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

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Abstract

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.

Original languageEnglish
Pages (from-to)355-368
Number of pages14
JournalBeitrage zur Algebra und Geometrie
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

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

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