On equilateral simplices in normed spaces

Peter Braß
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin, Germany
email: brass@inf.fu-berlin.de

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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