A symmetry treatment of Danzerian rigidity for circle packing

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...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2008-12, Vol.464 (2100), p.3237-3254
Main Authors: Fowler, P.W, Guest, S.D, Tarnai, T
Format: Article
Language:English
Subjects:
Circle Packing
Circles
Degrees of freedom
Heuristics
Mathematics
Point groups
Rigidity
Scalars
Spherical caps
Stiffness
Symmetry
Vertices
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2008.0164