This is a another flagstone tessellation that I did a month or two ago. I was exploring rhombuses interacting with parallelograms and did several that played around with those two shapes.  This one is simply alternating them in a linear pattern. I like how the rhombuses form rows of diamond shapes between the parallelograms.  It's not hard to fold at all. It's very basic for a flagstone .  Don't have the original diagram anymore. Will try to remember to add one soon.  It's pretty simple to reverse engineer, though. Just follow the shapes.  Other side is all triangles. 

 I did this flagstone tessellation probably at least few months ago. I don't think that it's been uploaded previously.  It's a linear style pattern of triangles and rhombuses. I did two rows of rhombuses and one row of triangles. Looking at it, I wonder why I didn't just do one row of each.  Another nice variant might be to change the direction of the rhombuses as the rows are repeated. Something for another day, I suppose.  It's a pretty typical flagstone tessellation . Everything is connected on the back using triangles.  In my opinion, linear flagstones are easier to fold than the circular kind. The shapes just seem to fall into place with a lot less coaxing. That's just my experience.  I doubt that I still have the original diagram. It's pretty easy to decipher. Just connect the shapes on the front in the usual way and add triangles in the gaps as needed.  Still, on principle, I will try to remember to draw a new crease pattern for it and upload...

  This particular tessellation was kind of a let me see if I can do it sort of idea. I knew that it wouldn't be one of those pretty design. It's just an exercise in execution. Several layers on top of each other that make sense in theory, but are rather difficult to make happen.  I did make it happen, for the most part. It turned out as expected.  It's from quite some time ago. So, I don't remember too much about it. Don't have my original diagram.  I do know that it starts with open back hexagons. And then I add those very small natural trapezoid off of them.  I think that I added some rhombus twists after that. Not entirely certain. I will have to unfold it to be sure.  If you're interested in testing how much stress your paper can take, this one will do it.  If you want to see how many layers of folding you can successfully wrest from a single piece of paper, this one is for you.  It's absolutely an advanced tessellation . A test of your mettl...

 Trying to keep things not too repetitive... so I have a somewhat different tessellation this time around.  The idea of small natural rhombus stars is not a new concept. I've done some in the past. Lots of other people have done them as well.  I'm not sure whether this particular iteration is unique or not. Unlikely, but who knows. Not me.  It was, however, new to me.  In this case, they have a hexagonal like connecting points between them. Which actually makes it very simple to do the repeats.  I left rather large gaps figuring that would help me create a neater finished fold. They could, of course, be spaced much closer together if desired.  It's not an easy fold because you have to twist the little rhombuses around the hex twists on the other side.  I've done these types of tessellations with both thick and thin paper. Either one works depending on how delicate you are as you work it.  There are a significant amount of overlapping folds...

 This intermediate tessellation is from a while ago. It's from my layering phase. It seemed like a really cool idea when I mapped it, but I wasn't that thrilled with the final product. Which is probably why I didn't upload it when it was new.  I recently found it in a box of old tessellations and noticed that it hadn't been posted. Just because I'm not that thrilled with it doesn't mean that someone else won't like it.  I like the concept... I think I just chose the wrong color paper. That doesn't seem like a very important decision, but it can have a big effect on how the finished model looks and photographs.  The center is rhombuses tucked into each other. Then I add trapezoids tucked on top of them. All well and good so far. It gets a little strange after that.  I add opposite facing trapezoid and repeat the center. The remaining gaps have an odd assortment of shapes. There are natural triangles, double wide triangles and tall isosceles triangles....