Deformations of Period Lattices of Flexible Polyhedral Surfaces

@article{Gaifullin2013DeformationsOP,
  title={Deformations of Period Lattices of Flexible Polyhedral Surfaces},
  author={Alexander A. Gaifullin and Sergey A. Gaifullin},
  journal={Discrete \& Computational Geometry},
  year={2013},
  volume={51},
  pages={650-665}
}
At the end of the 19th century Bricard discovered the phenomenon of flexible polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit non-trivial flexes. One of the most important results in this field is a theorem of Sabitov, asserting that the volume of a flexible polyhedron is constant during the flexion. In this paper we study flexible polyhedral surfaces in $\mathbb {R}^{3}$, doubly periodic with respect to translations by two non-collinear vectors, that can vary… 

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