Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design, 1st Edition (Paperback) book cover

Six Simple Twists

The Pleat Pattern Approach to Origami Tessellation Design, 1st Edition

By Benjamin DiLeonardo-Parker

CRC Press

118 pages | 165 Color Illus.

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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.


"Six Simple Twists is a gentle introduction to the vast, wide world of origami twist tessellations that brings the reader through the successive stages of folding, understanding, and, ultimately, designing origami geometric patterns based on the powerful hexagon grid system. The six twists of the title—interacting configurations of paper pleats—may be simple in isolation, but Parker shows how they can be combined in uncountable variety. Parker presents more than a bare plan; he gives tips and techniques, guidelines and hints, using standard origami notation where it is useful, but also introducing new notations (such as markings for mountain- and valley-like vertices) that aid both understanding and folding. Throughout the book are shown photographs of the author’s own beautiful tessellation creations: these serve to illustrate the concepts within the book and inspire the reader to her/his own inventions."

—Dr. Robert J. Lang, Origami Artist and Consultant,

"Origami tessellation, a form of abstract geometric paper-folding, has been growing in popularity in the last 10 to 20 years but unlike more traditional forms of origami, it does not have a consistent system of diagramming or even a vocabulary of its own. In this book, Ben Parker addresses this problem. The interested novice will find important information to get started folding tessellations, from techniques for folding the grid, to the basic twist folds, to composing complex patterns of multiple twists.

The advanced folder will find a thoughtful approach to defining and describing the geometry of origami as revealed in tessellation. Whatever level of experience readers bring to this book, they will find something to challenge them. Six simple twists are only a starting point for Ben’s analysis of tessellation. Ben brings artistry and an analytic perspective to this subject, and provides much useful information and inspiration."

—Joel Cooper, Origami Artist

Table of Contents

The Six Simple Twists

The Basics and Preparation

How Tessellations Differ from Traditional Folding

Fold Bias and Manipulation

How to Read the Exercises

Obtaining a Hexagon

How and Why to Fold a Grid

Basic Pleat Design

Diagrams of the Six Simple Twists

How to Use the Six Simple Twists

Intermediate Gridding

Tessellation Basics, without Folding

Applying Tessellation Knowledge to the Paper

Your First Tessellation

Your Second and Third Tessellations


Back-Twisting and Releasing Pleats

Pleat Flattening

Different Types of Pleat Formats

The Referential Method of Tessellation Formation

Flagstone Tessellations and Offsetting the Pleats

Twist Decorations and Progressions

Twist Expansion

Beyond the Six Simple Twists

The Next Step

Designing a New Tessellation

Describing Twists

We Don’t Care about the Middle

Tip for Tricky Twists

The Database

Final Thoughts

For Further Study

About the Author

Benjamin DiLeonardo-Parker is an origami pattern artist. He has taught and exhibited at origami conventions and art shows throughout the United States and at La Escula-Museo Origami de Zaragosa, an origami museum in Spain. He also uses his art career to explore other activities, including electronics, woodworking, and alternative photography. He studied French and Italian language and literature at the University of Pittsburgh.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Recreations & Games