Frameworks with crystallographic symmetry

Details Frameworks with crystallographic symmetry Frameworks with crystallographic symmetry

2011-10-20

arxiv.org/abs/1110.4662v1

Mathematics

Metric Geometry

Scientific paper

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometric setting for diaplacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.

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