Generic rigidity of frameworks with orientation-preserving crystallographic symmetry (results appeared as part of "Frameworks with forced symmetry II", 2013)
Justin Malestein, Louis Theran – 2011
Focus Area 1: High-complexity Geometry 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.