This tessellation builds off of one I did recently that I called Starfish Tessellation . They both have rhombus twists around offset small hex twists. The rhombuses alternate front to back.  In this case, I added some triangle twists to change things up a bit.  Both designs were absolutely inspired by some tesses that I solved by gatheringfolds where she did alternating triangle twists around a central offset hex.  Changing the shape from triangles to rhombuses yields entirely different configurations.  This one has a nice layered effect in the transition spaces between the repeating chessboard like central twists.  Crease pattern is included at the bottom of this post. 

  This is an open back hexagon twist based tessellation that uses short/wide triangle shapes to create some interesting geometry in the spaces between the repetitions.  The central triangle shapes are essentially a single edge of an open back hex twist.  I had a crease pattern, but I don't know what I did with it.  Will have to see if I can find it to add at a later date.  I really like the movement on this particular design. It almost feels like it's in motion, even though it's just a still piece of paper.  Coming up with it was pretty ordinary. Just decided to combine some familiar shapes in a different way. 

 This tessellation is one that kind of came to me quickly. I didn't spend much time conceiving of it. I am, however, quite pleased with the end result.  It has a similar look to some other tessellations I've seen, but I believe its architecture is different. That difference does make for some subtle variations in how it looks compared to the aforementioned similar designs.  It looks tricky, but actually, it's pretty frustration-free to execute.  The central points are small hex twists. From there, just some rhombuses and open back triangles. Repeat as needed.  The front has slightly curved right triangles.  The reverse side (second pic) is pretty interesting in its own right.  The crease pattern for this tessellation is at the bottom of this post. 

  This tessellation uses a combination of alternating rhombuses and triangles around small hexagons.  It's pretty dense and not an easy one to fold.  When I first mapped it out I had alternating rhombuses and standard triangle twists, but that idea was a little off.  You can see from the picture that the triangles actually turned out to be a little different than the usual kind, Which I actually thought was pretty neat.  I believe the geometry really wants rhombuses on both sides. I'll probably try it that way in the future.  Still, I'm pretty pleased with this configuration,  Crease pattern is at the bottom of this post. 

 This is a tessellation by ArseniyK. I haven't solved one of his in quite a while. His designs are quite sophisticated. They can be both difficult to figure out as well as next to impossible to execute. This one is no exception.  The front side didn't give me too much trouble solving it. However, the reverse side was a little more elusive.  I mapped out the front on some grid paper and was confident when I began folding.  As I went along it got trickier and trickier to get things into their proper places.  It was very late into the collapse that I finally realized I hadn't noticed a key element. I had been twisting the small hexagons on the back side not realizing that they needed to be stars. When I was nearly done with the front side, I finally saw it and was able to correct and adjust.  It's such an intense fold that my first attempt with semi-thick paper was a complete failure.  When I tried again with kraft paper, I was able to complete it. Howeve...

This is 'Hybrid Hex Weave' by gatheringfolds. I do a lot of her designs because she's generous enough to share them with the world and take lots of photos. More photos makes solving the mystery a little easier.  I'll admit that I was initially a little puzzled by the natural triangle that occurs in this particular tessellation. I mapped it out just fine, but I wasn't entirely certain how to execute it.  Undaunted, I forged ahead. When the other elements were in place and it came time to actually make that shape work, experience took over and it nearly solved itself.  A lot of tessellations are weaves. Twists of triangles, hexes and rhombuses on the other side create a layered look on the opposite side. It gives the appearance of multiple pieces of paper interlaced, when in fact, it's all done using a single uncut sheet.  To look at the front of the design, it's not always obvious how it's constructed. When you can see the other side the structure is much...

 This is a Joel Cooper tessellation called hex weave. I actually had the front photo for a while and fiddled with solving it, but got stuck and moved onto other things.  Some time later I came across another photo from someone else and decided to try that tessellation.  Turns out that second photo was the back side of Joel's hex weave.  Seeing the backside, there wasn't much solving involved. It was pretty obvious.  It was only after I started folding it that I realized that the two photos were from the same design. Pretty neat how that worked out the way it did.  At first glance, I thought it was standard open back hex twists, but I quickly discovered it was irregular open back hexagons. They're 1.5 pleats per edge.  Then there are rhombuses off of their axes.  When you go to sketch out the repeats you find  triangle twists in-between them.  It's a very elegant design.  My crease pattern sketch is at the bottom. 

 This is a tessellation that I discovered recently that builds off of what I call offset hexagons. A small hexagon that doesn't twist along the grid lines. Instead you twist it by bisecting the grid lines.  It's a technique that's used in many origami tessellations by many origami artists.  The second photo of the other side illustrates it pretty well.  In this case, I used that starting point to create right triangles emanating from it.  Since I couldn't just repeat the central module because it's asymmetrical, I used some triangles to make the transition to the next repetitions.  Originally, I was going to use small triangle twists, but instead opted for open back triangle twists because I thought it would work better with the paper I was using.  It was a soggy kind of day and this paper isn't particularly sturdy. I kept it as neat as circumstance allowed.  I'd love to try it again with the small triangles using a denser paper. I'd also be inter...