MATHEMATICS:
Polyhedra Can Bend But Not Breathe
Dana Mackenzie
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.