A configuration of a linkage Γ is a possible positioning of Γ in Rd , and the collection of all such forms the configuration space C(Γ) of Γ . We here introduce the notion of the symmetric configuration space of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.

Original languageAmerican English
Pages (from-to)527-569
Number of pages43
JournalJournal of Applied and Computational Topology
Issue number3
StatePublished - Sep 2023


  • Configuration space
  • Linkage
  • Planar polygon
  • symmetries

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Computational Mathematics
  • Applied Mathematics


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