Geometriae Dedicata

, Volume 22, Issue 3, pp 329–362 | Cite as

Rigidity and polarity

I: Statics of sheet structures
  • Walter Whiteley


Any projective polarity in 3-space transforms a statically (or equivalently, infinitesimally) rigid bar-and-joint framework into a statically rigid hinged sheetwork — a set of plane-statically rigid sheets, joined in pairs along hinge lines. In the more general class of jointed sheetworks, which is closed under polarity, static rigidity is also preserved by the polarities. In particular, the class of infinitesimally (or statically) rigid polyhedra, built with joints at the vertices and bars triangulating the faces, is closed under polarity.


General Class Hinge Line Static Rigidity Projective Polarity Rigid Sheet 
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Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Walter Whiteley
    • 1
  1. 1.Department of MathematicsChamplain Regional CollegeQuebecCanada

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