I was playing around with a triad of rhombuses off of a triangle twist. From there I just followed the trail the paper left for me. So there is a single small triangle twist dead center. Three rhombus twists come off of that. Then just repeat. As you form the repetitions some oddly offset hexagons naturally form. It reminds me of the triangle twist rings that are the bedrock of flagstone tessellations. Just another interesting variation on so many classic techniques.

This is one of those semi-accidental creations that have become my modus operandi. I began with a clear intent. That was the broad petal shapes that flank the center. I did not anticipate the triangles around the center hex. I guess that I should have.  I should know better by now. I'm fascinated by that small star that the grid can create. It folds the small hex like an open back hex rather than a traditional small hex twist. I guess you'd call it an offset small hex twist. This alters shapes and the way other folds can radiate from it. The bigger triangles on the back became obvious once the repetitions fell into place. I always expect some reverse side triangles in all my tesses. They're the mortar that makes everything else come together. Sometimes I see where they belong from the outset. Sometimes they just show themselves as I'm working out the other folds. If you listen, the paper tells you where it wants to go.

I saw a close up of this on flickr. It basically showed only the center. It's a Lydia Diard design if I remember correctly. Because it was a close in photo, the rest I improvised. It might be the same as the original or it might not. I don't know. When I first saw the design I was thinking it would look nice as repeating stars. It probably would. But once I'd done the center, it was obvious that would need a larger grid. So I changed the plan to fit the 32 pleat grid. I don't think I could do all those rabbit ears on a 48 pleat grid. Not without larger paper. Personally, I hate rabbit ear sink folds. They are a great way to make cool looking points in tessellations, but I find them incredibly tedious to fold. They're not so much difficult, as they are just annoying. That's how I feel about them anyway. I'm sure others feel differently. Give me a good hex twist any day. A nice triangle twist is great too. I do enjoy a nice flagstone fold. I love...

So after I finished folding that last flagstone, it inadvertently led me to this next design. That's the thing about tessellations. If I try to come up with one, I usually get stuck. But if I'm not trying, they just kind of happen. I suppose that is the nature of art. This isn't so very different from other designs. But it does take a slightly different approach. It's open back hexes. They are flanked by rhombuses. Then there are triangle twists between the rhombuses. All of these are mountain folds. There are also some valley folded triangle twists to make everything work properly together. The unlit photo shows the true structure a little bit better. I don't have a terribly thorough sketch, but I do have a very rudimentary one. Seen below. The mountain triangle twists do not appear in the sketch. But it's fairly obvious where they occur in the gaps formed by the rhombuses and valley triangles. Just connect tthe dots.

I found this flagstone on flickr. I think it was originally designed by Joel Cooper or maybe Peter Keller. The picture I saw belonged to someone else. For a flagstone it's pretty straightforward. I'm not great with figuring out flagstones, but this one is not complicated. It's just big hexes and triangles. It actually inspired a different flagstone pattern, which I've mapped out, but haven't folded yet. If you're familiar with flagstones this will make sense to you. If not, there are many flagstone crease patterns which illustrate the underlying structure. They all share a similar architecture. Personally, I have a love/hate relationship with origami flagstones. They are pretty predictable to understand, but not very friendly to fold. Everything is kind of dependent upon everthing else. So the fold is never fully realized until all of it is pushed into place. This photo of the rear shows the triangle twist triads that comprise the design that manif...