Six Simple Twists

The Pleat Pattern Approach to Origami Tessellation Design

Benjamin DiLeonardo-Parker

• Publisher: CRC Press
• Year: 2015
• Print ISBN: 9781138427198, 9781138427198
• eBook ISBN: 9781498777254
• Edition: 1
• Topic: Mathematics
• Subtopic: Games in Mathematics
• Index: Mathematics

Get Started with Tessellation Folding

Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design explains the process of designing an origami pattern. It answers the questions "how is a tessellation folded" and "what are the further possibilities."

The author introduces an innovative pleat pattern technique of origami design that is easily accessible to anyone who enjoys the geometry of paper. The book begins with basic forms and systematically builds upon them to teach a limitless number of patterns. It then describes a process of design for the building blocks themselves. At the end, what emerges is a fascinating art form that will enrich folders for many years.

Unlike standard, project-based origami books, Six Simple Twists focuses on how to design rather than construct. This leads to a better understanding of more complicated tessellations at the advanced level.

For Further Study

I hope that this book encourages you to explore the possibilities of paper design further. But where should you go from here? There is significant other literature on origami and a few books in English on origami tessellations.

Lang, Robert. 2011. Origami Design Secrets: Mathematical Methods for an Ancient Art, Second Edition. A K Peters/CRC Press.

Many tessellation folders, myself included, started studying this field because of Robert Lang’s first edition of this book. In it, there is a diagram of koi with a tessellation of scales down its back. If you wish to understand one of the pivotal approaches to modern origami design, this is an essential read.

Lang, R. 2016 (forthcoming). Twists, Tilings, and Tessellations. CRC Press.

Robert Lang is currently writing his own tessellation book, publishing date to be determined. While Six Simple Twists focuses on mainly the pleats that create twists, he will go into the mathematics that governs the twists themselves. Twists, Tilings, and Tessellations explores the three topics of its title and much more in addition, describing the underlying mathematics and techniques for designing, constructing, and folding a wide range of geometric origami.

Lister, D. The Lister List, British Origami Society. http://www.britishorigami.info/academic/lister/ (accessed January 1, 2015).

Hosted on the British Origami Society’s website, David Lister has many valuable articles on the history of origami. His tessellation history article discusses Yoshihide Momotani, Shuzo Fujimoto, and some of the founding models that inspired the tessellation studies. There are also many more articles that you may wish to explore regarding other paper-folding topics.

Gjerde, E. 2008. Origami Tessellations: Awe-Inspiring Geometric Designs. A K Peters/CRC Press.

Eric Gjerde presents a very popular and attractive introduction to origami tessellations with many excellent examples of patterns. His perspective is different from my own. I highly recommend his book for any origami artist, but especially if you have had difficulty with the exercises in Six Simple Twists or simply wish to have another perspective on how twists are formed.

Rutzky, J. and Palmer, C. 2011. Shadowfolds: Surprisingly Easy-to-Make Geometric Designs in Fabric. Kodansha USA.

Palmer has pioneered the technique of using the tessellation concepts to fold fabrics, rather than paper. Rutzky and Palmer present several projects in a beautiful format that offers another perspective on how the twists can be formed. The properties of the fabrics being different from the paper, this can offer new challenges for the aspiring tessellation folder.

Table of contents

• Preface
• Acknowledgments
• About the Author
• Chapter 1
• The Six Simple Twists
• Chapter 2
• How to Use the Six Simple Twists
• Chapter 3
• Beyond the Six Simple Twists
• Final Thoughts
• For Further Study