G-2008-20
The Small Hexagon and Heptagon with Maximum Sum of Distances Between Vertices
Charles Audet, Anthony Guillou, Pierre Hansen, Frédéric Messine et Sylvain Perron
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.
Paru en mars 2008 , 18 pages