Generic rigidity of frameworks with orientation-preserving crystallographic symmetry

Abstract

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear representation results that may be interesting in their own right. The same techniques immediately yield a Maxwell-Laman-type combinatorial characterization for frameworks embedded in 2-dimensional cones that arise as quotients of the plane by a finite order rotation.

70 pages, 9 figures

References in corpus (1)

• Generic combinatorial rigidity of periodic frameworks

Cited by in corpus (7)

• Generic combinatorial rigidity of periodic frameworks
• Infinitesimal Rigidity of Symmetric Frameworks
• Generic rigidity of reflection frameworks
• Frameworks with forced symmetry I: Reflections and rotations
• Matroids of Gain Graphs in Applied Discrete Geometry
• Henneberg constructions and covers of cone-Laman graphs
• Frameworks with forced symmetry II: Orientation-preserving crystallographic groups