Document Type

Article

Publication Date

6-2015

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 rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing 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.

Keywords

Maxwell’s theorem, periodic framework, periodic stress, liftings, periodic pseudo-triangulation, expansive motion, auxetics, ultrarigidity

Volume

53

Issue

4

First Page

747

Last Page

782

DOI

10.1007/s00454-015-9689-7

ISSN

1432-0444

Comments

Author's pre-print. A second version of the paper, as presented at the Symposium on Computational Geometry (SoCG'14), Kyoto, Japan, 2014, is also included.

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