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.