This is a flagstone style tessellation using triangles and rectangles.  The center is six triangle twists around a small hex twist on the other side.  The small rectangles connect to the tops of the triangles. It's from there everything repeats.  The negative spaces are blunt corner triangles on the other side.  I may or may not have done this before. It feels familiar, but I couldn't find an older version.  When you've been folding tessellations for as long as often as I have been, you start to lose track.  It's possible I saw someone else's rendition long ago and it laid dormant in the back of my brain until now.  I don't know for sure.  The best way to fold this one is to do the center first. Then twist the outer hexagons on the back. That will make it easier to get the rest of the repeats to fall into place.  I think that I have a crease pattern. Will add it here later if I can find it. But all the shapes are pretty obvious from the view ...

Nested shapes are a favorite of mine. This tessellation makes grand use of them.  I've explored similar patterns before. In this case, it's alternating trapezoids and triangles around an open back hexagon.  In order to tessellate the pattern, I found that a quadruple set of triangles did the trick.  The other side also has some rhombuses.  There are a lot of multi-corner intersections with which to contend. But patience is the key.   See the pic of the reverse view below for further clarification. A crease pattern diagram is also included at the end.

This tessellation is a hybrid of flagstone and tuck/collapse techniques. I've been finding a lot of new designs using this combination of folds.  The central component is a rhombus star twist around a small hex twist on the reverse side. There are triangle collapses tucked into the ends of the rhombuses. This kind of makes them look like snowflakes.  It's at the point that I begin to tessellate everything.  What's particularly nice about this tessellation is that the ends land rather fortuitously on my 32 pleat grid. So I was able to create pretty tidy borders.  It looks harder to fold than it actually is.  I would say it's an intermediate level tessellation to fold.  The reverse side is seven hex twists and a whole lotta triangle twists.  For further assistance see my crease pattern diagram below. 

 When I was folding this tessellation it did feel familiar, but I couldn't really remember why. So I pressed onward thinking it just reminded me of others, but was different.  Turns out, I've done this one not once, but twice before.  Each time, I created it from scratch in my head not remembering that I had  already done it. I guess that just means that my brain really likes this pattern a lot.  First time was in 2020 and I called it Hungry Rhombuses. I couldn't really get nice photos of it with the phone I had back then.  Second time was in 2021 and I called it Cannibal Rhombuses. I used kraft paper that time and it does not back light well at all.  This time around it came out pretty close to perfect. The pics are very nice. The execution is pretty spot on.  To fold it yourself just do rhombuses around an open back hexagon and repeat.  Be forewarned. Those triple intersections where three rhombus points converge are a tricky fold and there...

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 pattern is similar, yet also different to some others I've done. The central module repeats in six directions from the original starting point. A variant of that same pattern fills in the spaces that exist between them.  It's a lot of shapes, but one of your less intense tessellations to actually fold. Everything just tucks into each other.  The main pattern, which inspired the idea, is alternating rhombuses and trapezoids nestled into each other.  The tertiary arrangement is also trapezoids and rhombuses, they just land in a more twisting circular pattern.  The reverse side is all open back hexagons.  It's helpful to work the back side almost as much as you work the front during the folding process. Although, that's probably true for most origami tessellations.  A crease pattern diagram is included at the end for those that want it. 

 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 is a variation on some other tucked rhombus tessellations created by myself and others. It starts with a circular array of rhombuses tucked into each other around an open back hex twist on the other side.  In this case, I connected those rhombuses to the next set using a flagstone collapse fold. From there, the circular pattern is repeated.  A triad of triangles are used to fill in the gaps.  This design features a lot of closely nestled intersections where the points of the rhombuses and the triangles have to coalesce simultaneously. It's tricky, but not too terribly hard.  With designs such as this, working both sides of the paper helps everything come together more readily.  It's a lot of triangles on the back side. They need just as much attention as the front side does.  I used tant paper folded into a 32 pleat triangle grid.  A crease pattern is included below. 

  Here's a neat little tessellation that I was sure I'd done before, but I could find no evidence of that belief. I guess it just reminded me of some others from the past.  It's a pretty simple one. Relatively speaking. The main component is simple at least. Repeating it is a little tricky to execute as I wanted to keep things as close as possible.  This design is all about the back light. How the folds show through to create the pattern.  The shapes themselves are pretty basic. The arrangement just as much so.  It's a lesson in how a simple structure can still translate to an intricate result.  I don't have a diagram for this one. However, if I think of it, I will draw one and add it later.  The gist of it is small hex twists on the back and double length hex wings on the front. When you fold the wings some triangles form in the spaces between them. 

 When conceiving of tessellations sometimes we imagine a pattern that we think will be the front, only to discover that the other side is more wonderful than the one from our original idea.  It happens to me frequently.  Of course, it's personal preference and purely subjective which pattern, front or back, that you perceive as most amazing.  I'm still torn by this one. Each side is beautiful in its own right.  My original idea is expressed in the second photo. But when I saw the completed back side, I found it to be even more intriguing.  In my mind, there really are no backs or fronts. Only the shapes and how they inspire us.  My original crease pattern at the bottom shows how I folded this one. 

 This tessellation is made up entirely of trapezoids. It's similar to another one that I created called 'Deep Space Transmissions. You can see that tessellation here . That one tucked a double row of trapezoids into each other. This one is a little simpler version of that.  What's interesting in this tess are the triple intersections where the three corners meet. It's not really hard to do, but they are a little reluctant to cooperate and there are a lot of them.  This is also another example of a tessellation that is exclusively comprised of collapses and no twist folds.  What's nice about this method of creating origami tessellations is that you can fit a lot of shapes into a grid that isn't very large.  Another thing that's nice about this technique is that it's very transparent. The shapes you see are the only shapes that are used. Not much is hidden or obscured.  Even so, you can make very intricate designs using this method.  With all the various...

 The idea for this tessellation was just about a few triangles. Just up, down, up down. You can see what I mean in the left most portion of the crease pattern included below. However, for some reason, I decided at the time, that this pattern was too simple. So I added some rhombuses to the configuration. Which resulted in the finished model that you see here.  Although, now that I think about it, I still like the original idea and will probably want to fold it in the near future.  This tessellation is a symmetrical mirror pattern. Each side is a mirror image of the other.  It's a pretty straight forward design. No tricks or sneaky folds. However, it is somewhat labor intensive. There are a lot of creases and a lot of shapes to collapse.  I used thin paper for the sake of back lighting.  I imagine that it would look nice with a denser paper as well.  It's a 32 pleat grid.  Diagram follows. 

 Here's an extremely difficult tessellation that I recently created. Even though it was my own concept, I still needed a second attempt to actually fully execute the proper folding of it.  The design began with a circular series of triangles. Their connections alternating between tucks and flagstone style collapses. See the crease pattern at the end of this post for further details. That circle of triangles led me to discover the incredibly hard to collapse center portion. It's a small hex twist with upside down right triangles. They collapse into the next repetition.  The photo of the reverse view shows pretty well how it works. It's small and cramped and has a lot of fiddly little folds.  Thick and sturdy paper is a necessity. As is quite a lot of patience.  It's advisable to work much more heavily on the back side. Getting those collapses to cooperate really is the key to successfully folding this  particular origami tessellation.  Crease pattern is...

 I saw the crease pattern for this tessellation on the instagram feed of gatheringfolds. No solving required. I just followed her diagram.  Sometimes, it's helpful to turn off the deductive/creative part of your brain and just follow the map that's already been plotted.  Often, when I'm stuck without a new idea of my own, doing something like this will sort of reset my brain. Let it rest a little, but still keep the electricity flowing.  It's usually right after that a new inspiration or two springs to mind.  This one is an elegant configuration of small triangle twists paired with open back triangle twists.  Her original the crease pattern . Enjoy. It's a good fold.