Frameworks with forced symmetry II: Orientation-preserving crystallographic groups
Abstract
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 proofs make use of a new family of matroids defined on crystallographic groups and associated submodular functions.
Cite
@article{arxiv.1304.0756,
title = {Frameworks with forced symmetry II: Orientation-preserving crystallographic groups},
author = {Justin Malestein and Louis Theran},
journal= {arXiv preprint arXiv:1304.0756},
year = {2013}
}
Comments
46 pages, 4 figures. All the results in this paper have appeared previously in our other paper available at arXiv:1108.2518. This paper is a continuation of our paper "Frameworks with forced symmetry I: Reflections and rotations" arXiv:1304.0398. Minor changes to the exposition in v2. To appear in Geometriae Dedicata