• DOI:10.1007/s00454-014-9575-8
• Corpus ID: 15253022

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}
}

• A. Gaifullin, S. Gaifullin
• Published 2 June 2013
• Mathematics
• Discrete & Computational Geometry

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 continuously during the flexion. The main result is that the period lattice of a flexible doubly periodic surface that is homeomorphic to the plane cannot have two degrees of freedom.