Minimal diameter of certain sets in the plane (Q1279661)

The authors deal with the following question. Of all sets of \(n\) points in the plane such that the mutual distances are at least 1 what set has the minimum diameter \(D(n)\)? The following theorem answers the question for \(n=8\): The minimal diameter \(D(8)\) is \((2\sin(\pi/14))^{-1} = 2.246\dots.\) The minimal diameter is attained only if the convex hull of the points is a regular heptagon of sidelength 1.