This tessellation is about as basic as they get. Straight up rhombuses. One flowing seamlessly into the next. It's simple, but I just love the pattern.  When the paper is damp because the weather is wet, less complicated designs are a wonderful exercise in the fundamentals.  Someday, if it ever stops raining and being humid, I'll hopefully get back to some more complicated structures.  In the meantime, there are lots of interesting ideas to explore that are more rudimentary.  I like how in this tessellation the rhombuses almost appear to have movement. A little bit of an optical illusion effect.  The design is the same on both the front and the back. The two sides are mirror images of each other. Also known as mirror symmetry.  My diagram is included for reference. 

 Here's an interesting, almost linear flagstone tessellation that I created. It's almost both circular and linear at the same time. The shapes do rotate around hexes, but they also repeat in a kind of linear fashion.  It consists of trapezoids and triangles. Four trapezoids and two triangles per hexagonal twist. The repeats are petty standard. One iteration leads seamlessly into the next.  It features an interesting pattern on the reverse side. Mostly triangles, but also some linear connections between the trapezoids.  It's a little unusual compared to any of the flagstone tessellations I've done before. Similar, but different enough to make me think.  The back side of flagstones always look more interesting than the fronts to me.  Your mileage may differ.  It was a little difficult to fold, but nothing crazy.  For more insight see my crease pattern below. 

 Here's an interesting tessellation pattern that I recently found. It looks like there are small triangle twists, but it's actually rhombuses that are partially folded over.  When I drew it out on the grid paper, it looked pretty simple. When I went to fold it, it was kind of tricky.  I used standard printer paper, so a more substantial paper might facilitate the execution better. But I was more interested in a getting a nice back light.  The main circles of rhombuses twist around a large hexagon. However, the way that they twist and overlap kind of hides that fact. At the center you wiid up with just a small negative space hexagon.  On their outer edges the rhombuses are connected by small hexagonal twists.  When the pattern is repeated open back triangle twists take up the spaces between the small hexes, aligning with their axes so they can twist synchronously.  All of this is made much more obvious in the crease pattern that's included below.  The back side has an intere

Searching for something simple, yet interesting, I came up with this pattern.  The weather lately, has not been conducive to intricate designs. So I was hungry for something new and intriguing that I could fold without the dampness interfering.  I came up with a rhombus with triangles twisting at all four axes. In order to repeat the pattern, I used the corners on the outside of the triangle twists to facilitate the next array.  The shapes overlap each other in some areas. It's folders choice how they land from top to bottom.  It's pretty easy to fold, as was my intention.  It has interesting layers and weaving on the reverse side.  It's just one of those wonderfully simple designs that looks much more tricky than it actually is.  Crease pattern included below. 

 This tessellation is curious in that I conceived of what most folders would consider the backside when creating it. It wasn't until after I'd finished folding it that I noticed the other side had more of a 'front look'.  What is the front and what is the back? Maybe both sides are fronts. Can such a thing be? My initial idea was simply triangle twists around open back hexagons. Those then flow into a triad of triangle twists around collapsed triangle.  What happens on the other side are rhombuses around the open back hex. The rhombuses also form triads around the collapsed triangles which on that side are up facing. This side has a similar look to a flagstone tessellation, but the gaps are a little wider because of how the central triangles collapse rather than twist.  It's an interesting variation on familiar techniques. It also boasts a lot of repetitions for a relatively small 32 pleat triangle grid.  It's a lot of shapes, but it isn't too difficult t

 This tessellation by gatheringfolds had me stumped. She alluded to a fold she referred to as a closed hexagon twist. This was not something with which I was familiar. This was not something I'd ever discovered or encountered. It was totally new to me.  I've been doing origami tessellations for the better part of 5 years and I thought that I knew all the folds and all the tricks. I did not.  Watching the beginning of her video tutorial showed me the unusual fold which she had used in this particular tessellation. If I had not watched it, I'm not sure whether or not I would've ever figured out the concept.  So, my take away is that there's always more to learn.  Once I understood this new shape/fold, I was all good to finish the process of replicating the design.  It also occurred to me that it works in a similar fashion to what I call offset hex twists. Where in an alternating pattern, three of the shapes that emanate from it can exist on the front and the other thr

 This is an interesting little tessellation that I found. Essentially, it's a hex twist and then there are some more overlapping hexes around it. It's at that point that you can create the triangle twists that overlay the initial folds.  It has a similar look to triangle twists around a hex, but it has some more layers.  I drew the crease pattern to express the finished fold in two different ways because I wasn't sure just one way would get the point across.  You can fold this in stages.  First the central hex. then the outer hexes. Which aren't actually hexes. They're double wide. But when you overlay them you wind up with what resembles hex twists.  From there you can do the triangle twists. They're not easy to do in such close quarters, but I managed okay with pretty cheap paper.  See below for the diagrams. 

  Flagstone tessellations are one of my favorite variations on geometric origami designs. They are easy to solve, but difficult to fold.  This particular design was conceived of by Madonna Yoder (aka gatheringfolds). Essentially, it's just alternating rhombuses.  As with most flagstone tessellations, the reverse side is a fairly dense field of triangle twists.  I created a similar flagstone some time ago that was also all rhombuses. Mine all went in the same direction, while hers are more of a back and forth pattern.  Her design creates a really cool wave pattern. It's a brilliant find.  To fold it you'll need a lot of patience. Flagstones are fussy to execute.  You can see the triangle pattern that's created on the back in the second photo. The back side is almost more impressive than the front.  Crease pattern is pretty straightforward. See the image below. 

  This is technically not a tessellation. The pattern doesn't repeat. I fiddled around a little bit with the possibility of it repeating on a larger grid, but didn't find a suitable solution.  That's not to definitively say that it can't be repeated. Perhaps it can. I just didn't find a way. Maybe if you change out the first outer rhombus where the central rhombuses meet and work with a shape that is more natural to the corner that is formed. Or maybe a third rhombus on the outer edge.  I didn't really try that hard, since if possible, it would require a very large grid.  It is, however, a pretty cool pattern that can be folded from a 32 pleat triangle grid.  During the conception process, I just came up with the central pattern and from there free formed the remaining edges.  It's a neat little dense fold that isn't too hard to execute.  A crease pattern is included at the end of this post. 

 Conceiving of this tessellation I was remembering one by Arseniy K where he used the same central module. I added some blunted pyramids to the configuration to create a different pattern. In this case, I decided to have the center be latent and every other external repetition dominant.  The remaining repetitions are hybrid latent and dominant.  But this particular tessellation can be altered with how you choose to orient the folds. What goes up and what goes down has a lot of flexibility.   .  Crease pattern is included at the end. 

 This tessellation was created by gatheringfolds. It's one of her less complicated designs. An array of trapezoids arranged linearly.  She folded hers using a rectangle.  I went with a hexagon.  Even though it's very simple, I really like the arrangement.  Sometimes it's fun to just figure out something not too complicated and quickly get on with folding it.  The trick to solving this is just to fold two of the kissing trapezoids. Then  follow their axes. They will tell you where to go from there. You also need to be aware of spacing. Too close and it won't work. Too far apart and you'll wind up with a different pattern.  The reverse side has a pretty cool design as well.  Crease pattern is included below. 

This is a fun tessellation of trapezoids repeating on both the front and the back.  The trapezoids alternate amongst each other between front and rear facing.  Completing that trapezoid pattern results in some large hexagon twists.  There are also a multitude of triangle twists on the back side.  This is one of those patterns where you have choices about how to orient the folds.  What goes on the front and what goes on the back is personal choice. Some of those choices mean that other folds are mandatory in a certain direction. But you can mess around with the pattern to some extent.  I guess technically, that's true of a lot of tessellations. But some patterns present more choices than others.  I believe I drew a crease pattern, but I left it at work. Will try to add it at a later date.  Update: added crease pattern.

 This tessellation is by Arseniy K. It's one of his more straightforward designs.  It's pretty cool still the same.  Not a whole heck of a lot of solving on my part. It's a series of repeating small rectangles around triangle twists.  It is difficult to fold, even though it's not that complicated. Everything is quite tight.  I kept staring at it after I'd already completed it and wondering if there was something that I had missed.  Try as I might, even with fancy paper, I could not get my folds as neat as his.  If there is some subtle difference in how to execute, I'm unable to see it.  He only posted a photo of the front side. So I can't compare my reverse side to his. As far as I can tell the fronts look the same.  The one drawback to really fancy, thick origami paper is that it doesn't generally back light well.  In this case, the front didn't back light nicely at all, but for some reason the back view actually came out pretty cool (as see

 Here's another interesting linear style tessellation created from rhombus twists. It consists of rhombuses twisted in horizontal rows. It's repeated vertically by tucking the resulting intersections backward.  I forgot to take a photo of the crease pattern and I don't have the paper on which I drew it anymore. Duh on me.  But I will try to remember to draw a new one and upload it here sometime soon. It's a pretty simple design though. Not too tricky to figure out how it works.  I used a hexagon to fold it, but upon looking at it more carefully, I imagine a regular rectangle would've suited this particular configuration a little bit better.  The pattern on the back side is pretty cool as well. Nothing terribly intricate, but I like it.  It's always nice when everything tucks and nestles together so neatly.  Update: made a crease pattern. Added it below. 

 Recently, I purchased some tant paper on amazon. I was skeptical about whether or not it would work better for more complex tessellations. I was pleasantly surprised with how well it facilitated a small and intricate design.  This tessellation was my first time using it and I am quite happy with the final result.  I used it to fold 'Minty Flowers' tessellation by Arseniy K. It worked beautifully.  As far as solving the design, the shapes and techniques were all quite familiar and it came together quickly. It's an elegant pattern that I quite like. And thanks to the fancy paper, it was a pleasure to actually fold it.  The tessellation consists of micro rhombuses around small hex twists.  There are small triangle twists adjacent to the rhombuses and those lead into offset hex twists on the other side.  I did create a crease pattern sketch which I will include at the end.  You can see from the photo of the reverse side below that everything is pretty densely packed. It's

 The start of this tessellation was the idea I had for surrounding open back hexagons with long rectangles. It was from there that I had to figure out how to make it tessellate.  Mapping it out on some grid paper revealed that another open back hexagon with very closely nestled triangles could work to fill in the gaps.  Tessellations such as this utilize a combination of collapsing and twist folds.  Collapsing folds use the grid to compress the paper into smaller shapes.  In this case most of the work is collapsing. But there is some twisting necessary regarding the triangles close to the hexagons. Collapsing tessellations is an entirely different avenue of execution that can help you construct totally different patterns with the same common shapes.  Depending on how you conceive of them, they can be quite simple or quite complex.  In this case, it's of intermediate difficulty.  For further insight into how this tessellation and other collapsing folds are created, see my crease pat

 The inspiration for this tessellation came from thinking about another tessellation by Arseniy K called 'Paper Planes'. The triad of short wide triangles that he used in that was just stuck in my mind. That's how I arrived at this design.  It uses the same triad of those triangles, but wraps them around a completely different set of shapes.  On the front along with the triangles triads are a kind of offset pyramid.  On the other side there are small triangle twists and blunt tipped pyramids.  The photo of the reverse side shows this quite clearly. The crease pattern I have included at the end will also show it more clearly.  It's a bit tricky to fold, but not too terribly difficult.