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… 
View on Springer
link.springer.com
4 Citations
Highly Influential Citations
1
Background Citations
1
Methods Citations
1
Results Citations
1

4 Citations

Workshop ( hybrid meeting ) : Discrete Geometry Table of Contents

A number of important recent developments in various branches of discrete geometry were presented at the workshop, which took place in hybrid format due to a pandemic situation. The presentations…

A2 信頼度成長法を用いたロケットの成功率向上に関する研究(宇宙輸送・飛翔体)

The Alban Elved Dance Company and the computer science department will be collaborating to present the multimedia performance “Fibonacci and Phi” in the MainStage Theatre of the Scales Fine Art Center.

Domes over Curves

A closed PL-curve is called integral if it is comprised of unit intervals. Kenyon's problem asks whether for every integral curve $\gamma$ in $\mathbb{R}^3$, there is a dome over $\gamma$, i.e.…

Mathematisches Forschungsinstitut Oberwolfach Report No . 30 / 2020 DOI : 10 . 4171 / OWR / 2020 / 30 Discrete Geometry Organized

A number of important recent developments in various branches of discrete geometry were presented at the workshop, which took place in hybrid format due to a pandemic situation. The presentations…

References

SHOWING 1-10 OF 20 REFERENCES

Sabitov polynomials for volumes of polyhedra in four dimensions

A Flexible Planar Tessellation with a Flexion Tiling a Cylinder of Revolution

Due to A. Kokotsakis a quad mesh consisting of congruent convex quadrangles of a planar tessellation is flexible. This means, when the flat quadrangles are seen as rigid bodies and only the dihedral…

The Volume as a Metric Invariant of Polyhedra

A proof of the ``bellows conjecture'' affirming the invariance of the volume of a flexible polyhedron in the process of its flexion.

Periodic frameworks and flexibility

We formulate a concise deformation theory for periodic bar-and-joint frameworks in Rd and illustrate our algebraic–geometric approach on frameworks related to various crystalline structures.…

The Bellows conjecture.

Cauchy’s rigidity theorem states: If P and P’ are combinatorially equivalent convex polyhedra such that the corresponding facets of P and P’ are congruent, then P and P’ are congruent polyhedra. For…

Finite motions from periodic frameworks with added symmetry

Generic combinatorial rigidity of periodic frameworks

Generalization of Sabitov’s Theorem to Polyhedra of Arbitrary Dimensions

The Bellows Conjecture claims that the volume of any flexible polyhedron is constant, and it is shown that this is true not only for simplicial polyhedra, but for allpolyhedra with triangular $$2$$2-faces.

Volume of a polyhedron as a function of its metric

  • Fundam. Appl. Math. 2(4), 1235– 1246
  • 1996

Sabitov, Volume of a polyhedron as a function of its metric

  • Fundamental and Applied Math
  • 1996