Paper Folding in Beginning Interior Architecture Studio: Tactile Experience, Form, and Material

Paper folding models in a beginning interior architecture studio

Citation: Wu, J. (2108). From Paper Folding to Digital Modeling in Beginning Interior Architecture Studio, IDEC Exchange: A Forum for Interior Design Education, Winter 2018.

Paper folding is easy to do by hand and does not require sophisticated tools. The form generation in paper folding is a direct result of material manipulation through a series of actions by hand. While paper folding can be easily done by hand, describing paper folding scientifically and representing the morphology that happens when a flat sheet of paper is folded, however, requires complex mathematical and computational modeling. Current CAD technologies, such as 3D modeling tools such as Rhino and Revit, are inadequate for such a tactile design process. In courses such as Beginning Interior Architecture studios, it is extremely difficult for the beginning design students to generate innovative forms directly using 3D modeling tools, which they are just beginning to learn. However, when they are asked to work with pieces of paper using their hands in free experiments, they learn to discover new ideas and find new forms, which then inspire them to generate digital alternatives that can be used in various scales in their interior design activities. 

Work by Emma Hamlet, Spring 2019
Work by Evan Berger, Spring 2019
Work by Gabby Pierson, Spring 2019
Work by Kiara Henry, Fall 2018
Work by Lauryn Blank, Fall 2018
Work by Katie Gee, Fall 2018

In an introductory interior design and architecture studio, paper folding was introduced to the first year students to help them understand basic design principles such as symmetry, repetition, and modality. The goal was to produce a small-scale paper folded light sculpture that is volumetric and that can enclose a light source. The project was divided into three small parts that serve as learning scaffolds. In the first part, the students were asked to create small units of paper folds from pieces of small square paper. Students were asked to draw simple line drawings based on two-dimensional compositions they made in a previous project using straight edges and compasses. They then were asked to give mountain and valleys assignments to the line drawings and they started folding. The students quickly found out that preconceived mountain and valley assignments often didn’t give rise to successful volumetric paper folds. Instead, they learned that folding paper was a very tactile experience and that each paper fold works like a small mechanism. To manipulate these small paper mechanics, one needed to cut, fold, pinch, pull, roll, tuck, and pop through a series of freehand experiments, similarly in ways to how a sculptor works with lumps of clay. While they started with some predesigned line drawings, they had to add new crease lines and ignore some original lines in their new paper folds. In the second part, the students were asked to connect four to eight units of their paper folds together. Students were taught to connect the units by using ways to make symmetries, such as translation, rotation, reflection, glide-reflection. They learned that to connect units together, they must pay attention to the boundary conditions of their paper folds. Complicate boundaries of a paper fold might be difficult to connect in modular form. In the third part, they were asked to use as many units as they needed to create their final design. They learned that by connecting these small paper mechanisms, they would end up with larger pieces of mechanisms which they need to manipulate again by hand to create the final stable volumetric forms. In addition, they were also taught to use polyhedral geometries, including icosahedron, dodecahedron, rhombic dodecahedron, etc., to connect the units into fixed three-dimensional volumes.

The beginning students often achieved great results in making a paper light and they were very proud of their work, which motivated them with later designs using digital tools. They were sometimes asked to produce digital alternatives of their paper structures. These digital alternatives were merely approximations of the paper fold structures. The digital models can then be used later in their other interior design projects either as small-scale light shades or as large-scale interior volumetric surfaces.

Weaving Infinite Bi-foldable Polyhedral Complexes

I have been collaborating with mathematician Matthias Weber on a new class of infinite bi-foldable polyhedral complexes. Currently, our initial result has been published at: I would like to showcase two examples of triply infinite bi-foldable polyhedral complexes: Butterfly and Dos Equis. I made Butterfly and Dos Equis using a polyhedral weaving technique. The material is Mi Teintes paper. I’m also including two nice rendered videos made by Weber.

To learn more about the mathematics (explained in layman’s terms by Weber) behind these fun infinite bi-foldable polyhedral complexes, or the process of how we found them, I encourage you to visit Weber’s blogs here:

Weber’s blog on Butterfly
Weber’s blog on Dos Equis

Butterfly has three vertex types: valency 4, 6, and 8. Butterfly is named after the vertex of valency 8 as it resembles a symmetrically balanced butterfly. This vertex is translated to create the triply periodic construction. Butterfly is made using a polyhedral weaving technique that employs a four-color complementary scheme. Each color represents a distinctive zone using the concept of zonohedron proposed by H.S.M. Coxeter. Each face is alternated and interwoven by two zones of two colors. A few deviations from the regularity are inserted to create the rhythmic changes.

An isometric view of Butterfly.

There are three vertex types in Dos Equis: two of valency 4 and one of valency 8. Dos Equis is named after the vertex of valency 8 as it resembles the image of an X. Using a four-color complementary scheme, each color represents a distinctive zone using the concept of zonohedron proposed by H.S.M. Coxeter. Each zone, using two unique unit patterns, is then folded and interwoven with other zones. Notice that the four colored zones, with its two unit patterns, and its under or over weaving alternations, create a total of sixteen design variations for the quadrilateral faces.

Dos Equis

Light Harvest: Interactive Sculptural Installation based on Folding and Mapping Proteins


Wu, J., Ressl, S. & Overton, K (2018). Light Harvest: Interactive Sculptural Installation based on Folding and Mapping Proteins, Digital Creativity, doi: 10.1080/14626268.2018.1533871.

Download the free PDF here:


Light Harvest is an interactive sculptural installation that explores a protein called Light-Harvesting Complex II (LHCII) in the realm of materials, digital fabrication, projection mapping and interaction design. This article gives an account of the making of Light Harvest, a collaboration between an artist/designer, a structural biologist, and an interaction design technologist. The artistic concepts in material construction and digital techniques are drawn from protein folding, sophisticated mapping processes in protein X-ray crystallography, and the remarkable abilities of LHCI proteins to convert full-spectrum visible sunlight to useful energy for life. Through its interactive installation, Light Harvest engages us in an appreciation and understanding of the biological processes studied and the scientific techniques used to study them.

Ruga Lumina: Folding Interior Skin with Dynamic Light


Wu, J. (2018). Ruga Lumina: Folding Interior Skin with Dynamic Light, Journal of Interior Design, Volume 43, Issue 2, pp. TBD. doi: 10.1111/joid.12123

Link to full paper in PDF


Ruga Lumina investigates body–space relationships by leveraging digital fabrication and interactive technologies. Ruga Lumina is a spatial construct in the form of a smart luminous “skin” made of thin sheets of folded material that respond to the movement of live bodies within and surrounding its interior space. Spatial occupancy is registered through the use of smart technology; sensor information activates illumination and lighting effects, which, in turn, prompts perceptual and expressive aesthetic qualities as affects. This visual essay gives an account of the construction of Ruga Lumina at two exhibition sites: Detroit Center for Design and Technology (DCDT) in Detroit, Michigan, and 3Labs in Culver City, California. This account describes how bodies can be read and registered upon a spatial surface that points to a potential to re‐envision fundamental notions of surface interiority.

Washi Art + Design at the Ivy Tech John Waldron Arts Center

Washi Art + Design at the Ivy Tech John Waldron Arts Center, Bloomington, Indiana

Washi Art and Design, an international paper art exhibition, is the first group exhibition I curated and organized. The show runs from August 26th to September 21, 2017, at the Ivy Tech John Waldron Arts Center in Bloomington, Indiana. The participating artists are Yuri Kawai (Japan), Sachiko Kinoshita (Japan), Amanda Ross (U.S.), Rowland Ricketts (U.S.), Koji Shibazaki (Japan), Jenny Stopher (U.S.), Mikao Suzuki (Japan), Ruigan Zhou (China), and myself.

The Exhibition is focused on the theme of Washi and other paper art. Washi paper is made from the long inner fibers of three plants: Kozo (mulberry tree), Mitsumata, and Gampi. Due to these raw materials and the traditional craft techniques, Washi papermaking has no adverse environmental impact. The paper is very durable and can last as long as a few hundred years.  In Japan, Washi has played a significant role in the lifestyle and culture of the Japanese people. In addition to its more common uses in stationary and in the fine arts, Washi is used in many different cultural activities such as in religious and ceremonial events. Its fabric-like quality makes it suitable for applications in fashion, interior lighting, and interior furnishing. Though there is a long history of Washi papermaking in Japan, today only a few Washi papermakers are continuing their papermaking traditions, and Professor Koji Shibazaki’s Washi research lab at Aichi University of Arts is one of them.

A Surihaku (gold foil painting) workshop was conducted by artist Mikako Suzuki at the Waldron Arts Center. For more information about the workshop, please visit here.

The exhibition and workshop are supported in part by a workshop grant from Indiana University’s College Arts & Humanities Institute.

Washi paper light by Professor Koji Shibazaki of Aichi University of Arts

Jiangmei Wu explaining to Professor Katy Borner about the intricate Kirikane art by Japanese artist Mikako Suzuki as Professor Hamid Ekbia watched on

Japanese textile artist Sachiko Kinoshita’s Swing Circle is made of yarn and Kozo paper fiber

Method for Folding Flat, Non-rigid Materials to Create Rigid, Three-dimensional Structure


Wu. J. (October 31, 2017). Method for Folding Flat, Non-rigid Materials to Create Rigid, Three-dimensional Structures. Patent No: US 9,803,826 B2. Washington DC: The United States Patent and Trademark Office

Published_Patent in PDF

Priority Claim: The present application claims priority to U.S. Provisional Patent App. No. 61/893,519, filed Oct. 21, 2013, the entire disclosure of which is hereby expressly incorporated herein by reference.

Field: The present disclosure relates generally to creating rigid three-dimensional structures by folding flat, non-rigid materials. More particularly, the present disclosure relates to a method of folding a non-rigid material with a score or crease pattern into a three-dimensional structure for covering a light source.

Applying Helical Triangle Tessellations in Folded Light Art (Bridges Conference Paper)


Wu, J. (2017). Applying Helical Triangle Tessellation in Folded Light Art. In D. Swart, C Séquin. & K. Fenyvesi (Eds.), Proceedings of Bridges 2017: Mathematical Connections in Art, Music, and Science (pp. 383-386), Phoenix, Arizona: Tessellation Publishing


This article describes how I created a collection of lamps made of folded sheets of material using helical triangle tessellations, which are also called Nojima patterns. I started by working with a periodic helical triangle pattern to fold a piece of light art that is shaped in a hexagonal column. I continued by modifying the periodic pattern into a semi-periodic design by adding variations so that the tessellation could be folded into a light art that is shaped in a twisted column. I further developed tessellations that consisted of self-similar helical triangles by using a geometric construction method. These self-similar helical triangles form algorithmic spirals. I folded the tessellation design into a work of light art that is shaped in a conical hexagonal form.

External Links:

Link to PDF


Paper Folding Workshop at College of Architecture and Design, Lawrence Technological University


Folding a piece of paper can be simple and doesn’t require any sophisticated tools. I often tell the students who participate my workshop that paper folding can do a lot more than computer CAD modeling. Since paper folding is unstable and flexible, manipulation of the paper surface to achieve depth and volume is dynamic. The fold stores kinetic energy, which allows the folded form to contract and unfurl. It can then be balanced, connected, hinged, suspended, pulled and popped up to alternate states of disequilibrium and equilibrium. Paper folding is unforgiving and honest. A folded form embeds the memory of a series of actions of scoring, creasing, twisting, wrapping, pressing, bending and folding. Unfolding folded paper reveals a patterned map of creating and generating. Paper folding is generative and evolving. It is difficult to describe an abstract folded form through its visual characteristics. Paper folding is improvisational and unpredictable. A simple fold has many possibilities and can generate many visual results, and it can only be discovered by folding.

About twenty students from the College of Architecture and Design at Lawrence Technological University participated the workshop. The workshop was conducted in the gallery The students are from Interior Design, Architecture and other programs.

I often begin my process using a step-by-step procedure, or algorithm, first by hand only. I demonstrated this technique to the students.  They started by folding smaller pieces of square paper into simple designs, and they then repeated the same steps for a multiple of times to create repetitions of these simple designs. And finally, they worked on connecting the folded pieces to create a larger form. The students learned that small seeds can be compounded and aggregated to create something that is a lot of complex than the original simple design.


2017 Mathemacal Art Exhibition Awards

light_torus_night_1.jpgThe 2017 Mathematical Art Exhibition Awards were made at the Joint Mathematics Meetings last week “for aesthetically pleasing works that combine mathematics and art.” The three chosen works were selected from the exhibition of juried works in various media by 73 mathematicians and artists from around the world.

“Torus,” one of my folded light art, was awarded Best textile, sculpture, or other medium. I’m interested in how paper folding can be expressed mathematically, physically, and aesthetically. Torus is folded from one single sheet of uncut paper. Gauss’s Theorema Egregium states that the Gaussian curvature of a surface doesn’t change if one bends the surface without stretching it. Therefore, the isometric embedding from a flat square or rectangle to a torus is impossible. The famous Hévéa Torus is the first computerized visualization of Nash Problem: isometric embedding of a flat square to a torus of C1 continuity without cutting and stretching. Interestingly, the solution presented in Hévéa Torus uses the fractal hierarchy of corrugations that are similar to pleats in fabric and folds in origami. In my Torus, isometric embedding of a flat rectangle to a torus of C0 continuity is obtained by using periodic waterbomb tessellation.

The work is made of Hi-tec Kozo Paper and measures 45 x 45 x 20 cm.