When I did my 'Rotational Discretion' tessellation , I mentioned that the same pattern could be done without leaving any gaps. This tess is the fulfillment of that assertion.  At first glance, your eye might be drawn to the center where you'll see a six pointed rhombus star. However, if you change your perspective just a little you might see the series of multi-shape triangles rotating around the center. They are comprised of 3 each of rhombuses and small triangles.  As the tessellation repeats the same thing occurs. You get those six rhombus stars, but at the same time each of those rhombuses is a single piece of the larger multi-shape triangle patterns.  It's an interesting study in how the shapes of the grid can create and be a part of more than one pattern at the same time.  This is a difficult tessellation simply because all flagstones tessellations are. But once you get the hang of them, doing more and more, they do become much easier to execute....

 This is an interesting variant on your typical flagstone tessellation . I arranged a series of three rhombuses and three triangles into larger triangle shapes. Then used a wider spacing to repeat the pattern so that they stand out more than if they were tucked closely together.  I have done other tessellations using this same configuration in different ways. Although, I don't remember their names in order to reference them.  Everything could theoretically be tucked right up against each other for a different take. I or someone else may or may not have already done that. I can't quite recall for sure.  Either way, I think the wider spacing makes for a pretty neat design.  I would classify this as a lower level difficult tessellation . Good for intermediate folders looking to advance their skills.  The back side of the tessellation is an intriguing array of closely tucked rhombuses surrounding triangle twists at each center point.  It's easy to forget w...

 This tessellation is a very simple idea that I really can't believe I hadn't thought of before.  It's two classic configurations combined into one complete flagstone design .  The pattern alternates between six pointed rhombus stars and six triangles around a small hexagon. That's it. That's all there is to it.  My 32 pleat grid didn't allow for too many repeats, so I just tried to create clean edges. But it could keep going on a larger grid.  My original diagram that I used to start wasn't totally accurate, so I adjusted as I worked the fold. I will add an accurate crease pattern sometime soon.  It's a somewhat difficult tessellation to fold. Because all flagstones are sort of difficult. But it's nothing that can't be done with a little bit of patience.  Updating to add crease pattern... Filed under: August 2025 Origami Tessellations

 This is another right triangle tessellation. However, in this case, I decided to do a linear pattern.  I had this idea a while ago, but just recently worked out how to execute it properly.  It's a flagstone tessellation . Everything is nestled edge to edge.  The triangles connect to each other in both a mirror pattern and by offsetting for each new row.  As I was in the midst of folding it, it occurred to me that a really cool variation would be to leave bigger spaces between the rows. I think that would look pretty cool.  In this case, everything is tucked as close together as possible with just a lot of triangles on the back side.  It's a little more difficult than a typical flagstone tessellation because many of the folds on the back overlap each other. It works just fine, but it takes some finesse.  Crease pattern included.  Filed under: July 2025 Origami Tessellations

 Here's a really interesting flagstone tessellation that I recently created. I used my 'Drunken Stairways' tessellation as a jumping off point for how to configure it. But while that used hexagons and trapezoids, in this case, I used hexagons and rhombuses.  It's kind of a back and forth pattern of the rhombuses situated around the open back hexagons. It repeats pretty straight forwardly.  It's not hard to do, provided you follow the crease pattern.  It does remind me though, of just how many possibilites exist in the combination of a handful of basic geometric shapes.  There are so many more patterns to be found. It's fun to think about.  Crease pattern included. 

 This is a pretty cool little flagstone tessellation that I recently folded. It features several different classic configurations all rolled into one finished product.  You've got your six tirangles around a hexagon at the very center. Then there are some three rhombus cubes too. In addition to that, we also have some rhombus stars as well.  If I remember right, this was actually an accident. I had mapped out a different configuration where the center point repreats after some rhombuses flowing off of it.  But when I went to actually execute it, I drew out a slightly different (this) pattern on the paper. I didn't even notice until I had started the creasing process.  By that point, I figured, just go with what I have and save the other design for another day.  The crease pattern I created is for the other idea, which I haven't folded yet.  Not that I remember where I left it. Hopefully, I'll find it and be able to do the original idea. If I think of ...

 More fun with trapezoids in flagstone tessellations .  The idea for this was a triangle twist with three trapezoids spinning around it So even though the center is six triangles, that was just a way to make the shapes around the edges work.  Although, I would imagine that if you wanted to you could conceive of a design where the center point could repeat instead.  The six triangles with the trapezoids eminating out from it. That would be an interesting variation.  The back side is almost exclusively triangles except for the one center hexagon.  As far as flagstone tessellations go, this is one of the less difficult ones.  Crease pattern included.  Filed under: June 2025  Origami Tessellations

This an odd little tessellation that I recently created . It was conceived of as a collapsed hexagon to which I then added a multitude of triangle twists.  It became quite messy with so many triangles overlapping each other everywhere.  However, as I was folding it, what I discovered was that the other side became an interesting set of unusual shapes in a flagstone style pattern.  It's bascially a small hex flower with oddly shaped petals. Then there are open back triangle twists to connect the repetitions.  I was so focussed on all the various triangle twists on the other side that I didn't even really consider what might be happening elsewhere.  I used thin printer paper thinking it would be easier to fold all the overlapping triangle twists. Had I taken a step back and seen what was happening on the reverse side I mgiht've opted for a sturdier paper and gotten a neater finished product.  It's a somewhat difficult tessellation to fold because of how...

 This is a linear flagstone tessellation that I just recently created and folded. The idea for it came to me while I was thinking about some other tessellations that I've done that use trapezoids in an alternating directional pattern. And I thought to myself, what if I could do something similiar in flagstone style. And this is what I came up with.  Essentially, it's a cantilever pattern of trapezoids and hexagons.  Some might feel it's a difficult tessellation . While others might see it as only intermediate . I always find flagstones rather intuitive to fold. Sometimes it almost feels as if they sort of fold themselves.  But while the bulk of the folding process might flow rather smoothly, actually getting everything tucked close together can be a completely different situation.    If I had an iron, I would probably use that. But I don't have an iron, so I just use a heavy book and a dumbell. But not before I've spent far too much time pushing and cajoli...

* 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. 

 This is a really cool tessellation that I created . It's trapezoid based tirangle shapes connected by offset small hexagons with alternating small triangle twists around them.  Inspired by a previous tessellation I had created called 'Twister' I set out to create a new one that utilized the same trapezoid triangles in a new way. This is the result.  When I had finished mapping it out, I wasn't entirely sure if it would work. It seemed logical, but some of the gaps were unfamiliar to me in the context of flagstone style tess . Which is essentially what this is.  I guess, technically it's a hybrid of flagstone and classic twists. It's intriguing to think about what other hyrbid folds might be out there waiting to be found.  At any rate, it looked promising. So I forged ahead.  Relatively certain, but not 100% sure. Turns out it works beautifully. A lessson to trust your experience.  This is a difficult tesssellation , but it's also a fun one. The way th...

 It's time for a new flagstone tessellation. This one begins with three trapezoids around a small triangle twist on the back.  From there I repeat the trapezoids in three directions. Adding a repeating and widening pattern of triangles and more trapezoids in the other three directions to fill the ever expanding space. I consider all flagstone tessellations to be difficult . Just because of how everything has to converge almost silmultaneously. And also because the reverse sides are always full of so very many triangles. However, it's also worth noting that flagstone tessellations work more seamlessly with the triangle grid than other styles of difficult and advanced tessellations. So, if you're hoping to step up your tessellating game, I would say this is the style with which to start.  Crease pattern included.  Corrected crease pattern added.  It was pointed out that the original crease pattern I had uploaded had errors in it. I will try to add a corrected ver...

 If you're a fan of flagstone tessellations , as I am, here's another one. This one is trapezoids and rhombuses in a linear pattern.  Trapezoids have all kinds of fun linear possibilities to ferret out. This is just one of so many, many possibilities. I could probably spend years just creating trapezoid based tessellations and not ever run out of options.  This original tessellation is two trapezoids. One up and one down, then a rhombus. And repeat.  Triangle twists densely populate the back side.  This is a difficult tessellation . All flagstones are at least somewhat difficult. They are also a lot of fun and very satisfying to complete. Yielding fascinating finished results.  Crease pattern included.  Filed under: February 2025 Origami

Conjoined Stars Flagstone Tessellation  This is a tessellation that I came up with while mucking around with triangle twists around a small hexagon. It's a common starting point for a myriad of tessellations.  In this case, I added some rhombuses and triangles on the edge of the central point. Then I inverted those shapes in order to repeat the pattern. What I wound up creating was a series of of interconnected stars that are all joined together by shared shapes.  It's a pretty cool pattern in my opinion.  I folded it using green tant paper.  It's a difficult tessellation , but once you get used to doing flagstones they become much easier to execute. After a while, they almost become easy. Though they contain a lot of interconnected shapes, they seem to work quite naturally with the triangle grid.  Conjoined Stars by solvingorigamitessellations.com I also find flagstone tessellations much easier to conceive of than other tessellations. They follow a prett...

This is an odd one. It's another bullet shape based tessellation that I created . At the time of conception, I was thoroughly obsessed with creating this particular pattern. So much so, that I completely disregarded the fact that the grid and paper really don't want to make this design.  Nevertheless, I pressed onward.  It has some weird tucks, folds and overlaps. Which make it a difficult tessellation , possibly advanced. It's not the most elegant tessellation I've ever folded. That's for sure. However, in the end, I mostly, made it work.  I was right in the middle of finishing this when it dawned on me that triangles in the same pattern would be just as beautiful and also work much more fluidly with the grid. So, that's a fun tessellation for another day! It works like a typical flagstone in most ways. The small gaps on the back are triangles and the larger ones are rhombuses. But because of the atypical shape of the bullets, the points of the triangles need ...

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...

solvingorigamitessellations.com   This tessellation is kind of a funny story. I thought to myself, let me do something with repeating rhombus cubes. Meaning, three rhombuses around a triangle and then repeat that pattern with another shape or two.  I worked with it for a bit. Trying alternating it with open back hexagons.  Eventually coming to the conclusion that open back hexagons were the answer just in a different pattern.  That's how I wound up with this tessellation.  I changed up the edges to make a neater finish.  The funny part is that I later discovered I had actually done this tessellations years ago in 2018 and that it was originally created by Robin Scholz. And I had folded it from his crease pattern all those years ago.  solvingorigamitessellations.com I was a little disappointed to realize that it was not really my original creation even though I had dreamt it up without remembering that I'd already done it.  That happens sometime...

  solvingorigamitessellations.com Here is a new flagstone tessellation that I recently created and folded. The starting point is trapezoids and triangles around a central triangle. From there I just expand outward using the shapes that work with the space.  Because it starts from a triangle, everything repeats 3 x 3 instead of x 6. So 3 sides are a pattern and the alternating 3 sides are a different pattern. The pattern of shapes changes as the design expands outwards because there is more and more space to fill.  solvingorigamitessellations.com Because this is a flagstone, it is a difficult tessellation to fold. The reverse side is full of triangle twists.  As far as I know, this is an original origami tessellation . I've not seen it done before.  It occurred to me after I had completed this that the central module can probably be repeated if I flip the trapezoids of the second generation. I started to work that out on some grid paper, but haven't finaliz...