title: Frameworks with crystallographic symmetry.
abstract: Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in Euclidean spaces of arbitrary dimension. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometrical setting for displacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.
authors.affiliation: Department of Mathematics, Rider University, , Lawrenceville, NJ 08648, USA.
authors.forename: Ciprian S
authors.initials: CS
authors.lastname: Borcea
authors.forename: Ileana
authors.initials: I
authors.lastname: Streinu
keywords: crystallographic group; deformation; periodic frameworks; periodic sphere packings