%0 Journal Article
%T Deformations of period lattices of flexible polyhedral surfaces
%A Alexander A. Gaifullin
%A Sergey A. Gaifullin
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s00454-014-9575-8
%X 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 the 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.
%U http://arxiv.org/abs/1306.0240v1