Report B 97-12
November 1997
It is the aim of this note to improve the lower bound for the problem of Petty on the existence of equilateral simplices in normed spaces. We show that for each k there is a d (k) such that each normed space of dimension d >= d (k) contains k points at pairwise distance one, and that if the norm is not sufficiently near to the euclidean norm, the maximal equilateral sets behave like their euclidean counterparts.
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