When I'm stuck for ideas for my own tessellations I like to try to solve those of others. This one is by gatheringfolds. It's intriguing  in that it's mirror images on either side. She has a talent for creating/finding these kinds of designs.  It's composed of open back hexagons and triangle clusters.  I used yellow 20 lb printer paper to fold it.  When I first set about to solve it I was confident I knew it right away. I did fumble a bit, but  with a little persistence the solution coalesced.  Once I knew how to proceed it was still a little finnicky to fold, but nothing too difficult.  It's a wonderful design that I enjoyed figuring out and recreating. Kudos to her on another great idea.  My crease pattern is included at the bottom. 

 Way back in December 2021, I solved a tessellation by Arseniy K and posted it as Chasing the Folds Tessellation . Yesterday, I solved it again without realizing that I already had.  This time around I used a nicer paper and was able to take cleaner pictures.  I also drew a pretty clean crease pattern for it as well (see below). For some reason, there isn't a crease pattern in the original post.  His version used longer arms and therefore bigger triangles. My version is more compact.  It was maddening to fold. I probably should've stuck with original, larger  configuration. But It is done. Again.  No telling if I'll forget again and do it a third time. 

 This tessellation is a little different than my usual. Just an odd idea that I kinda made work, even though it didn't really want to do so.  Right triangles arranged around central hexagons.  It's very similar to open back triangles around hexes, except everything on one side is a little askew.  Sometimes I get stuck on the notion that tessellations have to follow certain rules. But really, they can be whatever you can imagine and can execute.  I believe I have a crease pattern. I just need to find it and upload a pic. Hopefully soon.  Update: added crease pattern below.  If I remember correctly, when I folded the model I actually moved the right triangles one pleat closer to the hexes  than is drawn in the sketch.  Either way works. 

 I found a picture of the crease pattern for this tessellation in my google photos.  It was from a few years ago. I don't recall where I originally found it. Although, it looks like it may be a Daniel Kwan. Not sure though.  Update: It is a Daniel Kwan. Link to his crease pattern is available at the bottom.  It looked innocent enough. So off I went to to fold it.  It was actually very difficult to fold. As I was going through the process, I had a dim recollection of possibly having tried to fold it before and not succeeding. It's also a configuration that I believe I've seen in its completed form and have attempted to reverse engineer, but never solved.  This time around I was able to complete the tessellation using the saved crease pattern.  It's a tightly packed configuration. Especially on the reverse side. It's pretty tricky to get the paper to do what you need it to do.  I used 28 lb. printer paper. It was touch and go for a while, but it worked out in the end.

 This is one from several years ago that felt ripe for the refolding. I folded it the first time almost exactly four years ago. I don't recall how easy or difficult it was to solve originally. You can view the original post for the  Stars formed by Hexes Tessellation  from way back then.  It worked out fine the first time around, but I was hoping to maybe get some nicer photos this time around. Which I did.  It was originally folded from someone else's pic that I'd found on google. I'm not sure who the creator is.  I used the crease pattern I had saved then to refold it this time. It worked well.  I'm actually more fond of the reverse side of the tessellation that appears as circles and tiny triangles. Your opinion may differ.  You can reference the link to the original post for a crease pattern.  I did however, create a new crease pattern as well. Which is below.  Which one will be most helpful depends on many factors. But between the two of them, it should be very

  Within the origami tessellations genre there are three distinct sub-sections. There are twist fold tessellations. There are flagstone tessellations. And there are collapsed shape tessellations. I've always found twist folds are easier to execute and generally less fussy. Collapsed shapes are in general, trickier to work.  Flagstones are kind of a hybrid of twists and collapses. I think they're easy, but very time consuming.  Each style offers its own unique array of possibilities for a finished design.  This is an example of a collapsed shape tessellation.  I came up with it just fiddling around with combining an assortment of shapes native to the grid.  At its most basic it's just different sized rectangles around hexagons.  The real handiwork is actually getting all those competing shapes to coalesce.  It's a tessellation probably best attempted in the dead of winter when it's very dry. But I went ahead with it even though it's been soggy here.  For a while,

  This is another tessellation from an old picture left in my google photos. I'm not aware of who is the original designer.  It's a very simple design that was quick and easy to solve.  It felt so basic that I wasn't really interested in folding it full size, but I wound up doing it anyway.  Mostly because the weather lately has made folding more intricate models not really feasible.  So I thought rather than trying to do something harder and failing because of soggy paper, I can least successfully fold something simpler.  And here it is.  Made up my own name for it. Don't know the original.  I actually wanted to fold a variation on this idea with closed collapsed hexagons where the triangles nested close together.  I gave it a go, but it didn't work out very well. Perhaps another time.  Still, this version of the tessellation is pretty nice.  To fold it, collapse the third size hexagon of the grid and fold triangle twists off of the points.  Crease pattern included

 This tessellation is folded from an old pic I found in my google photos. I don't know who the original designer is.  It's not a terribly complicated design. It's kind of basic. But I thought it was pretty cool just the same.  The original model used larger parallelograms than my version does. That modification also meant smaller triangle shapes between the parallelograms.  But other than some shrinkage, they are the same. 

 This tessellation is folded from an old crease pattern that I found in my google photos. Apparently, I had conceived of the idea, but had never executed it.  I actually found the crease pattern mistakenly associated with an entirely different tessellation than what it depicted. Weird.  Anyway, I finally folded it.  It's an interesting star pattern that I haven't seen before. It waited a long time to finally come to life and now, at long last, it has.  Crease pattern is at the bottom. 

 I have been looking back at some of the tessellations that I did several years ago. Back when the whole idea of creating my own tessellations was still a crazy, new concept.  It's certainly interesting to see how differently I thought then in terms of shapes, construction and overall concept.  In some respects, it feels like I was more creative back then. On the other hand, I feel more skilled today. More able to bring random ideas to fruition.  This tessellation is another design of my own which I had to reverse engineer because I didn't properly document it the first time. It tripped me up for a bit because I was trying to simply recreate the shapes using standard construction methods, but there's actually a secret to finishing this one. Its basis is a pretty simple design that is augmented by a series of reverse folds on the corners of the spirals. When you examine it from the back you can see better what shapes are involved.  There are the open back hexes. Then the plu

 Way back in January 2019 I created the pattern for the tessellation in this picture. This is a refold of that.  When I first did it, I failed to save a crease pattern. As I was looking at the photo of the original I decided it would be worth folding again.  For two main reasons.  One, to have a saved crease pattern. Two, to have a nicer photograph of the completed model.  My phone back then did not have a great camera. It's a bit of a strange feeling trying to solve your own design.  On the one hand, I felt confident that if it was my mind that created it, surely that same mind could figure it out in reverse.  On the other hand, I felt worried that if I couldn't figure it out that meant I was losing my origami mojo.  Fortunately for me, my mojo remains intact for now.  Honestly, it's not a very complicated design. It's just densely spaced.  I'm a sucker for those closely nested repetitions.

 This tessellation is a modification of one by @gatheringfolds that I solved. I believe she called it Criss Crossed.  Honestly, I initially found it a little confusing. It's not ideal trying to figure out the mechanics of an origami structure from an instagram pic on your phone.  I used to share them to my email and open the images full size on a regular pc monitor, but instagram has made that a lot harder to do. It may still be possible, but I've not tried that hard.  Given that I usually do these things at work, I'm limited in how I can obtain the larger images.  So I zoom in from the app on my phone and grumble and squint and usually can make out the details required. Usually.  I mapped out how her original idea worked on some grid paper, but decided to shrink it to better fit on a 32 pleat grid.  Basically just moving everything closer together. The back side is particularly interesting to me. It makes me think of a pulley system. I like it. 

 This is a tessellation that I came up with almost exactly 3 years ago. Fiddling around, I came up with it all over again. That happens to me a lot. Time goes by and I forget them and wind up unknowingly repeating myself.  It's all good though. It's a chance to fold it better. To photograph it better. To document it better.  It's larger offset hexagons on the one side and triads of rhombus twists on the other side.  I particularly like how the rhombus twists create ribbons that flow to the corners of the hexagons.  It's a pretty easy tessellation to execute. Nothing tricky about it. Any old paper will work.  Crease pattern included below.  It's a bit messy, but just the red lines apply.  It's not indicated in the crease pattern, but you do need triangle twists at the triple intersections of the rhombuses. They land on the reverse side. 

This is just a flash idea I had. There was no planning involved. No inspiration. I just started folding and followed the lure of the creases in the paper.  Upon seeing the finished result, It kind of reminds me of Robin Scholz's Triphilia tessellation, but the construction is definitely different and I was not thinking of that as I was crafting it. The similarity is that you can arrange the layering of the triangles into different patterns of your choice.  I went looking and discovered  I had folded this a few years ago and called it Triangle Temptations . I didn't realize this until after I'd completed this model.  Apparently, according to my original post, I'd seen someone else fold it on flickr and recreated it.  This happens sometimes. You hit on an idea and it's something you've done and forgotten. They linger in the back of your brain and come forward unexpectedly.  That previous version differed from this one slightly, in that it used double sized cross g

 Recursive origami used to be something that I did on a regular basis. Long before I discovered origami tessellations, recursive origami was what I did.  Recursive origami is similar to tessellations in that they're both a repeating pattern that can, in theory, go on infinitely. But while tessellations repeat along the x and y axes, recursive designs repeat along the z axis.  Shuzo Fujimoto was a famous recursive origami designer. Some of his most famous creations are the clover and the hydrangea.  Some origamists even took it a step further with what are known as high density recursive designs. Repeating the single layered model multiple times on a single sheet of paper.  For some reason that I don't understand the technique for folding the hydrangea has stayed firmly planted in my brain. Even years later, I still remember all the steps.  I also remember that it can be done at higher densities. I first encountered this idea at a website called. origamitutorials.com. But I had

 The tessellation that I folded prior to this one is what gave me the idea for this. I just kind of flipped things around and worked out how it would all fit together.  It took a lot triangles to construct. A. Lot. Of. Triangles.  Flagstone tessellations are generally very triangle intensive. This design is no exception.  The layout feels very familiar, but I searched and searched to see if I'd done it before based on someone else's idea and I couldn't find anything.  It's open back hexagons surrounded by trapezoids. That central idea repeats. There are some top-side triangles in order to make it a flat fold.  It's not the best time of year for folding flagstone tessellations. It's hot and humid. But inspiration is impatient. There are many triangles required on the reverse side. I knew there would be triangles needed on the back side, but I didn't anticipate needing quite so many of them during my initial conception of it.  But no worries, they were not shy