ABSTRACT
Origami tessellations are a broad field of folded structures with deep roots in origami, mathematics, and computational geometry. The term is usually understood to refer to a flat (or nearly so) folded shape in which some region of the plane is partitioned into a collection of sets by the pattern of the folded edges. Unlike conventional representational origami, in which the silhouette of the fold is paramount, what matters in origami tessellations is the pattern of the folded edges within the boundary of the folded shape. More often than not, the folded edges partition the plane into a mathematical tiling-and sometimes, those tiles include, or entirely comprise, regular polygons. In an early attempt to provide a mathematical description, Kawasaki and Yoshida [Kawasaki and Yoshida 88] defined “crystallographic flat origami” as a flat fold with certain crystallographic symmetries. Over time, the boundaries of the field have been extended to include figures with surface relief, 3D forms, and even curved creases, as well as patterns that are highly geometric but do not exhibit strict mathematical symmetry.
