This original origami tessellation is a little different from what I've been doing lately. It's nice to change things up occasionally.  It uses a technique that I learned a long time ago when I folded a tess by Arseniy K called razorblades .  It's right triangles situated around an open back hexagon.  However, in this case, I used that same central point, but changed the shapes that link up with it. I connected the right triangles via flagstone style collapses to additional open back hexagons. Then I repeated the center. In the remaining spaces the right triangles alternate around the hexagons in an interesting forward and back pattern.  I have a diagram. I'll included it at the end of this.  This is a difficult tessellation because of what needs to happen on the backside in order to make the front work.  In the razorblades tessellation there were large triangles to connect the repetitions. It was a very straightforward pattern. Because of the different...

 More fun with trapezoids in flagstone tessellations .  The idea for this was a triangle twist with three trapezoids spinning around it So even though the center is six triangles, that was just a way to make the shapes around the edges work.  Although, I would imagine that if you wanted to you could conceive of a design where the center point could repeat instead.  The six triangles with the trapezoids eminating out from it. That would be an interesting variation.  The back side is almost exclusively triangles except for the one center hexagon.  As far as flagstone tessellations go, this is one of the less difficult ones.  Crease pattern included.  Filed under: June 2025  Origami Tessellations

 This is one of your simpler ideas as far as tessellations go. A standard six sided shape with triangle collapses tucked into it. And repeat.  The main shape, besides the triangles. is a common one you might find it many origami tessellations. It consists of one cross grid crease, then one that follows the grid and continue until  you close the loop.  It's kind of a simplified version of the Bells tessellation I did several years ago using the same two shapes. In that case, I connected them using collapses, instead of tucks.  In that one there were only small triangles. In this one, there are small and open back triangles.  As you explore various shapes and folding techniques you'll find that many patterns can be recreated in similar, yet different ways. That's the amazing symmetry of the geometry.  Looking at the reverse side you can see the collapses of the small triangles as well as the larger ones. Because of the multitude of small triangle colla...

 This tessellation is a somewhat random idea. It's really only a pattern in the most liberal sense.  Basically, I started with rhombuses around open back hexagons.. Then I added small offset hexagons and repeated the two ideas as best as I could. Once you add a few offset hexes you can then repeat the larger hexagons. The pattern of rhombuses and triangles is rather unorthodox, but it does work.  It's anyone's guess how to arrange the moutnain and valley folds in order to create a consistent design.  It's make for a pretty picture though.  It's a lot of work, but it isn't very difficult.  My crease pattern is included below, but it's not all inclusive. I think I had to work some shapes out as I went along. 

 This is an odd one. I was just fiddling with small shapes I could nest around an open back hexagon. As I was trying to decide exactly how to repeat the pattern, I looked at the other side and decided I liked it when the spaces on the back were right triangles. So I went with that configuration. And here we are.  While the beginning idea for this tessellation was the narrow parallelograms around the open hex, the true inspiration point was when I looked at the other side to determine how to make it repeat. It was then that I saw that I could create negative space right triangles nested against the hexagon.  At that point, it was just map it and fold it and just like that another origami tessellation was born! I debated calling the back the front and the front the back. It's all subjective, I suppose. I like them both equally in their own way.  This is an intermediate level tessellation . Nothing too difficult. Nothing too easy either.  Crease pattern included....