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Origami folders often use the Japanese word kirigami to refer to designs which use cuts. In the detailed Japanese classification, origami is divided into stylized ceremonial origami (儀礼折り紙, girei origami) and recreational origami (遊戯折り紙, yūgi origami), and only recreational origami is generally recognized as origami.
Crease pattern for a swordsman. A crease pattern (commonly referred to as a CP) [1] is an origami diagram that consists of all or most of the creases in the final model, rendered into one image. This is useful for diagramming complex and super-complex models, where the model is often not simple enough to diagram efficiently.
The folding of two origami cranes linked together from the first known technical book on origami Hiden senbazuru orikata by Akisato Rito, published in Japan in 1798. The history of origami followed after the invention of paper and was a result of paper's use in society.
Crease pattern for a Miura fold. The parallelograms of this example have 84° and 96° angles. Animation of the folding and unfolding of a Miura-creased material. The Miura fold (ミウラ折り, Miura-ori) is a method of folding a flat surface such as a sheet of paper into a smaller area.
In the early 1980s, Professor Chatani began to experiment with cutting and folding paper to make unique and interesting pop-up cards. He used the techniques of origami (Japanese paper folding) and kirigami (Japanese papercutting), as well as his experience in architectural design, to create intricate patterns that played with light and shadow. [3]
The major question about such crease patterns is whether a given crease pattern can be folded to a flat model, and if so, how to fold them; this is an NP-complete problem. [32] Related problems when the creases are orthogonal are called map folding problems. There are three mathematical rules for producing flat-foldable origami crease patterns ...
Origami paper used for senbazuru is usually of a solid color, though patterned designs are available. Larger size origami paper, usually 6×6 inches, often has traditional Japanese or flower designs, reminiscent of kimono patterns.
For rigid origami (a type of folding that keeps the surface flat except at its folds, suitable for hinged panels of rigid material rather than flexible paper), the condition of Kawasaki's theorem turns out to be sufficient for a single-vertex crease pattern to move from an unfolded state to a flat-folded state.
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