- 03-36 Lewis Bowen, Charles Holton, Charles Radin and Lorenzo Sadun
- UNIQUENESS AND SYMMETRY IN PROBLEMS OF OPTIMALLY DENSE PACKINGS
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Feb 5, 03
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Abstract. We analyze the general problem of determining optimally dense
packings, in a Euclidean or hyperbolic space, of congruent copies of
some fixed finite set of bodies. We are strongly guided by examples of
aperiodic tilings in Euclidean space and a detailed analysis of a new
family of examples in the hyperbolic plane. Our goal is to understand
qualitative features of such optimum density problems, in particular
the appropriate meaning of the uniqueness of solutions, and the role
of symmetry in classfying optimally dense packings.
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