English

Frameworks with crystallographic symmetry

Metric Geometry 2011-10-24 v1

Abstract

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in RdR^d. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometric setting for diaplacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.

Keywords

Cite

@article{arxiv.1110.4662,
  title  = {Frameworks with crystallographic symmetry},
  author = {Ciprian S. Borcea and Ileana Streinu},
  journal= {arXiv preprint arXiv:1110.4662},
  year   = {2011}
}
R2 v1 2026-06-21T19:23:32.657Z