Making Polygons by Simple Folds and One Straight Cut - Demaine, Erik D.; Demaine, Martin L.; Hawksley, Andrea; Ito, Hiro; Loh, Po-Ru; Manber, Shelly; Stephens, Omari (Computational Geometry, Graphs and Applications, 2011)
We give an efficient algorithmic characterization of simple polygons whose edges can be aligned onto a common line, with nothing else on that line, by a sequence of all-layers simple folds. In particular, such alignments enable the cutting out of the polygon and its complement with one complete straight cut. We also show that these makeable polygons include all convex polygons possessing a line of symmetry.