Groupe d’études et de recherche en analyse des décisions

G-2008-20

The Small Hexagon and Heptagon with Maximum Sum of Distances Between Vertices

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The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, and by using a branch and cut algorithm for nonconvex quadratic programming. Lower bounds on the value on this sum are presented for polygon with a larger number of vertices.

, 18 pages