This origami tessellation is just a fun little idea that I had about a month ago. It's pretty basic, but I think it's a cute pattern. Something to do when you don't have a lot of time or aren't feeling up to doing the more complex stuff. The idea was to have small pyramids made up of micro grid triangles. That's all there is to it! To fold it I did a classic small hex twist on the back. Then I folded a series of 6 three pleat long arms all around it. These created the tiny triangles on the front.  That's it. Super easy to do. I used tant paper, but I think this particular origami design would've looked way cooler with thinner paper that could be backlit. I don't think that I drew a crease pattern before folding this. But I've unfolded it to create one. 

 This tessellation is kind of different from my usual modus operandi. We have tall isosceles triangles that wrap around six sided polygons.  My ' Fireworks Display Tessellation ' uses the same triangle shape in a much denser configuration.  I actually came up with this tessellation before I did that one. I had simply forgotten to take a photo of the diagram, so I was waiting on that to post this. In fact, it was this tessellation that led me to that one.  It's pretty common for one configuration of shapes to inspire something similar, yet entirely different.  This one is far simpler and easier to execute. The end result is a pretty neat pattern though.  Crease pattern included below.

 This is a tessellation that I was really thrilled to have created. The pattern utilizes a different triangle shape that I've not worked with much at all. It's a taller triangle than what you'll typically find in origami tessellations. Also known as an isosceles triangle. Two sides are equal and the bottom is smaller.   The longer sides of the triangles are 1.5 pleats long. While the bottoms are a single pleat.  I created a rotation of six of them around a classic small triangle collapse. They alternate forward and back as they go around the center point.  In order to repeat the pattern, there are natural triangle twists on their outer edges. Three of the isosceles rotate around those.  At that point, the repetitions can keep going ad infinitum.  All in all, not too difficult to execute, but a pretty remarkable end result.  I used tant paper folded into a 32 pleat triangle grid.  As with all origami tessellations, this is folded from a sin...

  If you're in the mood for a tessellation that looks complicated, but actually isn't, this one might interest you.  The pattern begins as open back hexagons with rhombuses collapsed along their edges.  From there, rather than a straight up repeat of the pattern, I added an additional rhombus before moving on to the next iteration.  Open back triangle twists fill in the gaps where six rhombuses converge. .  There are also small triangle twists on the back in the areas where two rhombuses connect along the edges of the hexagons.  In the center module, I alternated the valley and mountain connections of the double rhombuses in order to create consistent patterns for the outer repetitions.  The second photo shows all the triangles on the reverse side of the tessellation. I've also included some closeups of each side with less back lighting.  I have a diagram. Will add it soon. Diagram added.    

This tessellation looks pretty complex, but it's not that hard to actually fold it.  It features trapezoids rotating around  open back hexagons. Opposite facing trapezoids emerge from the edges of the first set. Those trapezoids then revolve around small offset hexagon twists.  This is an unusual tessellation that has a lot of flexibility in the valley and mountain folds. The way the various shapes interact with each other is such that there are a lot of options regarding what goes up and what goes down.  While this makes it somewhat easier to execute on the face of it, it can be frustrating to actually come up with a cohesive and consistent pattern.  Give it a try and you'll see what I mean.  I have a diagram somewhere. Will add it in the near future.  Update: added diagram below. 

 The inspiration for this particular tessellation came from my idea of three trapezoids around a small triangle. The points of the triangle poke into the short tops of the trapezoids.  As a way to further figure out how to repeat that pattern I added open back triangle twists to create another triad of trapezoids.  At that point it all coalesced and the final shape appeared as I repeated the array. A blunt cornered triangle revealed itself to be the last piece of the puzzle.  I actually liked how the back side photographed better than what I originally conceived of as the front. That's shown in the first pic.  But the concept was born of the shapes shown in the second photo. Interesting how that works out sometimes.  This particular orangey color of tant paper really gave me a hard time trying to get nice pictures of it. However, I managed to find a couple of good ones. Just barely.  Yet another aspect to consider when you're creating your own masterpi...

 Here's a tessellation that I've not seen done. The idea came from trying to find a new way to repeat right triangles around an open back hexagon. I used some rhombuses and it worked out to be a pretty cool pattern, if I do say so myself.  There are a bunch of triangle twists on the other side that are pretty fussy to fold.  In order to correctly twist the triangles you need to fold a little bit of the paper over on top of the edges of the open back hexes. It's difficult. Use strong paper and do it on a dry day.  There are also small hexagon twists on the back as well.  You could also say that the pattern is alternating right triangles and rhombuses around small hex twists with open back hexes in the gaps.  It's just a matter of perspective.  I do have my crease pattern, but need to take a photo of it. Will add it soon.  Updated to add diagram.

This tessellation began with the idea of three rhombus twists around a triangle on the other side.  I wanted to find a way to repeat that pattern.  I used open back hexagons to further that goal. From there I was left with large gaps that needed reconciling.  It turned out that a series of seven triangles worked to resolve the void.  Oh, this was an incredibly tedious tessellation to fold. The creases felt never-ending.  Getting all six triangles to work in all the gaps was an arduous task.  At times, I thought to myself, I'll never finish this.  Strong paper and an obsessive personality eventually resulted in the completed tessellation.  You can see from the first photo that I oriented four of the triangles upward.  The second photo shows the other three in the series on the back side.  This type of design has a lot of flexibility.  The shapes can be arranged in different variations of up and down.  Crease pattern diagram incl...

 This is a really interesting tessellation that I found. It has a lot of overlapping layers, which is always cool to find and fold.  I actually came up with the pattern for the back side and later decided I liked the other side better for the front view.  It uses open back hex twists as the beginning point. Some small natural trapezoids emanate from them. Then there are triangles twisted off of the trapezoids.  Everything is rather close together and tightly twisted.  A single module is pretty easy, but tessellating it is exponentially more difficult.  My first attempt with ordinary paper was unsuccessful. I had originally thought to make the repetitions closer together and only realized they wouldn't fit in the midst of that try.  I moved the repeats a pleat further out and was successful using tant paper.  The third photo shows pretty clearly how the trapezoids and triangles twist out from the central hexagons.  It also shows how you need t...

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 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...

 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....