Flexible Polyhedron

Flexible Polyhedron

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The mathematician Leonard Euler once wrote,"A closed spatial figure allows no changes, as long as it is not ripped apart." Proving the "rigidity" of polyhedra was another matter. In 1813, Augustin-Louis Cauchy showed that a convex polyhedral surface is rigid if its flat polygonal faces are held rigid. In 1974, Herman Gluck proved that almost all triangulated spherical surfaces were rigid. However, in 1977 Robert Connelly of Cornell University found a counterexample, that is to say a flexible polyhedron. He built this model of such a surface some years later. It is made of cardboard and held together with duct tape. Two cutout plastic windows allow the viewer to observe changes when the polyhedron is flexed. The top section has 12 large faces and a six-faced appendage. The bottom section has 12 corresponding faces but no appendage.
Currently not on view
Object Name
geometric model
date made
Connelly, Robert
Place Made
United States: New York, Ithaca
Physical Description
plastic (overall material)
paper (overall material)
overall: 14 cm x 47 cm x 25.5 cm; 5 1/2 in x 18 1/2 in x 10 1/16 in
ID Number
accession number
catalog number
Credit Line
Prof. Robert Connelly
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History
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