Equilateral Dimension

(Dimension Theory)

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Dimension Theory
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What is Equilateral dimension?

In mathematics, the equilateral dimension of a metric space is the maximum number of points that are all at equal distances from each other. Equilateral dimension has also been called "metric dimension", but the term "metric dimension" also has many other inequivalent usages. The equilateral dimension of a d-dimensional Euclidean space is d + 1, and the equilateral dimension of a d-dimensional vector space with the Chebyshev distance (L∞ norm) is 2d. However, the equilateral dimension of a space with the Manhattan distance (L1 norm) is not known; Kusner's conjecture, named after , states that it is exactly 2d.

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dimension theorymetric geometry

Synonyms

Kusner's conjecture

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