Uniqueness and Symmetry in Problems of Optimally Dense Packings
Metric Geometry
2018-07-11 v2 Dynamical Systems
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.
Cite
@article{arxiv.math/0302056,
title = {Uniqueness and Symmetry in Problems of Optimally Dense Packings},
author = {Lewis Bowen and Charles Holton and Charles Radin and Lorenzo Sadun},
journal= {arXiv preprint arXiv:math/0302056},
year = {2018}
}
Comments
Updated 2018 to version published in 2005. Plain TeX, 27 pages of text followed by 11 figures