Realizations of Isostatic Material Frameworks

Mahdi Sadjadi, Varda F. Hagh, Mingyu Kang, Meera Sitharam, Robert Connelly, Steven J. Gortler, Louis Theran, Miranda Holmes-Cerfon, Michael F. Thorpe

Research output: Contribution to journalArticlepeer-review


This article studies the set of equivalent realizations of isostatic frameworks and algorithms for finding all such realizations. It is shown that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. The complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions is enumerated and the impact of boundary length on the emergence of these realizations is studied. To ameliorate the computational complexity of finding a solution to a large multivariate quadratic system corresponding to the constraints, alternative methods—based on constraint reduction and distance-based covering map or Cayley parameterization of the search space—are presented. The application of these methods is studied on atomic clusters, a model of 2D glasses and jamming.

Original languageEnglish (US)
Article number2000555
JournalPhysica Status Solidi (B) Basic Research
Issue number9
StatePublished - Sep 2021


  • glasses
  • isostatic
  • jamming
  • networks
  • tunneling

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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