A symmetry treatment of Danzerian rigidity for circle packing-Reference-Cited by-同舟云学术

A symmetry treatment of Danzerian rigidity for circle packing

Published:2008-08-19 Issue:2100 Volume:464 Page:3237-3254
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Fowler P.W¹,Guest S.D²,Tarnai T³

Affiliation:

1. Department of Chemistry, University of SheffieldSheffield S3 7HF, UK

2. Department of Engineering, University of CambridgeTrumpington Street, Cambridge CB2 1PZ, UK

3. Department of Structural Mechanics, Budapest University of Technology and EconomicsMuegyetem rakpart 3, Budapest 1521, Hungary

Abstract

A symmetry-extended mobility criterion that incorporates Danzer's concept of bar-and-joint assemblies is derived and applied to the spherical circle-packing problem. The known scalar counting rule for Danzerian freedoms is strengthened in an equation that predicts not only the number, but also the symmetries, of distortion modes that may be used to improve a packing. Relationships between alternative candidates for best packing are consequences of the co-kernel structure of the representation spanned by Danzerian mechanisms, and in several cases lead to new local optima.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2008.0164

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