Edited by Scott Summers

“Six Simple Twists,” by Benjamin DiLeonardo-Parker, is not your typical origami book.

While this book does contain some diagrams, you’ll find far more text- and image-based references than traditional folding instructions.

This is a complete course in hexagonal-based tessellations and may be the best platform to fully understand this narrow field of origami.

Before you get started, you’ll need to retune your expectations. This book will provide the knowledge and skills you need to create tessellations, but it is a book focused on techniques, not models.

To be able to make the models, you have to understand the basics (Chapter 1), build a repertoire of solid techniques (Chapter 2), and deepen your understanding of the tesselation process (Chapter 3).

However, there is a price for such a comprehensive book. There are no step-by-step diagrams to show you how to fold a specific tessellation. You will have to read it more than once — and I do mean read — in order to fully grasp each concept before you try your hand at completing the projects.

The Technicalities

  • Number of pages: 307
  • Number of diagram pages: N/A
  • Number of models: N/A
  • Languages: English
  • Book Size: 8 by 10 inches
  • Paper Quality: High
  • Difficulty level: Beginner to high intermediate
  • Where to find it: Amazon, The Source


This book looks more like a high-school textbook than an origami book. It is heavy on text and short on diagrams. The lack of diagrams is compensated for with images — a lot of images.

The tendency to describe every step with words was tiresome for me, but I am sure there are readers who need this verbalization, especially if they are new to tessellations. Still, this over-texting results in strange cases where the text describes an image that is five pages ahead.

Chapter 1 is for absolute beginners. There are 11 pages describing how to make a grid of 16 in this chapter (and there are 2½ additional pages explaining how to create a grid of 32 in Chapter 2).

Once you get over that, Chapter 1 becomes a comprehensive guide for all the basic maneuvers you need. There are no complete projects, but you can unfold the model and use the same grid to practice the next maneuver.

Chapter 2 is the real thing. This is the place to learn and create some projects. Having learned the ABCs in Chapter 1, it is time to create a few folds of your own.

Here, you can learn how to perform a nub (rhombic twist), twist sink, back-twist, and other moves. Altogether, these are powerful and highly versatile techniques to have in your repertoire.

While Chapter 1 focuses on basic, academic instruction, Chapter 2 relies more on additional folding experience and assumes a much higher skill level.

Through this chapter, there are some sequences you could call “projects.” Yet, you do not get the complete picture. The author leaves it to you to determine the ideal starting point to achieve the size, grid, and spread of your desired module.

As you learn each pattern, the author includes various detours to answer specific questions and solutions relevant to a specific project. For example, a division of 36 is shown right after the Tulip Split Tessellation, although this is not the most logical or “orderly” place for it.

My personal preference would be to have all the grid instructions included together within the same chapter, not spread through the book, but I do see the benefit of having this extra knowledge when it is needed, after you have enough experience with simpler grids. This fits more with the concept of the book as a course rather than a collection of projects.

It is not an easy task to write a book that emphasizes technique rather than projects. It asks for more mental agility and discipline from folders, as well, as they must understand the more complex designs and overcome whatever obstacles they encounter along the way by studying the single molecule in the image.


There are no real diagrams. Instead, you have photos that show the details, along with step-by-step instructions. The major notations on the photos are numbers that represent the correct gap between two elements. Here and there, you will see thick lines designed to represent specific creases. Rarely, you will also see indication arrows.

The images are small and dark — far too dark to study details. This combination creates situations where it’s almost impossible to see what is going on. The images are critical to the flow of this book, and for a book that tries to teach mainly by using images, you may find yourself asking how this can be.

Take a look at page 127 in the photo below. Image 2.21.2 (center) has three arrows on it. Can you spot all the three? You can if you have the digital version, but in the printed version (at least, my review copy) the result is so dark, you just cannot see them.

If mine is a representative copy, it seems that CRC Press failed to control the print quality. I do hope this is not the case, but this was the copy I got.

Photos in the print edition are way too dark.
The original, digital image quality is much brighter than the printed version.

Unlike with traditional diagrams, the text runs in continuous paragraphs, rather than below each illustration, and refers to images by their number.

I am sure it was difficult to proofread this book, because I did find mistakes, but they were a minor nuisance.

The main problem is that you’re required to move your eyes back and forth from text to image (sometimes located on another page) in order to understand a technique. Often, this makes the instructions difficult to follow.


I tried my hand with the Shift Rosette Tessellation (photo of the model in progress above, and of the completed model below).

The first split (where a mountain ridge becomes two ridges) is four spaces away from the center. While it’s easy to count four from the center, the numbers are shown on the image of the completed step (second photo) rather than on the image of the paper before the move is made (first photo).

This is not easy to understand, and I was not sure which number related to each specific intersection.

I had to read and try my hand twice before everything was sitting correctly.

The natural behavior of the paper helped me a lot, and once I got it, the next steps were easier and quicker to grasp. As always, there is a sense of achievement once you manage to do it, but I am sure another mid-step image would have helped.

Shift Rosette Tessellation, single molecule.


This is the second edition of the book, but the makeover is so complete that we can consider it as a new one.

The scope and depth of the book is huge, and I am sure it will appeal to those who fancy hexagonal-based tessellations.

Yet the book raises a conflict. The skill level required to achieve and enjoy the content is high, and the only way you can achieve it is by using this book, as there is no alternative.

Because the book is comprehensive, however, I do believe that a determined novice folder could reach the potential heights demonstrated within.

Unfortunately, the quality of the images is not on par with the complexity of the folding process. This will cause moments of despair and frustration. I had too many moments where I tried to enlarge the images with a two-finger gesture, as I would have on a digital device. Unfortunately, this doesn’t work on paper!

Bottom line: For tessellation lovers.

Author Interview - The 5 Essential Questions

Q What is the essence of the book?

A The book is designed to teach my approach to origami tessellation (or pleat pattern) design and is divided into three chapters, each very different in purpose.

Chapter 1 goes over the fundamentals and introductory definitions, including how to grid and how to create the titular “six simple twists,” and it invites the reader to become comfortable with the processes.

Chapter 2 demonstrates how to use the six twists in different contexts — surrounded by other twists, with various pleats interacting — and different modifications of the twists.

Chapter 3 leads to more abstraction: ways that other artists have used these twists to remarkable effect, ways to catalogue and document twists, and ways to fundamentally understand what a twist is.

With these differing focuses, I suppose the essence of the book is to guide the reader through learning about pleat patterns from the basics to as far as they want to go.

Q Who is your target audience? What makes your book suitable to this audience?

A Given the scope of the book, different chapters ended up targeting different audiences.

Chapter 1 is the fundamentals, focused on building the reader’s vocabulary, and is targeted to those with little-to-no experience with origami or origami tessellations.

Chapter 2 is for those who have some experience with pleat patterns and want to learn new techniques for developing their own.

Chapter 3 is for folders who are interested in developing their mathematical understanding of twists, and want to cultivate their intuition on why twists happen the way that they do.

Q What changed in the second edition?

A A lot. This ended up being a top-down rewrite of the first edition.

In terms of scale, the second edition triples the number of pages and color photographs.

The photographs are clearer (not perfect, but better), and larger on the page. Also, at some point, I realized that if I were to diagram with numbered steps, each with a single photograph, it would be very difficult to see what a given maneuver was. For this reason, I decided to use step clusters, which used two to four photographs to show the setup, execution, and result of a given maneuver.

I really focused on getting definitions in place and adhering to those definitions as closely as possible. One of the difficulties for beginners is not having a cohesive vocabulary to fall back on, and everyone seems to use terms slightly differently.

A lot more time is spent on the foundational material in Chapter 1 to allow easier access to the pattern diagrams in Chapter 2. Without that foundation, it would have been too difficult to approach the more complicated patterns. This includes different ways of approaching some of the six simple twists and adds the concept of the “standing form” of a twist, which acts as a stopping place for a folder. Also, the notation system was introduced in Chapter 1 to give the reader a baseline for the analyses in Chapter 3.

Included in Chapter 2 is my counting method for spacing one twist off of another, which should help folders refine their understanding.

I also included other artists’ works in the gallery, and brought in math consultants to assist me with developing a notation system for pleat intersections, the latter of which is the biggest addition to the first edition.

Q What was most enjoyable in the process of the making of this book?

A Whew, that’s a tough one.

Toward the height of it, it was almost an obsession; I’d spend every moment I could at a local coffee shop typing and editing, and all of my thoughts were consistently on the best ways to explain something.

But I think the most enjoyable part with the development of the notation system and Brocard analysis with Matt Benet and Andrew Fisher — all of Chapter 3.

I learned things about twists that I’d never considered, or knew intuitively but could never describe, and I could finally write down difficult concepts in an intuitive way.

I asked CRC Press for a six-month extension so that I could get all of these concepts in there. It was some of the most fun I’ve had practicing origami.

Q What was left out of this book, and why?

A There wasn’t much left out; I tried to make sure to get everything I wanted in there.

There were a couple of patterns I had intended to include (like my geometry in the Jungle Pattern ), but I ultimately decided they didn’t contribute to further understanding and were just variations of techniques already present in the book.

It would be better for the reader to come across those patterns themselves.

Editor’s Note: Ilan Garibi is the author of Origami Tessellations for Everyone.


January 26, 2021 - 11:38pm teariana

I've been thinking of trying tesselations, I need both writing and photographs though I am better with crisp, concise explanations. The dark photographs would be a deal breaker. I think whoever does the graphics needs to look at photographs of good origami instructions. Lighting is critical, also the color and texture of the paper and how it reflects light needs to be considered, may need to use a paper other than what is generally used. The cover photograph is beautiful, I have a feeling this was professionally photographed while the others may have been self photographed. You can do both but need to research carefully and take time setting up each shot. Yes it's difficult but it is definitely possible.