Flexing Surfaces

  • Robert Connelly


Suppose a closed polyhedral surface is built from flat pieces of stiff cardboard taped together along their edges. Will the surface flex? That is; will it change its shape continuously without ripping the tape or bending the cardboard? As an example, let us consider the octahedron shown in Figure 1. If one builds this out of cardboard it turns out to be very rigid and does not flex. However, if the top is slightly smaller than the bottom, the top will pop down as shown in Figure 2. To do this, one must bend the cardboard. Figure 1 will not continuously move into Figure 2 without distortion.


Polyhedral Surface Flexible Surface Flat Piece Dimensional Polyhedron Octahedral Framework 


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Copyright information

© Wadsworth International 1981

Authors and Affiliations

  • Robert Connelly
    • 1
  1. 1.Cornell UniversityUSA

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