Filed in: Origami July 2024 Solvingorigamitessellations.com   It's time for another advanced tessellation . Those are my favorite kind. Rising to the challenge is oh so satisfying. And on so many levels.  There's the conception. Coming up with idea. Solving to make the idea work.  Then there's actually executing the plan. It can be a long process, but it's almost a zen experience. Going through all the steps. Slowly, but surely watching your hard work become what you had envisioned.  It's a tedious and wonderful journey.  What makes this particular tessellation so difficult are the series of triangles that are all interconnected. It's not an easy task to get them all working together.  The center of the tessellation is trapezoids around a small hex on the back. Then I add another set of trapezoids overlapping the first at a 90 degree angle. In order to repeat the pattern another set of trapezoids tucks into them. From there the inner module can be repeated. T

solvingorigamitessellations.com   This tessellation consists of many overlapping rhombus twists. They overlap a little differently than my usual designs. Rhombus collapses overlapping are a pretty standard technique. However, in this case, we overlap twisting rhombuses. The results are quite different.  To be honest, I don't recall how exactly I made the pattern repeat. I'd have to refer to my original diagram, which I have not yet taken a photo of.  It's quite a dense pattern full of many overlapping folds.  When I drew it, it seemed like a pretty simple idea, so I used thin paper. It turned out to be more intense than I anticipated. This thin paper worked, but just barely. A thicker paper would be advisable.  When I come up with twist based tessellations I usually try to create ones like this that are non-standard. There's no shortage of already existing twist based tessellations. But the really tight and dense ones, such as this,  are usually still undiscove

solvingorigamitessellations.com  If you like flagstone tessellations then you'll like this one. It's a cool one.  I actually mapped it out as rhombuses pointing at each other and then away from each other. Using some triangles to make it work.  When I finally folded it, the pattern came out more like vertical rhombuses flanked by triangles with a row of horizontal rhombuses between the repetitions.  That's how I see it anyway. I'm sure others will see it differently.  However you might perceive it, it's a pretty fascinating design.  All these years later. Hundred of tessellations folded and it still blows my mind what can be done with a single sheet of uncut paper.   It's a somewhat difficult tessellation   to fold. As are most flagstones. In addition to the shapes featured on the front of the paper there are a lot of triangles to work out on the back.  I used 28 lb white printer paper. And my crease pattern diagram is included at the end of this post.  I would

  solvingorigamitessellations.com This is one of those tessellations that when you come up with it you think that you've really hit upon something unexpected. And you have. But it's also one of those tessellations that is very difficult to actually fold .  It's well worth it though. The finished product is a dazzling array of rhombuses twirling around small offset hex stars.  It's a densely packed fold that's hard to execute and time consuming, but those are my favorite kind! I actually folded it quite randomly as my baseline. Then after it had a chance to rest under some weight, I went back and rearranged the mountain and valley folds into the final pattern.  For tricky tessellations such as this one, that seems to be the least frustrating way to go about it.  This is an original tessellation that I designed.  Crease pattern available at the bottom for those who might want it. 

 This is another tessellation designed by gatheringfolds that I reverse engineered and then folded. She calls it 'Hubble'. After the telescope, I'm guessing.  It was neither very easy nor very hard to figure out. The central array of seven hexagons was easy enough to determine. As were the triangle twists around them. I did get stuck for a little bit on the next layer. The two different kinds of connections that the rhombuses had to the hexagons took some fiddling to determine.   It was a very low humidity day when I folded it. So the paper was pretty crisp. I used ordinary printer paper. Widely spaced twist fold designs such as this almost always work very nicely with standard paper.  Her original model used a larger grid and therefore had more repetition. But my small grid fits the first part of the second iterations. It also still illustrates how to fold the entire pattern regardless of what size grid is used. It's always an excellent exercise to solve the tessellat