Philosophical Transactions A: Mathematical, Physical and Engineering Sciences
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in Rd. 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.
Borcea, Ciprian and Streinu, Ileana, "Frameworks With Crystallographic Symmetry" (2013). Computer Science: Faculty Publications, Smith College, Northampton, MA.