title: Liftings and stresses for planar periodic frameworks.
abstract: We formulate and prove a periodic analog of Maxwell's theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing features known for their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks.
authors.affiliation: Department of Mathematics, Rider University, Lawrenceville, NJ 08648, USA.
authors.forename: Ciprian
authors.initials: C
authors.lastname: Borcea
authors.affiliation: Department of Computer Science, Smith College, Northampton, MA 01063, USA.
authors.forename: Ileana
authors.initials: I
authors.lastname: Streinu
keywords: Maxwell’s theorem; auxetics; expansive motion; liftings; periodic framework; periodic pseudo-triangulation; periodic stress; ultrarigidity