Stars in Stars Origami Tessellation

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In the beginning, everyone learns origami from someone else.

As you become more advanced, you may start to rely more on recorded tutorials, books, and other diagrams.

At some point, you start creating your own designs - and then how do you learn more?

Well, I've learned a ton over the last few years of designing tessellations from other tessellation designers.

And not just in the regular meetings of the Community for Creators (CFC) or the informal Math, Origami, and Beverages group (email me for an invite!) - I've learned many new techniques, structures, and ideas from following other tessellation designers on Instagram.

My first attempt at something like Stars In Stars was on a mere 16-fold grid, so I wasn't quite able to see the repeats and I seriously doubted that it would work out.

However, Dirk Eisner was working on a similar idea, inspired by a tessellation I taught with Origami Maniacs.

When he posted his solution, I was able to immediately see how to continue the piece I was designing - and that it could be spaced more closely together too!

Clustering

You see, this design hinged on the behavior of clusters of twists - not just combinations of individual twists.

Just like Emergent Hexagons, this tessellation is built on clusters of four triangle twists grouped together.

These clusters are themselves rotationally symmetric - this means that there's a choice of a center twist and an outer twist, but every outer twist is the same - and can be used in many of the same ways you would use a single twist.

So, you can have these clusters mirroring their neighbors or alternating front and back - no matter what your choice of central and outer triangles are!

Look closely - can you see that there are three closed triangles for every open triangle?

Can you see that these clusters are also repeated on the back?

 Same on Both Sides

One of the things I'm seeing in this tessellation is a whole lot of 3:

- 3 small triangles making a pyramid

- 3 large triangles around each cluster of small triangles

- 3 clusters of small triangles around each large triangle

- 3 open triangle holes around each cluster of small triangles

- 3 closed triangles on the other side of the closed clusters

- 3 directions on the underlying grid

So, why is this called Stars in Stars instead of Triangles in Triangles?

Partly it's because the six triangles in a star are more true to the actual structure, and partly because I name my tessellations immediately after folding the prototype and I very rarely see many repeats before naming - or change the name after folding more.

Also, every single tessellation in this tiling uses only triangle twists - it's all triangles all the way down!

Prototypes and Practice

I see three different ways to fold tessellations, with three different purposes.

Most of what you'll see on Instagram (or this blog!) are display pieces - planned projects based on a crease pattern made to be photographed, framed, or otherwise displayed.

But as I alluded to earlier, this isn't the only way to fold tessellations - prototypes and practice pieces are essential for learning.

Small grids - I use mostly 16-fold - are great for trying out new ideas that you're not sure of.

I'll often try two prototypes of the same structure with different spacing, or two prototypes of the same pattern with a different center, to see what backlighting effects are available.

Medium grids - usually 24- or 32-fold - are excellent for practicing a new skill or pattern.

These are the typical sizes that I ask my students to bring to workshops and tutoring sessions, where I teach a new skill or pattern!

Custom grids - often rotated (like Stars in Stars was) and with odd divisions - are best for display pieces so you can control the border, decide how many repeats you want, and generally tailor the grid to the particular pattern you're folding.

So, the three distinct ways to fold tessellations are prototype, practice, and display, but the vast majority of what gets posted on the internet are display pieces - which may lead you to think that everyone else just magically got good at tessellations without practice!

That is so far from the truth.

In between the beginner and master stages of folding tessellations is a ton of practice and skill building and pattern recognition.

Now, it is possible to do all that work on your own - you can reverse engineer patterns from now until the end of time - but there's one question that can't be answered by looking at photos.

"Am I doing this right or is there a better way?"

Like most skills, tessellations are learned fastest when you have feedback on what you're doing and suggestions for improvements.

It's very hard to reverse engineer anything if you don't understand the basic structures - much less pick up on a new general pattern from someone else's design.

But once you are able to see the structure from a photo you are free to fold anything you see.

So if you're ready to take your tessellation folding to the next level, I can help you get there.

The fastest way to accelerate your tessellation folding skills is tutoring - and you can sign up here!