Unlocking Puzzling Polygons

Proof settles a wickedly prickly question about unfurling crinkly polygons

Polygons come in all sorts of shapes: triangles, squares, hexagons, stars, and a host of other straight-edged forms.

Pulling apart this jaw-shaped polygon (blue) without allowing any segments to cross proved to be a tough exercise in computational geometry. Illustrations courtesy Demaine

Segment lengths determine whether it’s possible to unfurl this eight-petal tree configuration without allowing segments to cross.