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 , the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space.
- 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
- Ball, Keith (2010), "High-dimensional geometry and its probabilistic analogues", in Gowers, Timothy, The Princeton Companion to Mathematics, Princeton University Press, pp. 670–680, ISBN 9781400830398. See in particular p. 671.
- Gardner, 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.
- Geometry: Reteaching Masters, Holt Rinehart & Winston, 2001, p. 74, ISBN 9780030543289.
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