J. Phys. I France
Volume 5, Numéro 12, December 1995
Page(s) 1539 - 1550
DOI: 10.1051/jp1:1995112
J. Phys. I France 5 (1995) 1539-1550

Dense Periodic Packings of Regular Polygons

Y. Limon Duparcmeur1, A. Gervois2 and J.P. Troadec1

1  Groupe Matière Condensée et Matériaux URA CNRS 804, Université de Rennes 1, 35042 Rennes Cedex, France
2  Service de Physique Théorique, Direction des Sciences de Matière CE Saclay, 91191 Gif-sur-Yvette Cedex, France

(Received 29 May 1995, received and accepted in final form 4 September 1995)

We show theoretically that it is possible to build dense periodic packings, with quasi 6- fold symmetry, from any kind of identical regular convex polygons. In all cases, each polygon is in contact with z=6 other ones. For an odd number of sides of the polygons, 4 contacts are side to side contacts and the 2 others are side to vertex contacts. For an even number of sides, the 6 contacts are side to side contacts. The packing fraction of the assemblies is of the order of 90%. The predicted patterns have also been obtained by numerical simulations of annealing of packings of convex polygons.

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