in a unit cube
Tychonoff cube, an infinite-dimensional analogue of the unit cube
Unit square
Unit sphere
References
External links
Weisstein, Eric W. "Unit cube". MathWorld.
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