When is a symmetric pin-jointed framework isostatic?

Details When is a symmetric pin-jointed framework isostatic? When is a symmetric pin-jointed framework isostatic?

2008-03-15

arxiv.org/abs/0803.2325v2

Mathematics

Metric Geometry

24 pages, 10 figures; added references, minor changes, revised last paragraph

Scientific paper

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.

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