Origami Folding and its Potental for Architecture Students

Words by Naglaa A. Megahed Publication by Joseline Ali

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Origami is the art of paper folding that originated in Japan and is commonly practised worldwide. It has received attention in science and engineering, getting credit for many innovative designs and applications (Cheung et al. 2014; Fei and Sujan 2013). Over the years, many artists and scientists have been intrigued by origami and have attempted to investigate and reveal its underlying principles.

The goal of this art is to create a representation of an object using geometric folds and crease patterns on a single piece of paper, preferably without gluing or cutting the paper.

The geometric and topological properties of origami folding have challenged several mathematicians, who have formulated folding principles and theorems.

Engineers have also been drawn to learn about this ancient art, in order to incorporate it into their designs. The origami technique has been utilized in many folding applications (Fei and Sujan 2013; Liapi 2002). These applications have led to the transition of origami f rom a form of art to a mathematical and engineering topic. Origami has proved to be useful in areas such as structural and architectural design. This folding strategy has been explored as a method to

generate spatial and structural concepts in architecture by applying complex geometry. Thus, both origami and architecture have become more sophisticated disciplines over the years. In the practice of architecture, it is not surprising to see the impact of origami as a medium to generate different architectural forms (Hemmerling 2010; Sorguรง, Hagiwara, and Selรงuk 2009). In this regard, when studying the inspiration behind an architectural design, one can take advantage of the recent developments in origami folding.

Japanese origamists, as well as mathematicians and artists, have been credited with helping to popularize the art in the twentieth century by developing a set of instructions based on pictures that serve as a universal language, thus fostering collaboration between artists and scientists (Lang 2007). Based on this collaboration, a source of inspiration for conceptual design is origami art through the understanding of origami science, which of fers a vast amount of opportunities for morphing architecture (Buri and Weinand 2008; Matsubara and Celani 2007; Osรณrio, Paio, and Oliveira 2014).

Against this background, this article describes a possible way to explore folding architecture based on the rules of origami.

This form of architecture aims to take advantage of the elastic capacities given to planar surfaces by folding them. On folding, the surfaces can assume different forms that create a range of spatial configurations. Based on these potentials, origami thinking is now used in a wide variety of applications. But what does paper folding have to do

with these applications? In this context, the following research questions on origami folding need to be discussed: • What is the science guiding the processes of origami art?

• What are the folding rules and techniques used to create origami structures?

• What kind of architectural applications are inspired by origami folding?

• What is the role of origami within the processes of architectural design?

• What potential does origami hold for architecture students?

In the following section, brief reference is made to the origin and development of origami.

This is followed by a review of the geometric features, topological properties, and structural capabilities of paper folding.

Later, some interesting architectural applications inspired by origami are discussed. Finally, based on undertaking a data collection exercise with architecture students, the potentials of origami in architectural education are presented.

Traditionally, the term origami refers primarily to the ancient art of paper folding that originated in China and was developed in Japan, in which paper is folded to create abstract or detailed sculptures of objects or ideas.

Thus, origami is a creative method of folding paper to develop beautiful shapes and forms.

In the mid-1990s, it evolved into a modern art form and became a trend in contemporary architecture, f rom which many architects took inspiration (Gilewski, Pełczyński, and Stawarz 2014; Lang 2007; Peraza-Hernandez et al. 2014).

Origami spread all over the world as people travelled internationally. The development of instructions made origami accessible to the west as a new creative tool. The traditional style of origami has been developed as a consequence of such a cultural exchange (Tantawy 2015). In this context, modern origami that started in the twentieth century is based on a completely different paradigm. One of the most influential origami artists and the-

orists, the American physicist Robert Lang, has not only contributed many publications on folding strategies but has also made great advances in applying origami to real-world engineering problems (Hemmerling 2010).

With these developments, origami has become an inspiration for engineers in the f ields of structural engineering, architecture, biotechnology, medicine, space engineering, and other technical applications (Gilewski, Pełczyński, and Stawarz 2014).

Another aspect worth mentioning is that designers and engineers are more conscious about including sustainable aspects in their design strategies (Kloepffer 2008). In this context, origami has inspired many designers and engineers to come up with novel ways to fabricate, assemble, store, and morph objects and structures. This trend has resulted in sustainable product designs that incorporate the use of green materials as paper via its high level of recyclable content (Wu 2015).

Due to recent advances in the material science of paper development, paper has started to be used for technical components and for three-dimensional objects. Cardboard is simply densely laminated paper. Its structural capacity is directly related to the density of its layers. Shigeru Ban used cardboard tubes as structural components in various constructions after conducting several technical tests. These tests make a paper-based product such as cardboard a logical choice to explore, since it can be investigated on multiple scales. Based on Ban’s explorations, construction practice pioneered the use of paperbased product as a structural element that advances modern construction technology and reduces negative impacts on the environment(Ban et al. 2009; James 2008).

Most people associate origami with skilfully crafted three-dimensional forms of living or non-living objects that are found in nature or in the built environment (Sorguรง, Hagiwara, and Selรงuk 2009). However, mathematicians, scientists, and engineers have discovered that an endless number of shapes could be created in theory by using traditional origami (Peraza-Hernandez et al. 2014). These discoveries have enabled new approaches for the manufacturing, assembling, and morphing

of devices and structures based on the principles of origami.

This is evident in the increasing attention given to the theories and tools related to origami in the past four decades (Fei and Sujan 2013; Lang 2004). This increased interest in challenging origami forms has eventually led to further investigation of the geometric features, topological properties, and structural capabilities of paper folding, which provide an invaluable medium for the inspiration of many architectural applications.

Later, several mathematical approaches were developed to understand the phenomenon generated on the paper by folding it and also to estimate the outlook of origami folding. The fundamental concepts and design application of folded forms have been presented by several researches in the f ields of mathematics, engineering, and architecture.

Based on the research by Buri and Weinand (2008), Falk and von Buelow (2011), Gilewski, Pełczyński, and Stawarz (2014), Hemmerling (2010), James (2008), Rihal (2013), Schenk and Guest (2011), and Trautz and Cierniak (2011), the basic origami folds may be classif ied as follows: mountains, valleys, swivels, pleats, diamonds, squash folds, sinks, pockets, petals, and reverse folds.

Although the number of basic folds may be limited, they can be combined in a multitude of ways to construct an unlimited variety of models and designs (Gilewski, Pełczyński, and Stawarz 2014; Hemmerling 2010).

By using these techniques and after unfolding a three-dimensional origami paper model until it reaches a flat conf iguration, a clearly def ined crease pattern is formed. This pattern consists of self-similar surface elements called tiles. The study of tiles and the component concepts embedded in the design of origami folding reveals some common geometric characteristics that form the foundation upon which creative works are developed – symmetry; growth, isometry, and repetition (Jogi 2012; Liapi 2002).

Based on these characteristics, origami can be used to construct various geometrical designs.

In addition to the geometric characteristics of origami, several theorems and principles have been formulated that determine what can, or cannot, be done by paper folding.

The topology is mostly based on Huzita’s axioms, Maekawa’s fundamental theorems, Miura’s patterns, and Kawasaki’s theorem (Fei and Sujan 2013). With these axioms and theorems, one can use origami to build several mathematical models under strict rules and regulations, such as platonic solids, f ractals, tessellations, symmetries, Voronoi systems, and developable surfaces (Hull 2002; Khademzadeh and Mazaheri 2007; Osório, Paio,

and Oliveira 2014). Origami’s topological properties are summarized by Liapi (2002) in the following points: • A general topological condition that any pattern of creases must fulf il requires that the number of creases originating at a vertex always be even.

• A second condition requires that when four creases meet at a common point, the difference between two adjacent angles has to be equal to the difference between the remaining two angles.

• Finally, a third condition requires that the angles a1, a2, a3 … a2n, surrounding a single vertex in a flat origami crease pattern satisfy the following requirement: a1 + a3 + a5+…+a2n − 1 = a2 + a4 + a6+…+a2n = 180 degrees

In simple terms, this relationship between angles surrounding a vertex prevents gaps between creases that meet at the same vertex when the paper is folded.

The particularity of these structures is the additional rigidity due to the inertia introduced by erecting the surfaces. In this context, origami folding is extended to a structural scale and application, following the innovations and latest developments in terms of the materials applied and the methods of connection. For these reasons, these folded surfaces are particularly suited to meet the demands of a structure that needs to be light, equipped with self-supporting properties, able to assume different forms, and having a kinetic behaviour. In addition, the tendency towards cost effective and quicker construction has pushed the folded structures made in reinforced concrete, and has led to the realization of construction in wood, steel, and other modern materials that eventually experience expansion applications (Haasis and Weinand 2008; Osório, Paio, and Oliveira 2014; Šekularac, Ivanović-Šekularac, and Čikić-Tovarović 2012).

In view of these capabilities, there are many structural patterns that may be particularly interesting for architectural applications. However, the most typical origami patterns are longitudinal, facet, egg-box, and Miura-ori patterns (Gilewski, Pełczyński, and Stawarz 2014; Trautz and Cierniak 2011). In addition to these origami patterns, the same surface can adapt to various geometries, volumes, and areas simply by increasing or decreasing the angles between the faces and by applying forces at strategic points (Osório, Paio, and Oliveira 2014).

In the development of origami folding, experimentation with new ideas went beyond f igural origami to gradually include more abstract forms, including developments in the various types of closed and open surfaces, which can also be transcribed into useful concepts in morphing architecture (Jiya 2014; Liapi 2002; Sorguç, Hagiwara, and Selçuk 2009). In this context, there are several kinds of folded structures. According to Šekularac, Ivanović-Šekularac, and Čikić-Tovarović (2012), these structures can be divided

into folded plate surfaces, folded plate f rames, and spatial folded plate structures.

• Folded plate surfaces are the structures in which all the elements of the highest and the lowest points of the folded structure belong to two parallel planes.

• Folded plate f rame represents a constructional set in which the elements of each segment of the folds mutually occupy a spatial form known as a f rame. This type of folded structure involves the spatial organization of two or more folds in the plane.

• Spatial folded structures are the type of structures in which a spatial constructive set is formed by mutually combining the elements of a folded structure (Šekularac, Ivanović-Šekularac, and Čikić-Tovarović 2012).

These conditions set the necessary geometric, topological, and structural f ramework within which the existing features of origami science can be understood or new ones can be created. In this context, the origami-inspired models seem to be very attractive f rom an engineering point of view as well as being in-

teresting for architects (Gilewski, Pełczyński, and Stawarz 2014; Liapi 2002). The magic of these models is that much of the folding happens by itself due to the physical properties of paper and the origamist only has to crease all the folds (Osório, Paio, and Oliveira 2014).

Thus, there are a surprisingly large number of contemporary architectural applications that take advantage of origami folding to solve design and structural challenges.

There is much that engineering can learn f rom art and vice versa. Origami folding in general, and particularly in architecture, has the potential to act as an interface to gain cognitive experience on spatial transformations and form f inding and as a medium of inquiry for structural designs in architecture (Bianchini, Siliakus, and Aysta 2009; Hagiwara 2008; Lang 2004; Sorguç, Hagiwara, and Selçuk 2009). These potential applications have inspired many kinds of architecture, as summarized in the following points.

• In biomimetic architecture: Nature presents many examples of folding principles being deployed in various forms and at different levels, adapted to different situations for different purposes. The deployable and foldable nature of origami provides a very powerful medium in understanding several deployment modes existing in nature and thus the structural relations among different components. Evidences supporting this potential can be found in leaves, flowers, seashells, and insects’ wings, which use the principle of folding imaginatively (Jiya 2014; Sorguç, Hagiwara, and Selçuk 2009). In this con-

text, Hachem, Karni, and Hanaor (2004) studied some samples of deployable forms in nature, in order to use their morphologies and potentials in man-made structural systems. This kind of architecture can be found in the Qi Zhong stadium in Shanghai, which has been inspired by a magnolia flower, and in the transformable roof of the Bengt Sjostrom Starlight Theatre in the US, which opens and closes like the petals of a flower (Asef i and Foruzandeh 2011).

• In transformable architecture: This is another kind of architecture done with origami. It includes the temporary, mountable, and demountable buildings.

This form of using origami takes more advantage of its capacities in which the structures can be collapsed for easy transportation and are self-supported with no need for additional structures, but when they are being used they remain static. Some examples are Packaged Art by Miwa Takabayashi, the Folded Hut by Ryuichi Ashizawa, and the Recover Shelter by Mathew Malone (Osório, Paio, and Oliveira 2014).

• In static architecture: In addition to all of the forms described above, architecture inspired by origami may also come in a f rozen state through the use of heavy materials (Osório, Paio, and Oliveira 2014). In this context, the Isozaki art tower by Arata Isozaki, the Yokohama port terminal by FOA Architects, the Automobile Museum by 3Gatti Architecture Studio, and, more recently, the St Petersburg airport by Grimshaw are wellknown examples of folding patterns in which the diagrams and structural relations of origami can be traced easily.

• In responsive architecture: Another important f ield of application of origami studies is responsive structures.

These structures are usually based on the modules of origami instead of surfaces. These modules usually have a small number of faces arranged around a central point, mainly because of the simplicity in predicting and controlling the open and closed geometries of the modules. These modules respond to stimuli as a whole, but function as independent units geometrically (Osório, Paio, and Oliveira 2014). Examples include Auxetic Origami at Yale University and Al Bahar Towers in Abu Dhabi.

• In recycled architecture: The unique features of foldable structures may change the traditional building maintenance and lifecycle models and offer reconf iguration as an alternative to demolition. In general, foldable structures have less environmental impact than traditional technologies as they are better suited for re-using, modif ications, and relocation (Wierzbicki-Neagu 2005). In this context, Helios House might just be the world’s most architecturally interesting gas station. Located in Los Angeles, it is the f irst gas station in the US to be submitted for LEED certif ication. Designed

by Off ice dA and Johnston Marklee Architects, its main feature is a faceted roof canopy made of recycled stainless steel panels (Solaripedia 2010).

Moving f rom origami to origamics, several international conferences are regularly held, in which mathematicians have helped to form the basis of further development (Buri and Weinand 2008; Sorguรง, Hagiwara, and Selรงuk 2009). In this context, the pedagogical issues related to origami have many directions. While mathematicians study the geometry of origami and use it to develop mathematical concepts, physicists and engineers research the structural applications of origami. Artists and architects explore not only the structural potential, but also the aesthetic aspects of folding techniques (Matsubara and Celani 2007).

For architectural education, origami not only plays an important role in the formf inding design process but also enhances the students’ coordination.

These are the visible endpoints of an architect’s vision in attempts to create something out of nothing. Any meaningful design that solves spatial problems is conceived through a design thought process. The process of thinking in design mainly includes understanding, observation, def inition, ideation, prototyping, and testing (Jiya 2014; Tschimmel 2012). In architectural design when the f inal form is importance, origami provides both prototype and test phases for further design processes (Sorguç, Hagiwara, and Selçuk 2009).

There have certainly been experiments in the different ways to design buildings using origami folding. Based on a simple technique, origami gives birth to an astonishing degree of formal richness and variability.

Different origami paper shapes were sectioned and used in scale models of buildings as roofs, walls, and slabs, in order to explore and conf irm their possible applications in architecture (Buri and Weinand 2008; Matsubara and Celani 2007).

Today architectural design has become a trans-disciplinary issue and the design needs to satisfy many requirements.

Thus, the complexity of the design is problematic and the process itself forces architects to explore new methods and media to provide suitable solutions. The main concern with regard to the architectural part is the form-f inding process, which may be inspired by origami.

Origami is the most important folding inspiration behind architectural design and has a direct effect on the f inal building conf iguration of folded structures, even if the architects are not aware of it. Based on this inspiration, the studio process relies primarily on modelling and prototype fabrication that explore the design potential of origami patterns by integrating materiality, geometry, and structure.

Analogue form-f inding based on origami principles by direct folding leads to intuitive and f reeform pattern variations with limitless outcomes in a continuous process, which support the students’ skills (Jiya 2014; Sorguç, Hagiwara, and Selçuk 2009; Trautz and Cierniak 2011).

Through the folding and manipulation of paper, origami actively enhances hand-eye coordination, which in turn positively influences and develops brain activities. It can be seen as a method for exploring the use of 3D symmetries in the design of spatial structures. In the earliest form of architectural education, Joseph Albers used paper folding in the preparation class of the Bauhaus to help his students discover the relationships between materiality, geometry, and structure (Buri and Weinand 2008; Matsubara and Celani 2007; Tantawy 2015).

In recent times, architectural school systems focus more on acquiring skills and competences.

The emphasis is more not on the knowledge acquired by students but on how they are able to work with it. Origami is especially suited to shape some of these competences (Winckler, Wolf, and Bock 2011). Thus, the mastery of mental focus on a particular task is harnessed in the process. Creative manipulations like these promote the ability to think clearly and coherently in terms of spatial reasoning, which is priceless for an architect’s conceptual and design process.

In this new f ramework, exercises using origami help to develop a better sense of spatial perception. Students develop the idea of how to turn a two-dimensional object into a three-dimensional one, exploring how the modules f it into each other. Many of them are able to set the models faster when they build them together with other students. They exchange ideas and thoughts with each other and are able to go further, possibly leading to the discovery of new forms and construction methods. Architectural students get to understand

spaces and geometry better when they are involved in physical and practical activities such as folding paper. As a result, origami is proposed as a method to explore shapes in the design process (Jiya 2014; Matsubara and Celani 2007).

In this context, origami should be encouraged amongst students in architecture schools in light of the cognitive advantages developed when a plane sheet of paper is folded and transformed into a detailed, three-dimensional piece of art. This may enhance the architect’s ability to conceive spatial conf igurations that are functional by nature, f irm in structure, and aesthetically pleasing (Jiya 2014). There have been hands-on studies in architectural schools in different countries, where their students have experienced with origami thinking. These include the Cardboard Banquet at Cambridge University, the Constructive Geometry Pavilion at the University of Porto, and the Cardboard Pavilion designed by the Facoltà di Architettura di Siracusa (Sorguç, Hagiwara, and Selçuk 2009).

Based on the importance of incorporating origami thinking in architecture education, the Architecture and Urban Planning Department at Port Said University, Egypt has many attempts.

Several ARC courses have been designed to incorporate different assignments which allow students to explore form-structure space concepts both in real and digital world. Among them students have experienced and shared spatial and structural potentials of a sheet of paper by hands on a wide range of activities that will get workshop participants thinking and talking about shell structures based on contemporary Japanese architecture. The students recognize origami potential and present how successfully a piece of paper turns into a structure by simple origami folds to be used as medium and guide not only

to design new forms, but also to explore the potentials of a plate and a shell structure. This educational approach has been successfully addressed in all studio-based courses as well as in one or two-week exercise assignments in other lecture-based courses as architectural theory, building technology, interior design, mathematics in architecture, and computer-aided design courses. These assignments are many and differed according to the objective of every course.

Through these activities, students can overcome flat thinking, engage with their designs on a physical level, and have truly compelling three-dimensional experiences in a collaborative environment. From this point of view, architectural education should encourage some courses to allow architecture students to explore spatial conf igurations both in the real world through origami folding and in the digital world through computer-aided design systems. In addition, these courses should encourage digital design studios and take advantage of origami as an art spanning mathematics, engineering, and architecture.