It's been a while since I've posted a new bit of origami. I've had origami writers's block being away from work this long. That's where I come up with my best ideas. At last, I have a new structure.  A central triangle has teardrop shapes off of it.  I added additional iterations of the central fold where the geometry permitted.  Filling in the empty spaces between with shapes that aligned. I tried to keep it all symmetrical. 

After some struggles, I've come up with a new design. New to me anyway. It's typical of my style - close together and circular. I've learned that I create and fold origami tessellations much more relaxingly and skillfully at work than I do at home. Better lighting. Better desk/seating. Less distractions. Since the corona virus I've been furloughed from work for several weeks. So I've been doing some origami at home. I can't just stop. You may as well ask me to stop my heart from beating. So I sit at my kitchen table and grumble and complain as I work the paper that normally bends so easily to my will. Eventually, the paper relents. I almost exclusively use a 32 pleat grid because I use somewhat small paper. I also have very small fingers. Even small paper is no mean feat to fold. So I try to come up with patterns that can repeat nicely within those constraints. This pattern was easy enough to conceive and tessellate. It was not, however, easy to ...

I'm not entirely sure if the method employed in this origami tessellation is considered a form of flagstoning. Although it's folded somewhat differently, it has a similar feel and end result. I've folded this odd triangular shape before in recreating other people's tesses. I just wanted to keep it simple and see if I could get a really clean, tight pattern. So it's just the little triangles and the bigger odd ones repeating. The odd shape triangles are made by alternating between two grid pleats, one offset until it becomes a closed shape. Pyramids on the rear create the negative shape triangles on the front. .  In this particular technique the little triangles are not twists. Picture the triangle inside of a hexagon. Then you invert the edges that make it a hexagon, leaving a triangle on top. The same is done to the edges of the other shape which are offset from the grid.

The beginning of this idea came to me quite easily. How to make it tessellate I struggled with for a bit. But when I get an idea in my sights, there's very little that's going to stop me from bringing it to fruition. It's inspired by the tessellations of others that use the same technique.Ben Parker and Arseniy K come to mind. It was a fussy fold. But it taxed the folder much more than the paper. I took a pic of the crease pattern for those that want it.

Here's a new tessellation. It feels similar, yet different to others I've encountered. It's a square grid tessellation using a 32 division grid. While my first major tessellation was Eric Gjerde's spread hexes , Fujimoto's clover tessellation was probably the very next one I went on to tackle. Between the two of them, my love of the art was permanently cemented in my psyche. This is much less complex than either, but still a wonderful exercise in the art of geometric paper folding.

I was fiddling around with triangle and rhombus twists again. Oh, rhombus twists, how you fascinate me. I'm a little lost since work closed. Coronavirus sucks! I do some of my best origami there. But the muse beckons just the same. I landed on a nice triangle based tessellation that is new to me. Three rhombuses off of a triangle. Repeat. They eventually come full circle to create open back hexagon twists on the other side. Quite accidentally, the backlit pic of this tessellation reminds me of the coronavirus. It was not intentional. At least, not on a conscious level. It didn't look that way as I was working on it. But the camera often shows a different view than the human eye sees. If you look carefully at the center you can see the initial triangle and the triad of rhombuses that emanate from it. The unlit photo below shows a very different view of the same tessellation. It's nothing ground breaking, but it's a pretty nice finished product.

I obsessed over this idea for a while before I finally came up with a working solution. Somehow it seemed much cooler in my mind that it does in pictures. It was kinda tricky to execute. I did the hex twists on the back first. Then I pushed out the spaces between the pointy rectangles. Some double wide triangles on the back were coaxed into place with a few small folds to allow the hexes to remain flat. It's a nice pattern, but I was disappointed with how it backlit. On the plus side, I've not encountered it before. So, it may be new, or at least, uncommon.

I've had this idea for a while, but wasn't really sure quite how to execute it. The empty spaces really didn't want to cooperate. But some weaker paper proved to be answer. It's unusual for me in that it's not a flat design. The triangles have dimension. It is possible to flatten them into irregular triangles on the back, but I chose to keep them active on the z axis. I remember when I was first learning origami, I was into a John Montroll book about stars. He had a design for a star just like the one repeated here. Many of his books really inspired me and taught me a lot. So This particular design has some sentimental value. It's interesting to think about how various styles of origami converge and relate to create new designs and possibilities.

Everything feels like chaos right now. It's a scary time to be alive. We all deal with that in our own ways. One of the ways I deal is with origami. When immersed in folding everything else about the world and myself falls away. There is only the paper and my desire to coax it into the shapes that make it art. I've done a few tessellations that are what I refer to as faux flagstones. They have patterns similar to flagstones, but they are folded along the natural structure of a triangle grid and don't require any special manipulations on the reverse side. I'm sure this techniques has been explored before now, but it's relatively new to me. This tessellation is a teardrop shaped example of that. I believe I saw a photo on google of Ben Parker creating the same design. So I just sought to reproduce it. These types of designs are fairly easy to fold and great for those looking to better understand tessellations as a whole. A short while back, I did one using...

I'm fairly certain absolutely no one cares about origami tessellations right now. Nevertheless, distractions are useful coping techniques. This is another Ben Parker design that I decided to attempt. It was a pretty straight-forward pattern. Nothing terribly tricky in the structure itself. It wasn't easy to fold though. It wasn't super difficult, but it was pretty finicky. This style of flagstoning really interests me. The way all the shapes nestle together into almost impossible configurations. I just love it. It's also striking how beautifully flagstones show up in backlight. Another thing that's always amazed me about origami tessellations is how the reverse side can be as stunning and sometimes more stunning than the front side. The second photo is a backlight of the rear. I like to figure these things out on my own if I can. Most folders do. Still, I kept a crease pattern sketch for those that might want it. It's down below.

This is a mock flagstone of rhombuses. It's not a true flagstone. It's simply small hex twists on the back and natural rhombus folds on the front. I love the challenge of real flagstone tessellations. They are beautiful and diabolical. Still, there is something wonderful about the simplicity and ease of folding this type of design. It yields an impressive result with far less effort. All these years of folding so many tessellations, I'm still amazed by what one can do with a single sheet of paper.

This one is small offset hex twists with teardrop shapes off of them and blunt pyramids on the back. The pyramids on the back overlap some, but not enough to make it easy to nestle them together. So when I went to flatten it, I just did the best I could to get everything to play nicely together. It didn't work out perfectly, but the front has a nice finish in my opinion. I like how the backside pyramids result in funky shapes on the front. The benefit of using small hex twists that are folded similarly to open back hex twists is that you can create tessellations that fit nicely on a smaller grid that are not possible using a classic small hex twist. 

This is a pretty run of the mill tessellation. I may or may not have folded it in the past and forgotten. I have no doubt others have already folded it. It has a nice appearance though. Open back hex at the center with the pyramids around it. I'm thinking this would be much cooler using small hexagons folded offset. You'd get more repetitions for a cooler pattern. It's a pretty easy fold. Do the center hex and then create the arms on the other side. Use a a small hex to link the next repetition. The pyramids form as you move outward, but it helps to know they're there. You can use them to work the other side more easily. It's simple, to be sure, but it's elegant.

This is a variation on rhombus stars. There are a lot of rhombus flower/star tessellations out there. This one may or may not be slightly new. It backlights really nicely though. Small hexagon twists have rhombuses directly off of them. Repeat as needed. The small hexes are folded offset, like open back hexes. To link the iterations to the center it was just a matter of pushing some paper backward. The outer ring just needed some offsets to create the veins between them.

I found an image of this flagstone on google. It felt familiar, yet different. I wasn't really keen to do another flagstone, but it was fun to figure out the pattern. I didn't do a great job folding it as I was kinda figuring it out as I went. It's a little uneven. It still came out pretty nice though. I don't have a proper crease pattern for it because I mostly just worked it out on the paper that I used to fold it. It's not terribly complex. Central open back hex. Triangle twists and rhombuses off of that. Small hex twists on the other side between the repetitions.