Volume 25 (2017) Pages 601-609
Isometries always exists to fold a paper to match a non-expansive folding of its boundary. However, there is little known about designing crease patterns that satisfy multiple constraints at the same time. In this paper, we analyze crease patterns that can fold to multiple prescribed folded boundaries, as well as flat-foldable states, such that every crease in the crease pattern is finitely folded in each folding. Additionally, we show how to layout simpler units in a grid to approximate triangulated surfaces.