Frameworks with forced symmetry II: orientation-preserving crystallographic groups

Authors: Justin Malestein and Louis Theran
Journal: Geometriae Dedicata, 1701219–262, 2014.
Full text: arXiv DOI

We give a combinatorial characterization of minimally rigid planar frameworks with orientation-preserving crystallographic symmetry, under the constraint of forced symmetry. The main theorems are proved by extending the methods of the first paper in this sequence from groups generated by a single rotation to groups generated by translations and rotations. The proof makes use of new families of matroids and submodular functions defined on crystallographic groups.