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Uniqueness and Symmetry in Problems of Optimally Dense Packings

Lewis Bowen·Charles Holton·Charles Radin·Lorenzo Sadun
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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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Lewis Bowen, Charles Holton, Charles Radin, Lorenzo Sadun. 2018-07-09. Uniqueness and Symmetry in Problems of Optimally Dense Packings. https://arxiv.org/abs/math/0302056

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