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Unit cube

Cube with edge length one

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated October 3, 2024
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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.

01Unit 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 {\sqrt {n}}, the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space.

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This article is adapted from the Wikipedia article “Unit cube”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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