Unit distances and diameters in Euclidean spaces
Metric Geometry
2009-03-12 v1 Combinatorics
Abstract
We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d >= 4 and n sufficiently large, depending on d. As a corollary we determine the exact maximum number of unit distances for all even d >= 6, and the exact maximum number of diameters for all d >= 4, for all sufficiently large, depending on d.
Cite
@article{arxiv.0707.0213,
title = {Unit distances and diameters in Euclidean spaces},
author = {Konrad J Swanepoel},
journal= {arXiv preprint arXiv:0707.0213},
year = {2009}
}