Martyna Ziółkowska

Written by: Martyna Ziółkowska - Wroclaw University of Technology, Poland - Universita degli Studi di Firenze, Italy

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Paper tesselation

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A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes ( dimensions) is called a tessellation. Tessellations can be specified using a Schl채fli symbol. The breaking up of self-intersecting polygons into simple polygons is also called tessellation (Woo et al. 1999), or more properly, polygon tessellation There are exactly three regular tessellations composed of regular polygons symmetrically tiling the plane. Tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular tessellations, or sometimes Archimedean tessellations. In the plane, there are eight such tessellations, illustrated above (Ghyka 1977, pp. 76-78; Williams 1979, pp. 37-41; Steinhaus 1999, pp. 78-82; Wells 1991, pp. 226227). There are 14 demiregular (or polymorph) tessellations which are orderly compositions of the three regular and eight semiregular tessellations (Critchlow 1970, pp. 62-67; Ghyka 1977, pp. 78-80; Williams 1979, p. 43; Steinhaus 1999, pp. 79 and 81-82). In three dimensions, a polyhedron which is capable of tessellating space is called a space-filling polyhedron. Examples include the cube, rhombic dodecahedron, and truncated octahedron. There is also a 16-sided space-filler and a convex polyhedron known as the Schmitt-Conway biprism which fills space only aperiodically. A tessellation of -dimensional polytopes is called a honeycomb.

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The types of paper tasselation are among others: origami, kirigami or pop up. No matter what tools we use, folding paper can give us good results, which we can use in landscape architecture, architecture, fashion or industrail design. The pictures on the left show two tiypes of folding. Interesting structure could be used as an extraodrinary roof, repeated facade module, element for seating or modern table (shown in the picture below)

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These extraordinary paper sculptures by Martin and Erik Demaine are made up of pre-creased papers designed to bend and fold naturally due to gravity. Called Computational Origami, the pieces completely reimagine the ancient art of paper-folding. “Computational Origami” is technically a triptych of paper art which is now part of the permanent collection at the Museum of Modern Art (MoMA). In the three-part work, each piece is connected together using multiple circular pieces of paper. “The title “Computational Origami” refers to our underlying algorithmic goal of determining the mathematical curved surface that results from different kinds of pleated folding,” explains the Demaine website. “This kind of “self-folding origami” may have applications to deployable structures that can compress very small by folding tightly and later relax into its natural curved form.” The complex pieces are part of the duo’s ongoing experiments and search for complete comprehension of the entire algorithmic system behind selffolding origami.

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Origami (from ori meaning "folding", and kami meaning "paper" (kami changes to gami due to rendaku) is the traditional Japanese art of paper folding, which started in the 17th century AD at the latest and was popularized outside of Japan in the mid-1900s. It has since then evolved into a modern art form. The goal of this art is to transform a flat sheet of paper into a finished sculpture through folding and sculpting techniques, and as such the use of cuts or glue are not considered to be origami.

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Origami is one of the most known method of folding paper. Our first expierience with folding paper is from kindergaden or primary school where we tried to fold an animal or create some flower. That is why most of adults thinks that origami is only game for children. Nothing could be more wrong! Strange forms created of paper could be useful for designers. Extraordinary shape could be used in architecture. If we look closer, many existing buildings were inspired by playing origami. In the pictures below, we can see origami structure, model of the city and famous scyscraper – Norman Foster’s 30 St Mary Axe (more known as ’London’s cucumber’).

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When we look closer at detail of window, the stucture reminds us popular forms of origami and kirigami. Even if Norman Foster wasnâ&#x20AC;&#x2122;t inspired by folding paper, chracteristic spiral shape could be used similar. Next pictures show a lot of shape variation and idea of creating facade with origami/ kirigami structure.

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modularity The purpose of folding paper is trying to find attractive form which could be used in design. Moreover it could be first inspiration for future project. Interesting shape could be multiply modify and use as repeated module. This chapter shows some examples of this method.

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Images on the left show different variants of configuring the same element. As we can see, there is a lot of possibilites to create strange extraoridnary structure. We can multiply module, rotate elements or stick them together. Depending on technique, we will get another final product. The structure could be dynamic or static, elements could be ordered or be in mess. In the picture below we can see interior of recording studio with walls made of repeated elements.

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Good reference is project of Luisa Robinson, which also uses one module. Designer Luisa Robinson debuted a gorgeous set of Dragon Tail Lamps, which look both dangerous and delicate at the same time. The lamps are made with chromed origami paper and they taper to small curve at the bottom resembling a prickly tail, brining an edgy twist to the soft glow of light they emit. Based in the Philippines, Robinson integrates locally sourced organic materials into her designs including palms, seagrasses, bamboo, abaca, and rattan.

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Famous â&#x20AC;&#x2122;Fortune Teller Gameâ&#x20AC;&#x2122; (also origami) was inspiration for another architecture project. With their origami-shaped Bengt Sjostrom Starlight Theatre, Jeanne Gang of Studio Gang Architects has proven that we don't have to go to the big city to see incredible architecture. Completed in 2003, this project is an oldie but a goodie worth revisiting, not only because it's just so doggone beautiful, but because it demonstrates what can be done on a limited budget. Incorporating a retractable roof into the new theatre allowed the architects to keep the sense of openness during sunny weather, while the elegant petal-like roof panels that fold into one another ensure that the show can go on when it rains.

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The striking glass exterior of this Health Department building in Bilbao, Spain isn't just a pretty face(ade). Coll-Barreau Arquitectos conceptualized the folded facade in response to the city's restrictive building code that requires stepped setbacks for all multistory buildings along its main streets. The folded facade consists of two layers. The outer one is a glazed skin made up of framed glass set in a tubular frame while the inner layer is the buildingâ&#x20AC;&#x2122;s windows. There are two major benefits to the design: noise from the busy boulevard is noticeably reduced and solar heat gain is decreased via radiation reduction and a breathable wall system. In addition to the increased energy efficiency afforded by the double skin, the building holds meetings in a daylit, two story atrium that opens to a roof deck. To promote denser land use, the seven stories below roof contain office space and a subterranean three floor robotic parking lot.

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kirigami kirigami Kirigami is a variation of origami that includes cutting of the paper (from Japanese "kiru" = to cut, "kami" = paper). It is also called "Kirie". From "Kiru"= to cut, "e"= picture.

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Typically, kirigami starts with a folded base, which is then cut; cuts are then opened and flattened to make the finished kirigami. Kirigami are usually symmetrical, such as snowflakes, pentagrams, or orchid blossoms.

Elements of kirigami should be useful in creation of public space. Perforatedl structure could be material for green wall, which is vertical garden as well as an acoustic barrier. Simmetric solid could create a place for sitting or even be an extraodrinary sculpture.

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During the folding paper, we can use scissors to create fabulous forms. Spiral shape deservs special attention, because it’s a symbol of human being and it’s often repeated by Nature. ’Roselooking’ structure could be used as small architecture as well as for bigger buildings. Beautiful structure could be an element of elevation or even used as contruction.

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Spiral, perforated construction based on dense grid might find many uses. One of them is construction of roof or extraordinary dome. Another idea is connected with small architecture. Form could be used as expo pavillon or garden arbor.

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Repeated small elements could create one bigger structure which could be use even as an architecture object. Soft curves could be use in creation of landscape architecture or more organic designâ&#x20AC;Ś

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Dynamic shape could be very useful, when we want to create special atmosphere of interior or exterior. One of architectâ&#x20AC;&#x2122;s tool is modulation of light. Structure full of geometric holes, could pass rays of sun or artfical lighting and thereby make our object more intersting.

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Smooth profile which was rotated and multiplied before, could be idea of extraordinary facade. Good example could be the project of Busan Opera in South Korea , which was created for competiotn. Opera houses usually get great architectural designs compared to any other building and this Opera House truly adds up to that expansive library. Set to be located in South Korea, this marvelous concept is a design entry by Architecture firm OODA and as you can see the theme is pretty clear, a sea shell by the sea.

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When we cut and folding the paper we can create specific grid which reminds birdâ&#x20AC;&#x2122;s nest. This type of structure could be dynamic or more static and can find many uses. Below: idea of place to seat and also element of the equipment of playground.

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Cutting paper, folding, rotating and twisting leads us to another structure, which could be used even in civil engineering. In the left: paper models, below: visualisation, how we can use form in the spatial arrangment. Thanks to unified element, we can create simple to build but very interesting structure.

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Another type of kirigami is inspired by wicker basket weaving. In that method, we cut thin stripes of paper and interleaved by other. Final product doesn’t look so impressive as 3d structure, but could be very useful. Picture on the left shows idea of extraoridnary roof. It could be used in airport, where the fifth elevation plays an important role. This type of structure it’s also good for facades of public buildings as well as small architecture (for acoustic isolation, vertical garden, so on…)

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Playing with paper shows us clearly how many â&#x20AC;&#x2122;Starchitectsâ&#x20AC;&#x2122; use this old technique in order to create something new, fresh and modern. In the pictures on the left we can see the structure made of repeated module, which was only roated. On the right there are some visualisations of famous rotating tower in Dubai of David Fischer.

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â&#x20AC;&#x2122;Pop upâ&#x20AC;&#x2122; is that kirigami is made out of a single piece of paper that has been cut into a design. Pop ups can be made of several pieces glued together.

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How to make your own Pop Up: 1. Choose Your Subject Well: Be sure to choose a subject that your child will want to revisit again and again. Something that is not only memorable, but also includes elements that you can make pop. Field notes from a trip to the Natural History museum or re-telling family history (using old photos) are great ideas. The last thing you want is for the fruit of your recycled book-making project to end up in the recycle bin.

2. Keep Your Materials Green: Using environmentally friendly materials such as homemade rice glue or crazy crayons, along with clippings from recycled magazines will help keep your project fun while also keeping it sustainable. The best purchasing advice is to purchase nothing at all. Make use of what you already have at home.

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3. Donâ&#x20AC;&#x2122;t Complicate Things: It is a good idea to keep your animated pop-up elements simple and durable. Use sturdy paper and limit the number of cuts required to have your elements come to life. Have a look at the simple shapes created in the included step-by-step instructions and incorporate them into your book. to be turned in at the thrift store.

4. Make It Unusual: A great way to personalize your project is by incorporating elements that keep things interesting. You might try your hand at a few flip pages, or use bits of fabric from outgrown clothing too worn

5. Sometimes Itâ&#x20AC;&#x2122;s OK To Cheat: A quick way to breathe new life into an old, tattered book is by dissecting it and using its elements (illustrations, story line) to create something that pops! The only warning with this method is that when converting a conventional book to a pop-up book, you will quickly realize that you are only able to use one side of the conventionally printed double-sided pages. Choose your pages carefully. - See more at: http://www.inhabitots.com/make-yourdiy-book-projects-pop/#sthash.3jTRK2UB.dpuf

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Nature is the best inspiration in order to find interesting shape or structure. If we look closer all world is created of repated molecules (electrons, protons, atoms), which builds bigger elements (tissues, organs) which are grouped together and make some system.. Natural creation is based on repeated modules. Therefore modern design is only immitation of Nature beauty.

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Fishbones or skeleton of other animal could be good inspiration for architects. Since the time of secession, architects tried to immitate nature. Antoni Gaudi and his architecture is the best proof.

Nowadays Santiago Calatrava observes animal sketeletons and tries to repeat some connections in construction of his buildings.

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Repeated parallel stripes could give us extraoridnary structure which doesnâ&#x20AC;&#x2122;t have to be static! Itâ&#x20AC;&#x2122;s worth to notice the connection between the form and light. Multiplied, similar elements could create interesting pattern of the shade.

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When we observe the Nature we can see some analogies, which could be quantified and even written as a mathematic function. Many existing elements in Nature are built like fractals.

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A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers.[Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". Fractals may be exactly the same at every scale, or, as illustrated in Figure 1, they may be nearly the same at different scales. The definition of fractal goes beyond self-similari typer se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.

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In this chapter, there are described examples of architecture design based on numerical counts and parameters entered before modelling final conception.

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The site specific installation done by Live Components (on the right) was recently exhibited at SeMA (Seoul Museum of Art). It was temporary movie theatre using recycled material for playing independent film. Through parametric process controlling 930 recycled pallets, which are used for cargo loading, were assembled tectonically to newly become a theatre space.

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This study on the left is to investigate â&#x20AC;&#x2DC;adaptive conformationâ&#x20AC;&#x2122; and generate productive prototypical models for tectonic optimization which requires analytical mechanism through four inter-related elements: grid, density, scale, and structure. The unit was devised to simplify 3-dimensional surface structure with 3 points. And the radial grid had been developed to accommodate constant proportion of hexagonal grid which changing geometry. This study was for actual following fabrication project.

This project was to materialize study of ‘adaptive conformation’ with representing ‘Opening Chronometry’. It was installed with assemblage of units and minimized structures which were designed at precise points. Collaborated with prof. Hyundai Kim, and recently constructed with our Ewha Womans University students. It was located in front of ECC (designed by Dominique Perrault) in Ewha Womans University campus, Seoul, Korea.

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Shigeru Ban, Cardbord Cathedral Christchurch, New Zealand The February 2011 Christchurch earthquake (magnitude 6.3) inflicted crippling damage on the Christchurch Cathedral which was the symbol of city. In response to this situation, architect was asked to design new temporary cathedral. Paper tubes of the equal length and 20 ft containers form triangular shape. Since geometry is decided by plan and elevations of the original cathedral, there is a gradual change in each angle of paper tubes.

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Shigeru Ban, PAPER TOWER - London, 2009

The tower was built by paper tubes which were connected in tensegrity construction. Tensegrity, tensional integrity or floating compression, is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually bars or struts) do not touch each other and the prestressed tensioned members (usually cables or tendons) delineate the system spatially.

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Shigeru Ban, PAPER BRIDGE - Remoulin, France, 2007

The shape of the arched bridge was selected for the situation of the site and the structural rationality. There was the contrast of the materiality where Pont du Gard is made of stone which is heavy, hard and durable, and Paper Bridge which is made of the paper tubes that are light, weak and short-lived. At the same time, there is a harmony between the two as the geometry of Paper Bridge uses the same arc dimension as the Pont du Gardâ&#x20AC;&#x2122;s arches.

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Shigeru Ban, VASARELY PAVILLION - Aix-en-Provence, France, 2006 This temporary architecture was built as an homage to the artist, Paul Cezanne, in commemoration of the Cezanne in Province festival in 2006 on a site at the Vasarely Foundation with a panoramic view of Mont Sainte-Victoire. 8m in height and 16m in diameter at the crown, this umbrella form was created from a self supporting paper tube structure. From beneath the membrane covered canopy and amongst the trees and nature, one can enjoy the great views of Mont Sainte-Victoire.

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Shigeru Ban, HAESLEY NINE BRIDGES GOLF CLUB HOUSE - Korea, 2010 The Nine Bridges Country ClubClubhouse is a 16,000squaremeter facility that serves a golf course. It has an underground level and three floors above grade. There is a main building, VIP lobby building, and a structure with private suites. The atrium and the upper portion of the main building include timber columns and a glass curtain wall, while the base is made of stone (random rubble masonry typical of Korea). The timber area includes the reception zone, a memberâ&#x20AC;&#x2122;s lounge, and a party room. The stone podium houses locker rooms, bathrooms, and service areas. The roof over the main building measures 36 x The unusual tree-like timber 72 meters. Columns in the atrium reach to a height of three stories. The partial-timber structure was used to conform to Korean regulations that do not allow timber buildings to exceed 6 000 square meters in size.

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Shigeru Ban, BAMBOO ROOF - Rice University Art Gallery, Houston, Texas, USA, 2002 This project for the Rice University Art Gallery began when Shigeru Ban was in Houston, Texas to give a lecture. Following the talk, he was asked by the director of the gallery, Kimberly Davenport, to design an installation on the campus. This is a 36' x 36' undulating canopy of interwoven bamboo boards. Groups of four boards are overlapped in a spiraling pin-wheel connection, and different orientations of the overlap results in a change in curvature. This arrangement of pin-wheel connections creates a pattern of large and small squares, and forms a concave or convex geometry resulting in a shell structure or grid shell.

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Zaha Hadit Architects, Floating staircase, London 2012

The floating staircase maintains the lightness of the gallery space. each suspended step is articulated as a separate ribbon cast, an ultrahigh performance concrete with expectional structural as well as aesthetic qualities.

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Zaha Hadid Architects, Cirrus, Cinncinati, USA

Cirrus was installed five years after the completion of the seminal Lois&Richars Rosenthal Center for Contemporary Art in Cincinnati. guiding the flow of circulation around the suspended galleries, its striated articulations unravel from the wall to the ground. The resulting series of voids give the sculpture its structure and define niches for sitting, reclining, leaning or lying.

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Zaha Hadid Architects, Aqua at Dover Street Market, London

Dover Street Market has commissioned a sitespecific installation to be showcased intheri London store during the Olympic Games. entitled "Acqua", the concept references the formal language of Hadid's renowned London Aquatics Centre.

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Santiago Calatrava, Milwaukee Art Museum The pavilion features a spectacular kinetic structure, a brise-soleil with louvers that open and close like the wings of a great bird. When open the shape also becomes a sign, set against the backdrop of the lake, to herald the inauguration of new exhibitions. The pivot line for the slats is based on the axis of a linear mast, inclined at 47 degrees, as a parallel to the adjacent bridge mast. Calatrava's designs are often inspired by nature, featuring a combination of organic forms and technological innovation. The Milwaukee Art Museum expansion incorporates multiple elements inspired by the Museum's lakefront location. Among the many maritime elements in Calatrava's design are: movable steel louvers inspired by the wings of a bird; a cabled pedestrian bridge with a soaring mast inspired by the form os a sailboat and a curving single-story galleria reminiscent of a wave.

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Santiago Calatrava mediopadana station, reggio emilia, italy The new 'mediopadana station' for the controversial high-velocity rail line (TAV) stretches 483 meters visible from the highway and serves as a new portal to the town. In keeping with his signature white buildings, the structure is a large undulating form composed of 457 steel frames spaced about one meter apart that progressively outline a fluid wave and frame translucent glass panels above the platforms for protection from the elements. each of the ribs is partially supported by a curved longitudinal beam supported every 25 meters by a composite concrete and steel column.. Embedded in a completely flat landscape, the modules arranged in the shape of a three-dimensional sinusoidal curve create a compelling dynamic structure: a perfect wave.

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Santiago Calatrava-designed World Trade Center Transportation Hub

Spanish Architect Santiago Calatrava, designer of the station, said the Oculus resembles a bird being released from a child's hand. The roof was originally designed to mechanically open to increase light and ventilation to the enclosed space.

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Observation of Nature is the best method to search for inspiration. Folding paper helps us to create a lot of structures with extremely different shapes, such as: static form with regular geometry or dynamic with irregulate curves. With scissors and other cutting tools, we can create perforated structure which could look impresive thanks to game of light and shades. Moreover, it is worth to notice how many interesting soultions gives us one module which is repeated and a little bit modified. Summing, there is no matter which form we create everytime we can use it in architecture, landscape, fashion or industrial design as a construction, 3d object or some detail. Anyway we have to observe world which surrounds us and donâ&#x20AC;&#x2122;t forget that form should follow function.

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http://www.calatrava.com/ [28.10.2013] http://www.shigerubanarchitects.com/ [28.10.2013] http://www.zaha-hadid.com/ [29.10.2013] http://en.wikipedia.org/wiki/Fractal [28.10.2013] http://en.wikipedia.org/wiki/Kirigami [28.10.2013] http://en.wikipedia.org/wiki/Origami [28.10.2013] http://en.wikipedia.org/wiki/Tensegrity [28.10.2013] http://inhabitat.com/computational-origami-is-paper-art-thatfolds-itself/origami-erik-demaine4/ [02.11.2013] http://inhabitat.com/origami-like-glass-building-has-a-strikingfolded-facade/basque-health-department-headquarters-5/ [02.11.2013] http://www.apk.wsg.byd.pl/index.php?id=109 [02.11.2013] http://gadzetomania.pl/2012/01/23/niesamowite-obiektyarchitektoniczne-wykonane-z-pojedynczej-kartkipapieru/papierowa-architektura-ingrid-siliakus-2/top [02.11.2013] http://hovercraftdoggy.com/2013/07/17/we-make-cuts-2/ http://krazykrishmagraphics.blogspot.it/2011/02/miyamotospaper-architecture.html [02.11.2013] http://szczecin.sarp.org.pl/westival/2007.htm [01.11.2013] http://vanguarq.wordpress.com/tag/fractal/ [02.11.2013] http://livecomponents-ny.com/ [01.11.2013] http://livecomponents-ny.com/page/7/ [01.11.2013] http://archinspire.org/arab-world-institute-architecturebuilding/ [01.11.2013]

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Taccuino vol. 1
Taccuino vol. 1

- empirical form investigation - researches for course of prof. Giuseppe Ridolfi: System and Coponents (curicullum on Architecture Design)...