Unit distances and diameters in Euclidean spaces
Swanepoel, K.
(2009).
Unit distances and diameters in Euclidean spaces.
Discrete and Computational Geometry,
41(1), 1-27.
https://doi.org/10.1007/s00454-008-9082-x
(2009).
Unit distances and diameters in Euclidean spaces.
Discrete and Computational Geometry,
41(1), 1-27.
https://doi.org/10.1007/s00454-008-9082-x
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 and all n sufficiently large depending on d.