LAUSR

The maximum separation problem is to find the maximum of the minimum pairwise distance of n points in a planar body $${\mathcal {B}}$$ B on the Euclidean plane. In this paper this problem will be considered if $${\mathcal {B}}$$ B is the equilateral triangle of side length 1 and the number of points is 13. We will present the exact separation distance of 13 points in the equilateral triangle of side length 1 and we will prove a conjecture of Melissen from 1993 and a conjecture of Graham and Lubachevsky from 1995.