Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex

  • Victor AlexandrovEmail author
Original Paper


We derive fundamentally new equations that are satisfied by first-order flexes of a flexible polyhedron. Moreover, we indicate two sources of such new equations. These sources are the Dehn invariants and rigidity matrix. The equations derived provide us with fundamentally new necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex.


Euclidean 3-space Flexible polyhedron Infinitesimal bending Dehn invatiant Rigidity matrix 

Mathematics Subject Classification




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© The Managing Editors 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Department of PhysicsNovosibirsk State UniversityNovosibirskRussia

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