Frameworks with forced symmetry I: reflections and rotations

Authors: Justin Malestein and Louis Theran
Journal: Discrete & Computational Geometry, 2015.
Full text: arXiv DOI

We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a new technique for deriving linear representations of sparsity matroids on colored graphs and extend the direction network method of proving rigidity characterizations to handle reflections.