This is a crazy one. I don't really remember how I arrived at this particular pattern. Most likely, I was just messing around with a small experimental grid to see what caught my eye.  I guess that I was feeling especially bold at the time I landed on this idea. This ia definitely an advanced origami tessellation .  Some of the shapes in this one are almost impossibly small. At least, for the size of paper that I normally use. Which in this case was standard 8..5 x 11 inch printer paper. I figured tant paper would be too thick to let me make such teeny tiny folds. And also, that it would be too thick to allow for all the overlap that was required. For the most part, that worked out to be true.  Of course, the converse of that is, such thin paper stresses easily and doesn't stand up well to too much fussing and cajoling.  Anyhow, it turned out mostly successful. Could've been neater, but considering how tricky it was, I'll call it a win just that I was able to finish ...

 This is a reverse engineer of a  flagstone tessellation designed by Joel Cooper. I do not know it's name. I was not aware of its existence until I was emailed by a reader (Jessie) asking for help solving how to fold it.  I sent them a couple of diagrams. The first of which, I thought at the time was good, but was not right at all. Sorry! The second time, I was pretty close, but later realized, it was still not quite there.  Finally, I decided to just try folding it myself to see if that could help me figure it out once and for all.  The mostly successful result is shown above. It's somewhat scruffy because I was still solving as I was working the paper that I used to fold it.  I will unfold it soon and use it to create a finished crease pattern. Then I'll upload it here.  The design is three interconnected rhombus stars which are surrounded by open back hexagons. The design is repeated by adding new triads of rhombus stars.  I found it a confusi...

I haven't posted an advanced tessellation in a while. So here is a new one. It's an unusual pattern that also features some very small folds. There are tiny rhombuses and compressed triangles with which to contend. It is an original origami tessellation that I just recently created. The main shape is a six sided polygon of alternating edges. One pleat bisecting the grid, then one pleat following it and so on until you close the loop.  One the other side are open back hexagons and some oblong six sided parallelogram-ish shapes.  When I folded it the small rhombuses weren't actually on the front at first. It was after I had completed it that I realized I could reverse some of the folds to bring them up to the top.  There are some very tight folds and also some very small ones, which is why I believe this to be an advanced tessellation .  Evenso, I actually used thin printer paper because I figured thick paper would never let me make some of the tighter/smaller fold...

 This is a wacky one. A just to see if I can pull it off kind of tessellation . For the most part, I was able to do so successfully. Could be better, but it's a tough one .  It's basically just layers upon layers of elongated hexagonal folds around open back hexagons.  I used thin paper because I figured I would never be able to layer everything using anything thicker.  When I first plotted it out using a small grid of only 16 pleats it seemed so easy and worked beautifully. However, as with many tessellations , adding more repetitions made it exponentially more difficult.  The crease pattern looks pretty innocent, but it's anything but.  As I was folding it, I found myself wondering if maybe medium thickness paper might've been a better choice.  Most of the folds are mountain folds with the exception of the open back hexagons and a set of convergence points. In the diagram the blue dots indicate where the paper should be tucked under. When I drew it I...

  As promised, this is my additional manipulation of my Inclined Planes Tessellation . It's the same design posted previously, but taken a few steps further.  Essentially, all I did was take a bunch of the folds and reverse them.  Reverse folds are pretty common in standard origami. Like when you're folding a cat or a sheep. They are less prevalent in origami tessellations , but they are sometimes used.  A reverse fold is just as the name implies. You turn it inside out. It can be employed in many ways to change the structure of a tessellation.  However, with your typical twist based folds, reversing is just a matter of chocie during the inital process. Many of the folds are an either/or type of deal.  With some more complex tessellations you may only have that option after the folding is complete. As is the case here.  Robin Scholz's triphilia is a really good example.  This tessellation is another one that takes that same approach.  Fil...

 This tessellation is a sort of  a semi-original . The center point is something I saw on the Insta feed of Arseniy K. But I then took the rest of the tessellation in my own direction.  When I first saw his tessellation , I was struck by how creative his central idea was. It just made me want to use that as a jumping off point.  This is the result.  The idea of his that I loved so much is rhombuses around an open back hexagon. But instead of twisting off the axes of the hexagon, the rhombus are situated right up against it. With this setup you can tuck half of each rhombus kind of under itself to create the central pattern.  It's a finnicky design with lots of overlaps and tricky intersections.  Even after I mapped it out on some grid paper, I still needed to do a first fold using basic paper just to get a better understanding of how the folds would all work together.  It was only then that I moved on to the fancy paper and executed the fi...

 I haven't done a tricky collapse tessellation in a little while. So, this is a new one I created. It begins with rhombuses around an open back hexagon. From there, I add two more rhombuses progressing outward from the center ones. Then it's time to repeat.  In order to fill in the remaining spaces, I used triangle collapses.  I do love a good set of 3 or more triangles tucked into each other. It can be very hard to execute, but it's worth it.  You don't need to stop at three rhombuses. You can keep going. I haven't mapped it, but I would guess that it would require more and more triangles in the gaps. Of course, the more triangles that you try to tuck into each other the more difficult the tessellation becomes. Isn't that the fun of it, though? This is a difficult tessellation , bordering on advanced . I do have a crease pattern. I haven't yet taken a photo of it, but I will try to add it soon.  Filed under: January 2025 Origami Tessellations

Breaking Infinity by solvingorigamitessellations.com  This tessellation was inspired by one by Peter Keller. His design was large cubes formed by  rhombuses.  In my case, I did a series of six diamonds formed by rhombuses. I used the idea I learned from his design to separate the 'shapes' of the flagstone by leaving a larger gap in the appropriate places.  I would call it a flagstone tessellation even though the larger gaps technically disqualify it. The overall concept still fits the category.  created by solvingorigamitessellations.com The reverse side is just as interesting as the front. Featuring linear rows of rhombus wings with six triangle twists between each of them.  The first time I did this, I mapped the central point incorrectly. I used that mistake to help me determine the right way to do it.  The second time around, it all worked out quite nicely as can be seen here.  This is a difficult tessellation, as are all flagstones. I might...

created by solvingorigamitessellations.com This tessellation reminds me of ones I've solved by Arseniy K because of the way the shapes interact and layer upon each other. This particular tessellation, however, it is an original origami tessellation that was created by me.  Despite being the creator, I found this hard to execute. Everything is on top of each other. It's a difficult task to get it to actually work as envisioned.  It turned out pretty good considering I was kind of learning to fold it as I went. A second attempt would, no doubt, turn out better.  created by solvingorigamitessellations.com These kinds of intense tessellations rarely photograph as beautifully as the simpler ones. The light simply doesn't shine through because of the thick paper required and the multitude of layers. It's a great shame because these are some of the most extraordinary tessellations of all.  They require patience, perseverance and a deep understanding of all the nuances of...

Kaleidoscope Tessellation by solvingorigamitessellations.com  This tessellation is a variant of my ' Wheel of Fortune' tessellation . Kaleidoscope  actually came first. Then I later, decided to try the same idea, but spacing things further apart and that became 'Wheel of Fortune. Kaleidoscope is a dense configuration of small and 1.5 triangle twists all precariously overlapping each other.  On the other side there are open back hex twists and small right triangles.  It's a very tight fold. My paper wasn't really too keen to cooperate, but it was mostly successful nonetheless.  It's an advanced tessellation to be sure. It requires sturdy paper.  It's not the prettiest of  origami tessellations , but it's interesting with all abundance of triangles smothering and banging into each other.  I knew that before I started it wouldn't be a showy, ooh and ahh design, but I like the concept and wanted to see if I could pull if off. Layered tessellations ar...

an original tessellation by solvingorigamitessellations.com  This is an original tessellation idea that I had that I really like. It's somewhat complex and therefore difficult to fold.  This is my first attempt. While I was able to complete the design, it was not as successful as I would've liked.  I don't know if it was the weather or some other factor. But for whatever reason, the paper became very weak half way through folding it.  created by solvingorigamitessellations.com I had hoped to be able to re-orient some of the folds to create a more consistent design, but the paper was just too far gone by the time I'd gotten everything into place.  At some point, I would like to give it another go and see if I can execute it more to my satisfaction.  The idea itself, is one that I really like, so I figured that I'd share it now.  It's an intense array of trapezoids and triangles all collapsing into one another.  It's a lesson in expectations. Espec...

Tessellations: August 2024 an original design by solvingorigamitessellations.com Rhombus stars are a pretty common element in origami tessellations . They're a great starting point for a vast array of possible designs.  In this case, I added several triangle collapses to the exterior of the central star before repeating.  I've been a little obsessed lately with how many ways I can find to add large series of triangles in the spaces between various other shape clusters.  This is another original tessellation design that was born out of that.  It can be quite difficult to get all those triangles to cooperate with what you're trying to do. Even with high quality paper.  an original design by  solvingorigamitessellations.com It is doable though.  My preferred method is just to let the folds decide which way they would like to land and not concern myself with the ups or downs of each shape.  Then, I'll come back later and adjust everything to suit th...

Filed in: Origami July 2024 Solvingorigamitessellations.com   It's time for another advanced tessellation . Those are my favorite kind. Rising to the challenge is oh so satisfying. And on so many levels.  There's the conception. Coming up with idea. Solving to make the idea work.  Then there's actually executing the plan. It can be a long process, but it's almost a zen experience. Going through all the steps. Slowly, but surely watching your hard work become what you had envisioned.  It's a tedious and wonderful journey.  What makes this particular tessellation so difficult are the series of triangles that are all interconnected. It's not an easy task to get them all working together.  The center of the tessellation is trapezoids around a small hex on the back. Then I add another set of trapezoids overlapping the first at a 90 degree angle. In order to repeat the pattern another set of trapezoids tucks into them. From there the inner module can be repeat...

I have learned that the contents of this post have been plagiarized at a site called openai24 dot com.  Thank you to Peter Whitehouse for informing me of the situation.  I have informed the hosting company/domain registrar of the copyright violation and hopefully they will take action sometime soon.  Please know that this is my original design and I am the artist who conceived of and executed it.  If you're feeling as outraged as I am by this blatant theft feel free to leave a comment on their site condemning their actions. Or write an email to their hosting company (namecheap dot com) to express your displeasure.  Thank you.  So, I decided to buy some fancy tissue foil paper from France. I had this tessellation idea that I wanted to do, but I couldn't quite get it done using any of my usual papers.  From what I had read online, tissue foil is supposed to be really great for tessellations because it's both thin and resilient.  This tessellation ...

This is a tessellation that I came up with after having done a very similar one. That first one ( Controlled Chaos Origami Tessellation ) had exceedingly small rectangles, which made it nearly impossible to execute cleanly on both sides.  In this case, I made the rectangles bigger and it became infinitely more manageable.  I'm pretty sure that I've seen this one before. I think that I've seen it done by  Daniel Kwan as a crease pattern posted to his flickr account.  I was not using that crease pattern while conceiving of this, though I did have some recollection of having seen it in the past.  The front is all right triangles.  The back side is small offset hex twists, the aforementioned rectangles and small triangle twists.  Even with the larger rectangles, it's still a difficult to fold tessellation. The triangles and rectangles overlap each other.  My crease pattern diagram is at the end of this post. 

 This tessellation is interesting because I actually messed up the pattern that I had created. It still looks really cool, but it is asymmetrical.  My original diagram called for all the repetitions to match each other.  This is also another difficult to execute to design. Regardless of whether you follow the pattern precisely or you accidentally deviate from it as I did, it's a pretty intense to fold.  My tant paper actually tore a little bit in one spot from all the stress.  The center is easy enough to get situated, but after that all bets are off.  It starts with an open back hexagon around which are situated interconnected rhombuses.  From there I just add a whole lot of triangles and more rhombuses. The pattern is meant to be three triangles and two rhombuses and then repeat the center.  I have included my crease pattern diagram at the end of this post. 

This tessellation was a pretty ambitious undertaking. When I plotted it out on some grid paper, I knew that it would be kind of crazy, but I loved the design too much to not try.  At the center point is an open back hexagon. From there I add three trapezoids and three triangle collapses.  Then I add another layer of trapezoids.  This in turn, creates the opportunity to add a whole bunch more small triangle collapses. Ten total per third edge.  It is ridiculously difficult to get all those triangles to work together while also making them behave nicely with the repeating trapezoids.  Obviously, it is doable, because I did it, but it's pretty tedious.  Well worth it though, for the end result.  I actually messed up the orientation for one of the triangles. Can you spot it? The nice thing about folds like this one is, once you get everything collapsed, it's not hard to re-orient the directions  of some of the folds if you need to do so.  Wh...