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== Helly dimension ==
If a family of sets is a Helly family of order ''k'', that family is said to have '''Helly number''' ''k''. The '''Helly dimension''' of a [[metric space]] is one less than the Helly number of the family of metric balls in that space; Helly's theorem implies that the Helly dimension of a Euclidean space equals its dimension as a real [[vector space]].
The '''Helly dimension''' of a subset S of a Euclidean space, such as a polyhedron, is one less than the Helly number of the family of [[Translation (geometry)|translates]] of S. For instance, the Helly dimension of any [[hypercube]] is 1, even though such a shape may belong to a Euclidean space of much higher dimension.
Helly dimension has also been applied to other mathematical objects; for instance M. Domokos ({{arxiv|archive=math.AG|id=0511300}}) defines the Helly dimension of a group to be one less than the Helly number of the family of left cosets of the group.
== The Helly property ==
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