A sufficient condition for a polyhedron to be rigid

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing its dihedral angles only. We prove that for every flexible polyhedron some integer combination of its dihedral angles remains constant during the flex. The proof is based on a recent result of A. A. Gaifullin and L. S. Ignashchenko.

Original languageEnglish
Article number38
Number of pages11
JournalJournal of Geometry
Volume110
Issue number2
DOIs
Publication statusPublished - 1 Aug 2019

Keywords

  • Bricard octahedron
  • Dehn invariant
  • Dihedral angle
  • Flexible polyhedron
  • Hamel basis
  • BELLOWS CONJECTURE
  • FLEXIBLE POLYHEDRA
  • CROSS-POLYTOPES
  • VOLUME
  • INVARIANT

Fingerprint

Dive into the research topics of 'A sufficient condition for a polyhedron to be rigid'. Together they form a unique fingerprint.

Cite this