I am working with polytopes that are defined by half-planes in \Re^N. So they are defined by a number of inequalities (half plane representation), but can also be represented by the intersection points of these half planes (vertex representation). Computing the vertices is expensive, so I...
The upper limit comes from an observation that in the plane hexagonal spacing (each point has six equidistant neighbours) maximizes the distance between neighbours for a given density. You can read about it in this reference:
"Distance to Nearest Neighbour as a Measure of Spatial...