ABSTRACT
The smallest flat-foldable vertex is the degree-2 vertex, a vertex that has several creases emanating from it. There are very many origami crease patterns that are composed exclusively of degree-4 vertices. Within a crease pattern, crease lines come together at points called vertices, and it is there that the conditions of flat-foldability begin to apply. In representational folding, the crease pattern is rarely a map of all of the folds in the design; it is a selected subset, chosen by the artist to convey the important properties of the structure and/or internal symmetries. Dashed lines and chain lines stand out when there are only a few of them, but for complex crease patterns, which arise in both figurate and geometric origami, they dissolve into a visual morass of indistinguishable strokes. For crease patterns, which can contain hundreds of folds, we need to adopt drawing conventions that provide a much stronger visual distinction between mountain and valley lines.
