MPEJ Volume 11, No. 1, 34 pp.
Received: Jul 13, 2004. Revised: Feb 22, 2005. Accepted:  Mar 3, 2005.

L. Bowen, C. Holton, C. Radin, L. Sadun
Uniqueness and symmetry in problems of optimally dense packings

ABSTRACT:  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.


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http://www.ma.utexas.edu/mpej/Vol/11/1.ps
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