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A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.cite-ref-pcm-1-0[1]cite-ref-cbm-2-0[2] The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.cite-ref-3[3]

• Unit hypercube

• See also

• References

• External links

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.cite-ref-pcm-1-1[1]cite-ref-cbm-2-1[2]

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].cite-ref-pcm-1-2[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.cite-ref-cbm-2-2[2]

• 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

cite-note-pcm-11. ↑ citerefball2010Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy (ed.), The Princeton Companion to Mathematics, Princeton University Press, pp. 670–680, ISBN 9781400830398. See in particular p. 671.

cite-note-cbm-22. ↑ citerefgardner2001Gardner, Martin (2001), "Chapter 13: Hypercubes", 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, W. W. Norton & Company, pp. 162–174, ISBN 9780393020236.

cite-note-33. ↑ Geometry: Reteaching Masters, Holt Rinehart & Winston, 2001, p. 74, ISBN 9780030543289.

• reference-mathworld-unit-cubeciterefweissteinWeisstein, Eric W. "Unit cube". MathWorld.