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Polyhedra Can Bend But Not Breathe

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Science  13 Mar 1998:
Vol. 279, Issue 5357, pp. 1637
DOI: 10.1126/science.279.5357.1637

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Mathematicians showed 20 years ago that a closed, three-dimensional figure made of rigid triangles could be squeezed or stretched into a new shape without distorting the faces, upsetting the belief that a structure whose surfaces are made of triangles must be rigid. But a new proof shows that such flexible polyhedra still face constraints: Their volume remains constant as they move.