Deformations of Period Lattices of Flexible Polyhedral Surfaces

Alexander A. Gaifullin, Sergey A. Gaifullin
2014 Discrete & Computational Geometry  
In the end of the 19th century Bricard discovered a 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 the 3-space two-periodic with respect to translations by two non-colinear vectors that can vary continuously during
more » ... he flexion. The main result is that the period lattice of a flexible two-periodic surface homeomorphic to a plane cannot have two degrees of freedom.
doi:10.1007/s00454-014-9575-8 fatcat:3rwcpgwg4zda5mvrvbdifsyvgm