Robust Tensegrity Polygons

János Geleji, T. Jordán

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A tensegrity polygon is a planar cable-strut tensegrity framework in which the cables form a convex polygon containing all vertices. The underlying edge-labeled graph T=(V;C,S), in which the cable edges form a Hamilton cycle, is an abstract tensegrity polygon. It is said to be robust if every convex realization of T as a tensegrity polygon has an equilibrium stress which is positive on the cables and negative on the struts, or equivalently, if every convex realization of T is infinitesimally rigid. We characterize the robust abstract tensegrity polygons on n vertices with n-2 struts, answering a question of Roth and Whiteley (Trans Am Math Soc 265:419-446, 1981) and solving an open problem of Connelly (Recent progress in rigidity theory, 2008).

Original languageEnglish
Pages (from-to)537-551
Number of pages15
JournalDiscrete & Computational Geometry
Volume50
Issue number3
DOIs
Publication statusPublished - Oct 2013

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Tensegrity
Polygon
Struts
Cables
Cable
Hamilton Cycle
Rigidity
Convex polygon
Open Problems
Graph in graph theory

Keywords

  • Rigid framework
  • Tensegrity framework
  • Tensegrity polygon

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

Cite this

Robust Tensegrity Polygons. / Geleji, János; Jordán, T.

In: Discrete & Computational Geometry, Vol. 50, No. 3, 10.2013, p. 537-551.

Research output: Contribution to journalArticle

Geleji, János ; Jordán, T. / Robust Tensegrity Polygons. In: Discrete & Computational Geometry. 2013 ; Vol. 50, No. 3. pp. 537-551.
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