Home > Research > Publications & Outputs > Frameworks symmetry and rigidity

Electronic data

  • FSRarxiv2

    Accepted author manuscript, 259 KB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License


Text available via DOI:

View graph of relations

Frameworks symmetry and rigidity

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>12/2010
<mark>Journal</mark>International Journal of Computational Geometry and Applications
Issue number6
Number of pages28
Pages (from-to)723-750
Publication StatusPublished
<mark>Original language</mark>English


Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in ℝd. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.

Bibliographic note

The paper was published in December 2010. (No record of acceptance date.)