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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2011
- DOI:
- 10.48550/arXiv.1108.2518
- arXiv:
- arXiv:1108.2518
- Bibcode:
- 2011arXiv1108.2518M
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Combinatorics;
- 52C25;
- 52B40
- E-Print:
- 70 pages, 9 figures