Levels of Origami Tessellation Difficulty

Origami tessellations are patterns created by folding that can repeat infinitely on a single sheet of paper.

In the origami community there’s an additional distinction between corrugations and other tessellations, where corrugations are patterns folded so you can still see the whole surface of the paper while in other tessellations some parts of the surface are hidden.

Patterns where some parts of the surface are hidden are often folded flat and usually use structures called ‘twists’ that rotate certain shapes in the paper.

These twists are referred to by the shape that they rotate and the size of the hole that you see on the opposite side of the paper, so the Stars in Stars pattern pictured below is made up of closed and open triangle twists folded on both sides of the paper.

These patterns are often shown with light shining through them (backlit), which shows how the layers have accumulated during the folding process.

Herringbone Corrugation (tutorial), traditional; Stars in Stars (tutorial), designed by Madonna Yoder

Usually tessellation patterns are documented by crease patterns instead of by step-by-step instructions, although you’ll also find video tutorials and books of step-by-step instructions for some patterns.

Since these patterns can repeat forever, all instructions must necessarily be a subset of the true pattern, and likewise the amount folded is a subset of the true pattern.

This means that you get to choose how many repeats you want to fold of each pattern depending on your skill level, the size of your paper, and how many grid divisions you want to fold.

Tessellation Folding Methods

There are two main approaches to folding origami tessellations: you can fold all of the lines that will be used by the final pattern first before collapsing it into shape or you can fold one twist at a time using a background grid of folds to define the pleats coming out of each twist, which creates the folds in the final pattern as you go.

Sometimes it’s necessary to precrease a tessellation, like when you can’t fit the pattern on top of a background grid or when there’s so much overlap between twisting shapes that it would be impossible to fold one twist at a time.

There’s a variety of options for precreasing these patterns, from a laser cutter to a Cricut machine to a ruler and ballpoint pen on a printed pattern.

If the crease pattern is on a background grid then folders will usually fold the grid first before creating pinch folds in the appropriate locations, often using a bone folder.

Rattan Weave, folding and crease pattern, by Robert Lang, photo from https://www.techbriefs.com/component/content/article/51671-folding-nasa-experience-into-an-origamists-toolkit

Usually it’s much easier and faster to fold your tessellation patterns one twist at a time.

These patterns are always based on a background grid, which must be folded before starting to fold the pattern, and all of the off-grid folds are part of twists.

There are many different shapes and sizes of twists and they can be folded on either side of the paper in many possible arrangements of shapes, so you’ll never run out of new patterns to fold!

Cluster 6 Front (tutorial), folding and crease pattern, by Madonna Yoder

What makes some patterns harder than others

Just like we see in other kinds of origami, there’s a huge range of folding difficulty inside of the category of twist-based tessellations.

Tessellation patterns are harder to fold when the twists used are harder to fold, when there’s more distinct positions in the part of the pattern that repeats, and when the twists are folded closer together.

These are actually three different kinds of difficulty (hard until you practice it, hard to hold in your head at the same time, and hard to physically manipulate the paper) with three different solutions (practice pieces of the pattern in isolation, use drawings to offset the mental load, and practice tricks to move layers of the paper around).

When you’re learning to fold origami tessellations and trying to improve your tessellation-folding skills, it’s better to increase only one area of difficulty at a time so you can still have fun while folding a challenging new pattern.

This means that you either need to follow an established curriculum or learn how to identify these levels of difficulty for yourself.

I’ve designed over 600 twist-based origami tessellations, so I developed this rubric for rating the difficulty of my own designs.

It measures twist difficulty and structural complexity in three categories each, from simple to moderate to advanced.

Some of these categories are still quite broad and I’d recommend practicing several patterns in a category before moving on to the category below or to the right.

For example, if you’re starting with patterns matching the 1A criteria (two alternating simple twists) I’d recommend practicing several patterns, including some with twists on opposite sides of the paper, before moving to patterns with rhombus or right triangle twists in alternating structures or moving to patterns with simple twists in more complicated arrangements.

Then I’d recommend practicing patterns matching the 1B criteria and patterns matching the 2A criteria before moving on to patterns matching the 2B criteria.

Patterns with twists that are very close together (like flagstone tessellations) can be considered to have an extra difficulty star in addition to their twist and structure difficulty rating.

From Easier to Harder

Grid-Only Patterns

Goran’s Wave (Tessellation Foundations), Dragon Heart by Helena Verrill (tutorial)

The easiest patterns to fold are ones that use only grid lines without adding any additional folds to create the final pattern.

Folding the background grid precisely is the foundational skill for folding any origami tessellation by hand, and there’s more to folding grids than you might think (folding on squares/hexagons/rectangles, division by 2/3/5/etc., diagonal grids, and more).

All of these skills are taught in the free Tessellation Foundations course from Gathering Folds along with eight projects that introduce pleat management skills and two basic twists.

Test your skills at this level with a tutorial for Helena Verrill’s Dragon Heart tessellation:

Basic Twists in Basic Arrangements

Closed Square Weave and Closed Triaxial Weave, traditional designs (Basic Twists Bootcamp)

Once you’ve mastered patterns that use only grid lines, it’s time to move on to patterns that use basic twists in basic arrangements (the 1A category on the rubric).

The eight basic twists of origami tessellations include the closed and open forms of square, equilateral triangle, and hexagon twists and the closed forms of rhombus and right triangle twists.

Each of these twists can be used in alternating arrangements where there’s only two twists to keep track of and the pattern repeats very quickly.

The Basic Twists Bootcamp course from Gathering Folds focuses on these alternating patterns, with 10 lessons that introduce each twist and teach a pattern that uses that twist.

Test your skills at this level by folding an open square twist and by alternating hexagon and triangle twists on opposite sides of the paper:

Basic Twists in Moderate Arrangements

Artificial Reef (tutorial), Lens Garden (tutorial), designed and folded by Madonna Yoder

There’s so many different ways to arrange basic twists that you could keep folding at this level forever (1B and 2B on the rubric).

Whether you’re using the same structure of shapes in a new way (like Artificial Reef) or changing the structure while using the same pattern motif (like Lens Garden compared to Lens Stars), there’s always more patterns to figure out.

The skills at this level are more about recognizing symmetry points, reading crease patterns, and building an awareness of how the structure of the shapes impacts the folding order of the pattern.

These are precisely the skills taught in the Tessellation Starter Sequence course from Gathering Folds, which covers everything from gridding to folding in moderate structures over the course of 50 video lessons.

Many of the patterns in the free Advent of Tess series from Gathering Folds also fall in this category, as do the alternate endings of these patterns that can be found in the Advent of Tess ebooks.

Test your skills at this level by folding Artificial Reef and Lens Garden:

Advanced Twists

Spilled Bricks (tutorial) and Mix Depth Jewels (tutorial), designed and folded by Madonna Yoder

There are many ways to create variations on the basic twists that lead to new tessellation designs (1C in the rubric).

Hybrid twists and mixed-depth twists can be used to create new decorative motifs and new structures of shapes, respectively, all of which lead to an explosion in the number of possible patterns.

Each new twist that you learn will unlock a whole new set of patterns - and there’s dozens of twists available.

The techniques for making and using advanced twists are explored in the Advanced Twist Techniques course from Gathering Folds, which includes crease pattern template files so you can come up with your own advanced designs.

Test your skills at this level by folding Spilled Bricks and Mix Depth Jewels:

Flagstone Patterns

Open HT6 Flagstone (tutorial), traditional and Star Power (tutorial), designed and folded by Madonna Yoder

Some of the most appealing origami tessellations are flagstone patterns where the entire surface (of one side) of the paper is covered in twists.

These patterns may look simple, but they all have at least as many twists on the opposite side of the paper as on the flagstone side and the dense spacing of the twists makes them particularly hard to fold (often 2B in the rubric, with an extra star for dense spacing).

Just like all of these other categories of patterns, there’s a wide range of difficulty among the flagstone patterns and it’s worthwhile to build up your skills through a curated sequence of patterns.

The Flagstone Tessellation Techniques playlist from Gathering Folds provides that sequence and you can test your skills with flagstone patterns by picking the tutorial of your choice:

Even Harder Patterns

Summer Islands and Coronas, designed and folded by Madonna Yoder

One of the best things about folding origami tessellations is that you’ll never be left without a challenging pattern to fold (categories 2C, 3A, 3B, and 3C in the rubric).

Interestingly, the mindset needed to figure out how to fold these complex patterns is almost identical to the mindset needed to design new ones and once you learn that mindset you can always come up with harder designs with more distinct twist positions, more advanced twists, and more flagstone motifs.

Thinking like a designer is the focus of the Tessellations by Tiles course and the Tessellation Academy membership from Gathering Folds, where you’ll learn the options available for a different structure of shapes in each lesson.

Test your skills at this level with Clematis and Counterbalanced:

Infinitely many designs

Quicksand and Inner Workings, designed and folded by Madonna Yoder

There’s a few different ways to prove that there are literally infinitely many different origami tessellations.

My favorite two proofs are that there are infinitely many structures of shapes that can be used to design tessellations and that you can always apply symmetry in infinitely many different ways to these structures.

My job as an origami tessellation designer is to find and communicate my favorite patterns from that infinite potential.

So far I’ve found over 600 tessellation designs and you can see crease patterns for all of them inside of Tessellation Garden, which you can sort by pattern name, structure, and difficulty rating and see whether there’s a video tutorial for each design.

My design style focuses on patterns that can be folded one twist at a time on a grid, especially when those patterns have fun coincidences or set a familiar motif in an unfamiliar setting.

Learn more about structures for origami tessellations here:

Learn more about symmetries used in origami tessellations here:

Summary

It’s hard to know where to start with a goal like “learn to fold origami tessellations” because there are so many different kinds of tessellations at so many different skill levels.

While there’s no limit to the number of possible tessellation designs, the number that are beginner-friendly is relatively small, and they’re not the ones that you’ll see modern tessellation designers posting.

Now that you’ve seen some examples at different levels of difficulty it’ll be easier for you to pick out patterns that are closer to your current skill level and to have more success in folding them.

I’m also happy to recommend specific patterns for you as you go through your tessellation folding journey - send me a DM or drop a comment on one of my designs you’d like to learn on Instagram and I’ll help you on your way!

You can also find more examples of each of these kinds of tessellations and practice assessing their difficulty levels here: