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When is a symmetric pin-jointed framework isostatic?

Research output: Contribution to journalJournal article

Published

  • Robert Connelly
  • Patrick Fowler
  • Simon Guest
  • Bernd Schulze
  • Walter Whiteley
Journal publication date02/2009
JournalInternational journal of solids and structures
Journal number3-4
Volume46
Number of pages12
Pages762-773
Original languageEnglish

Abstract

Maxwell’s rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.