par Akiyama, Jin;Demaine, Erik D. ;Langerman, Stefan
Référence Graphs and combinatorics
Publication Publié, 2019-02-01
Article révisé par les pairs
Résumé : We prove that two polygons A and B have a reversible hinged dissection (a chain hinged dissection that reverses inside and outside boundaries when folding between A and B) if and only if A and B are two noncrossing nets of a common polyhedron. Furthermore, monotone reversible hinged dissections (where all hinges rotate in the same direction when changing from A to B) correspond exactly to noncrossing nets of a common convex polyhedron. By envelope/parcel magic, it becomes easy to design many hinged dissections.