Uniqueness and symmetry in problems of optimally dense packings

• Autores: Charles Holton, Lewis Bowen, Lorenzo Sadun, Charles Radin
• Localización: Mathematical Physics Electronic Journal, ISSN-e 1086-6655, Vol. 11, Vol. 1, 2005
• Idioma: inglés
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• Resumen

  • Part of Hilbert's eighteenth problem is to classify the symmetries of the densest packings of bodies in Euclidean and hyperbolic spaces, for instance the densest packings of balls or simplices. We prove that when such a packing problem has a unique solution up to congruence then the solution must have cocompact symmetry group, and we prove that the densest packing of unit disks in the Euclidean plane is unique up to congruence. We also analyze some densest packings of polygons in the hyperbolic plane.