Frameworks with crystallographic symmetry
classification
🧮 math.MG
keywords
frameworksperiodicsymmetrycrystallographicaffinebar-and-jointboundsdeformation
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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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