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arXiv · 1306.0240

Deformations of period lattices of flexible polyhedral surfaces

Alexander A. Gaifullin·Sergey A. Gaifullin
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Abstract

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.

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Alexander A. Gaifullin, Sergey A. Gaifullin. 2013-06-02. Deformations of period lattices of flexible polyhedral surfaces. https://doi.org/10.1007/s00454-014-9575-8

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