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...

* This is a tessellation that was folded by 'Jessie'. We had a little e-mail exchange. They were interested in folding the ' hexagons and trapezoids tessellation ' designed by Peter Keller. I had previously posted my fold and solution for this tessellation back in 2022.  The crease pattern I had originally posted was pretty basic. So, they emailed me to ask for something a little more extensive.  I drew one and sent it to them the next day. And the day after that they emailed me again to show their completed tessellation (as shown above). It turned out quite well. Kudos to Jessie.  For better tightness on flagstone tessellations you might want to use sturdier paper or wait for a low humidity day. Otherwise, a really nice effort. Keep on folding! The  extended crease pattern is below. My original posting of Hexagons and Trapezoids fold and solution.  * photo used with permission from the creator. 

 I haven't solved someone else's tessellation  in quite a while. This time around I did. This is Orbits designed by gatheringfolds.  I surprised myself with how quickly I was able to reverse engineer it. It was no trouble at all.  True to her classic form this is a symetrical design that is a mirror image on either side. Knowing her tendency toward such ideas made it easier to figure.  The main components are small offeset hexes with triangle twists alternating front and back and open back hexagons.  It was a pleasant fold that I did with regular printer paper. I even did it on a rainy day and still didn't have any trouble. Loosely spaced twist folds such as this are perfect for when the paper might be a little soggy because of the weather.  There's no need for a pic of the reverse side since it's the same just mirrored.  Depending on your skill level this might be an easy tessellation or it might be an intermediate one. Objectively, I've say i...

 This is a tessellation I came up with after having seen and solved one by gatheringfolds. I don't know what she named it because I actually saw it on the instagram of someone else who had folded her design and they didn't specifically reference the title.  When I saw it, I really liked it, but even moreso it made me think of what else I could do with one of the components. In this case, the six rhombus pyramid.  So, after I mapped out her original tessellation , I used that foundation to create this one.  For my design, I repeated the rhombus pyramids by spacing them out from each other. Then I worked out what shape would fill in the rest. It's  just some very large hexagons.  I'll probably fold her original idea since I already have the crease pattern diagrammed. But I chose to fold my idea first.  My diagram follows.  I drew the crease pattern using one of the hexagons as the center. This would work just fine. But ultimately, I decided to u...

solved by solvingorigamitessellations.com  This is a tessellation by Ben Parker titled Snowflakes that I reverse engineered and folded about 4 years ago. I wanted to give it another try to see if I could work it a little better. And also to be able to create a crease pattern as I hadn't done so the first time around.  When I first solved this tessellation I was still learning how to extrapolate the architecture behind already completed tessellations of other artists. I don't remember how easy or hard of a time I had back then, but  I do remember that figuring out how to fold it taught me a lot.  Funny thing about this tessellation, I had actually originally intended to refold a similar, but slightly different design by him called Hidden Treasure .  For whatever reason, I must've gotten distracted and wound up doing snowflakes instead. Go figure.  Once you understand either, the other is already solved.  Ironically, I don't have the crease pattern...

Flower Tessellation solved by solvingorigamitessellations.com I actually solved this tessellation before I solved her 'Bouquet' tessellation . Both are designed by gatheringfolds. This one is a little simpler. Straight up repeats of the central pattern. In 'Bouquet' it takes that central idea and gets a little more complicated by adding small hex twists.  This one is just the 'house' shapes and some large triangle twists.  I'm pretty sure she called if 'Flower'. Although, I'm not 100% certain.  I can't seem to find the post again on her instagram.  The center was easy enough to figure out. It did take me a minute or two or more to realize how the  'houses' connected to each other. I simply didn't suspect that she would use that technique in what appeared to be a mainly twist based tessellation. I think that I'm just out of practice for solving other people's designs. I've been doing so many of my own lately that my ski...

solved and folded by solvingorigamitessellations.com  Another interesting origami tessellation by gatheringfolds. Utilizes an unusual shape. Looks like a house. But in origami/geometric terms it's an open back hexagon with the bottom sliced off. Or you could say it's a rectangle with an isosceles triangle on the top. Whichever way you wish to classify it, it ultimately means new possibilities for origami designs.  The center pattern didn't give me any trouble figuring it out. However, I did get blocked for a bit on how the small hex twists connected to the rest of the pattern. My stubbornness prevailed though. And after more time fiddling than I care to admit, I did come up with the solution. I really should have figured it out sooner than I did, but we all have off days.  solved and folded by solvingorigamitessellations.com The back side of the tessellation is exclusively small triangle twists. When I was stuck on how to connect the small hexes, I used the triangles on ...

  solvingorigamitessellations.com It's been a little while since I've solved someone else's tessellation . So, I've worked on a few of those.  This first one is 'Barnacles' by gatheringfolds.  I kind of have a love/hate relationship with reverse engineering tessellations. It's fascinating, frustrating, and fulfilling.  This one in particular, gave me no trouble at all. As it shouldn't. It's not anything very tricky. Just some trapezoids around hexagons with a some open back triangles in the mix.  solvingorigamitessellations.com I reverse engineer a lot of her tessellations because she always comes up with ideas very different from anything I would probably think up. She's a master of twist based designs. While I am pretty skilled with flagstones and collapse based tessellations, my twist skills could use some work. And the best way to improve is to learn from those who are more advanced. I also reverse engineered another tessellations of hers j...

 This is another tessellation designed by gatheringfolds that I reverse engineered and then folded. She calls it 'Hubble'. After the telescope, I'm guessing.  It was neither very easy nor very hard to figure out. The central array of seven hexagons was easy enough to determine. As were the triangle twists around them. I did get stuck for a little bit on the next layer. The two different kinds of connections that the rhombuses had to the hexagons took some fiddling to determine.   It was a very low humidity day when I folded it. So the paper was pretty crisp. I used ordinary printer paper. Widely spaced twist fold designs such as this almost always work very nicely with standard paper.  Her original model used a larger grid and therefore had more repetition. But my small grid fits the first part of the second iterations. It also still illustrates how to fold the entire pattern regardless of what size grid is used. It's always an excellent exercise to solve the t...

 It took me a little while to solve the 'emergent triangles' tessellation by gathering folds. I was kind of stuck on the idea that it was a group of six triangles and then another group of six rhombuses. When that kept leading me to dead ends, eventually, I tried a different approach.  Instead, I solved for the set of three rhombuses around the large hexagons. It was from that starting point that I finally worked out that the triangles  and rhombuses had to alternate.  It was definitely a eureka moment.  It's a wonderful design. Another one of her trademark mirror image tessellations. Each side is a mirror of the other.  I do have a diagram, but I haven't taken a pic of it yet. Hope to add it soon.  Update: diagram added. 

 This is a tessellation by gatheringfolds called 'cogs'. I didn't have any trouble solving the center, but my 16 pleat tester didn't fit the rest of the design.  I decided to just go ahead with a full 32 pleat execution and figure the rest out as I went.  Once I had enough space to work out the rest, it wasn't too difficult. Some plain printer paper stood up pretty well to my final adjustments.  It's a rather large tessellation that doesn't really repeat on a 32 pleat grid. Still, I liked it enough to go ahead with it anyway.  I gave a little thought to how it might repeat in a smaller space. But that's an idea for another day.  The center is a small hex twist with trapezoids emanating from it. Open back triangle twists fill in the gaps of the central module.  To repeat it there are large pyramidal shapes as well as long parallelograms. Personally, I like the pattern on the back (second pic), a little better.  I used ordinary printer paper. The va...

 This is a modification of a tessellation by Arseniy K called 'Pixelated Chrome'. I changed it up to repeat  on a smaller grid.  The structures are very similar, but the results are different. Mostly because I used paper that backlights really well.  I used the same size rectangles, but smaller, natural triangles.  It's a pretty easy to fold tessellation. I encountered no difficulties with the execution.  I used white, 28 lb printer paper folded into a 32 pleat triangle grid.  The diagram for my version is included at the end of this post.  The crease pattern for his is available on his instagram feed. 

 This is a variation on an old image I found on my hard drive. According to the tag in the corner of the original image, it's a Peter Keller design that is untitled.  His design used larger cube modules. on a much larger grid.  I decided to do small cubes so that they could repeat nicely on a smaller grid. Other than that, the concept is the same.  His design used cubes made up of 12 rhombuses each.  I simplified things with cubes made up of only 3 rhombuses each.  The reverse side of the tessellation is comprised of small triangle twists, open back triangle twists and blunt corner triangles.  What I particularly like about this design is how it utilizes space. Leaving those bigger gaps between the groups of rhombuses creates a totally different pattern than what you would get if you kept the same distances between all of them.  My diagram for this tessellation is included at the end. 

This is a tessellation by gatheringfolds that she called 'Epicycles'.  Every so often, I like to solve someone else's tessellation to give my mind a different perspective on things.  It really does help reset my creative process so that I can come up with new ideas of my own.  It also keeps me sharp in recognizing how to extrapolate the structure of other people's finished designs.  And it's a nice respite from the sometimes arduous process of thinking up and sorting out a completely unknown tessellation from start to finish.  It's an elegant design of open back hexagons and rhombuses.  There are a lot of designs that utilize these two shapes in conjunction with one another. This one is particularly interesting in how the rhombuses twist in a way that almost makes them look as if they're dancing.  The reverse side is exclusively open back triangle twists.  My diagram follows. 

Folded this one just cause I liked it. I am always impressed with the great patterns that she conceives. They're mostly not overly complicated, yet they are always innovative and inspired.  There wasn't a whole lot of solving going on on my end. The shapes are clearly defined. It was just a matter of ensuring everything landed in the right places.  Repeating rhombus twists combined with trapezoid twists.  A great idea. I don't know if I ever would've thought to combine those two twists if I hadn't seen her do it.  She's the twist expert. I'm more of a collapser when it comes to creating.  Anyway, a fun fold for anyone interested.  Fits nicely on a 32 pleat grid. Works with ordinary paper.  My sketch is at the end. 

 This tessellation is one by gatheringfolds. It consists of rhombus twists and open back triangle twists. As is the case with a lot of her designs, this is a mirror symmetry fold. The front and the back are mirror images of each other. She's very good at creating these types of folds.  I enjoy solving them because they aren't difficult, but they are always interesting and pleasing to execute.  They also get my mental juices flowing with either ideas of my own or variations on the original.  I folded this using ordinary 20 lb printer paper that just so happened to be blue. Other than the color, there is nothing special about the paper. It's a 32 pleat grid. I rarely use any other kind.  You can see pretty well from the unlit photo exactly what shapes are needed and how they must interconnect.   However, I did sketch out a crease pattern diagram, but haven't yet taken a picture of it. Will update and add that soon.  Update: added crease pattern....

 This origami tessellation is a variant of one by Arseniy K. He named his 'What If Caviar Could Talk'. After I had solved his design, I decided that I wasn't up to  reproducing it exactly as he had folded his. Perhaps another time, in the future. So I changed things up a little to make it slightly less difficult.  Both designs have a foundation of open back hex twists with triangle twists around them, He used micro rhombuses between the repeats.  In my case, I used larger natural rhombuses instead.  Still a difficult fold to execute, but much less so.  It still required thick paper. I used tant folded into a 32 pleat triangle grid.  You can see from the photo of the reverse side how densely packed everything is.  It's a few layers deep. So be prepared to wrestle with that.  My crease pattern for this iteration is included at the end.  To fold his, sub out small natural rhombuses in place of my larger ones. 

 This tessellation is from a design by gatheringfolds. However, I only used the center portion of their design. I just really liked the center so much that I wanted to see how it would look in straight up repeats. It came out pretty cool.  Interesting thing about this design is that the axes of the small hex twists flow into one another rather than all in the same direction.  It was while solving her design that I came up with a different design using the same principle. It is featured in my " Idling Time Machines Tessellation ".  This tessellation is just me repeating the center point from her idea   It's open back hexagons with small hex twists and blunt triangles in the spaces that facilitate the repetitions.  But actually, I found it problematic trying to fold it from that perspective.  Folding it mostly from the back side (second pic) made a lot more sense to me  Your results may vary.  For further insight see my diagram below....