Folding Polygons into Polytopes
Erik Demaine, Martin Demaine, Anna Lubiw, and Joseph O'Rourke
The basic problem we have been studying is in what ways a polygonal piece of
paper can have its boundary glued to itself and then be folded to form a convex
polyhedron. This line of research was initiated in the paper
``When Does a
Polygon Fold to a Polytope?'' by Anna Lubiw and Joseph O'Rourke.
The problem is also intrinsically related to Aleksandrov's theorem,
which gives a simple characterization of what gluings lead to convex polyhedra,
and says that a gluing can lead to only one convex polyhedron.
For more information on our work, see
More information to come soon.