Interviewer: Professor Tachi, you are both an origami designer and engineer. When was your first experience with origami?
Tachi: I think I was probably four or five years old when I folded my first origami cranes and other such figures. As a child I was fond of folding origami while following the instructions in books, but once I became a college student I started to make my own origami designs. The result of perceiving origami in mathematical terms was the three-dimensional origami design system that I call the “Origamizer.” If you compute the geometry and algorithms of origami, it is possible to solve the folding from a given shape. If you input a shape that you desire, the system outputs the crease pattern that folds the paper to the desired shape.
Interviewer: So you can create a rabbit, a teapot or even a crumpled piece of paper?
Tachi: There have been similar trials in the past, but these left gaps in the resulting paper surface or failed to achieve a concave or saddle surface. I have been able to overcome these problems by adding folded tuck-like structures between each facet. For example, the rabbit (*1) appears to be composed of triangle panels on the surface, but in fact there are many folded tucks hidden in the interior. The ultimate challenge for origami design is whether it is possible to fold any kind of shape from a single sheet of paper, and I believe that I have provided one answer to this challenge.
*1 A triangular mesh model (left) is transformed into a two-dimensional crease pattern by the “Origamizer” (center). The picture on the right shows the results of ten hours of determined folding on the crease pattern!
Interviewer: I hear that you have engaged in joint research with Professor Koryo Miura, the astrophysicist known for the “Miura fold.”
*2 Rigid-foldable cylinders and cells made by origami. Force applied to one point is spread out evenly across the entire structure, thus allowing it to expand or collapse.
Tachi: In 2006 I attended the Fourth International Conference on Origami in Science, Mathematics and Education (4OSME), where I gave a presentation on origami simulation software. I used the Miura fold for my demonstration and, auspiciously, Professor Miura himself just happened to be at the conference. Yes, the person who had thought of the exciting folding method featured in the book I used to look at as a child was there in the room. When I found this out, it was a source of great encouragement for me. After that we engaged in joint research, and in 2013 we published our design of “rigid-foldable cylinders and cells” (the Tachi-Miura polyhedron (*2)). This design is for a cylindrical structure that can be folded away and is a design that combines the Miura Fold with my folding method. Professor Miura devised the Miura fold in 1970 when he was at the Institute of Space and Aeronautical Science of the University of Tokyo, researching methods to develop structures in space. The Miura fold consists of a tessellation of parallelograms in a regular pattern. As paper folded using the Miura fold can be opened out and folded in with one touch, this fold is now often used in portable maps.
Interviewer: Speaking of practical applications of origami, don’t coffee and alcoholic beverage cans (*3) that feature diamond patterns belong in that category, too?
*3 A can of Kirin Hyoketsu chuhai alcohol that uses the diamond-cut can developed by Toyo Seikan Co., Ltd. One of its characteristics is that when the can is opened, the pattern becomes visible.
Tachi: That diamond pattern is known as the Yoshimura Pattern. The pattern appeared in a paper written in 1951 by Professor Yoshimaru Yoshimura of the Aeronautical Research Institute of the University of Tokyo, who was researching the buckling phenomenon that occurs when airplane fuselages break apart. When you crush a thin cylinder from the top in a vertical direction, diamond-shaped creases appear in succession on its sides and the stiffness against compression increases simultaneously. Professor Miura used this pattern as his inspiration to create the Miura fold. Usually, research involving structures is concerned with making them unbreakable. Both Professor Yoshimura and Professor Miura, however, focused on the phenomenon observed when a structure breaks, through which they made interesting discoveries to be applied to different purposes.
Interviewer: Are you using your origami techniques in architecture, utilizing thin pieces of paper to create buildings?
*4 An origami piece that acts as a foldable architectural structure. This exhibit was displayed by Professor Tachi at the “Form of Computational Origami” Exhibition at the Komaba Museum in 2013.
Tachi: If you apply the theories of origami, it is possible to create a structure that can be folded up and carried (*4). Such structures would be versatile in that their shape could be changed according to need?made smaller to accommodate only a few people, and expanded out when there are more people. When using origami on a large scale such as at the architectural level, you need to use thick and rigid panels and hinged folds. However, without proper consideration of the geometry, repeatedly folding up and expanding out such structures creates stress on the materials, eventually causing them to collapse. By calculating a pattern using a theory known as rigid origami, it is possible to create an architectural structure out of origami that can be repeatedly folded up and opened out.
This technology is not limited to architecture. In fact, the applications for origami are truly wide-ranging. They include foldable furniture such as chairs, solar panels and solar sails for deployment in space, medical devices that open up in blood vessels to prevent ruptured aneurysms (origami stent-grafts), and packaging including cardboard. Modern origami features across diverse areas of specialization, including mathematics, information science, materials science, structural engineering, design, fine arts and education.
I like both aspects of origami, the theories behind it and also actually folding materials by hand to create origami. It is a process of repetition: thinking about the theory, then folding, then thinking once again before making another fold. By continuing to use both my head and my hands, I want to continue to probe the world of computational origami and all its various possibilities.
Assistant Professor, Department of General Systems Studies, Graduate School of Arts and Sciences