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| [[Image:Unitcube.svg|thumb|300px|right|Unit cube]]
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| A '''unit cube''', more formally a '''cube of side 1''', is a [[cube]] whose sides are 1 unit long.<ref name="pcm">{{citation|contribution=High-dimensional geometry and its probabilistic analogues|first=Keith|last=Ball|title=[[The Princeton Companion to Mathematics]]|editor-first=Timothy|editor-last=Gowers|editor-link=Timothy Gowers|publisher=Princeton University Press|year=2010|isbn=9781400830398|pages=670–680}}. See in particular [http://books.google.com/books?id=ZOfUsvemJDMC&pg=PA671 p. 671].</ref><ref name="cbm">{{citation|contribution=Chapter 13: Hypercubes|first=Martin|last=Gardner|title=The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics|publisher=W. W. Norton & Company|year=2001|isbn=9780393020236|pages=162–174|url=http://books.google.com/books?id=orz0SDEakpYC&pg=PA162}}.</ref> The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.<ref>{{citation|title=Geometry: Reteaching Masters|publisher=Holt Rinehart & Winston|isbn=9780030543289|year=2001|page=74}}.</ref>
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| == Unit hypercube ==
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| The term ''unit cube'' or '''unit hypercube''' is also used for [[hypercube]]s, or "cubes" in ''n''-dimensional spaces, for values of ''n'' other than 3 and edge length 1.<ref name="pcm"/><ref name="cbm"/>
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| Sometimes the term "unit cube" refers in specific to the set [0, 1]<sup>''n''</sup> of all ''n''-tuples of numbers in the interval [0, 1].<ref name="pcm"/>
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| The length of the longest diagonal of a unit hypercube of ''n'' dimensions is <math>\sqrt n</math>, the square root of ''n'' and the (Euclidean) length of the vector ''(1,1,1,....1,1)'' in ''n''-dimensional space.<ref name="cbm"/>
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| == See also ==
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| *[[Robbins constant]], the average distance between two random points in a unit cube
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| *[[Tychonoff cube]], an infinite-dimensional analogue of the unit cube
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| *[[Unit square]]
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| *[[Unit sphere]]
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| ==References==
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| {{reflist}}
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| == External links ==
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| * {{mathworld | urlname = UnitCube | title = Unit cube}}
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| [[Category:Euclidean solid geometry]]
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| [[Category:One]]
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| [[Category:Cubes]]
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| {{Elementary-geometry-stub}}
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The name of the author is Jayson. He is an purchase clerk and it's something he truly appreciate. What me and my family adore is bungee leaping but I've been using on new things lately. Alaska is exactly where he's always been residing.
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