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From the Beginning

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This tessellation is straight from Eric Gjerde's book 'Origami Tessellations: Awe-Inspiring Geometric Designs'. I don't recall the title of the design. I just have a memory of how much I loved how it backlit. . I folded it years ago, but had never posted it here.  So feeling both nostalgic and lacking for any new ideas, I decided to fold it again.  I actually first learned the fundamental principles of origami tessellations from that book. It set me off on a path where I just kept digging deeper and deeper into more and more complex folds. I'm still obsessed with the craft and always learning. So thanks Eric.  All these years later, what once seemed such a difficult concept to wrap my head around, now feels elementary. I banged it out in only minutes once I'd completed the grid.  Nevertheless, It still backlights beautifully. Another great example of how the simpler designs produce some of the most wonderful results.

Rolling Stones Tess

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Just riffing on " Joel Cooper's Sunflower Tessellation " that I folded not too long ago. Playing around with other possible combinations of shapes.  When I mapped this one out it was clear it would not fold flat. But I liked the idea enough that I was ready to try to do another 3D fold for a change. Was hoping it would generate a cool design when backlit. This is subjective, of course. But here are the results.  So it's a classic circle of triangles with a small hex twist on the reverse side.  Then where the sunflower tessellation employed rhombuses off of that, I wanted to do open back hex twists.  Because the design doesn't flatten the backlit images show odd shapes that don't match up with the what you would expect to see.   My crease pattern drawing is included below. 

Supernova Tessellation

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  This is an odd variation on triangle twists around a small hexagon. I folded the triangles in on themselves. Folded them in half. Once two such were done this created the point connecting them. Tucked a hexagon backward off that point to be able to flatten it. I hate reverse rabbit ear folds. I avoid them whenever possible.  The whole affair is a bit of tight fit. They're not normal hexagon twists. Several of the axes have to bang into each other with one tucked below the other. Still, it does work without much fuss.  The paper got a bit curled up on itself during the thick of it, but nothing a careful eye can't handle.  I would've repeated the central design, but my grid was much to small for that. Only a single star point repeated. So I just adjusted it to what I thought made a nice looking finished edge..  Rather less complicated than my usual fare. A nice change of pace.  I do have a crude crease pattern. It's included below. 

Hello and Goodbye Origami Tessellation

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 My previous square grid triangles tessellation gave me an idea for another. It's not that different. It seemed way cooler in my head. I wanted them pointing at each other as well as going in opposite directions. Same basic principles. Just reverse a few things. I thought about leaving no gap between the flat sides and decided against it. But maybe that would've been more interesting.  Honestly, I didn't want to do all the extra folding that would've been involved. 

Triangles North and South

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 Decided to do some square grid tessellation work. Just to keep up my understanding of it. Thought triangles might be interesting. I've casually wanted to do something with triangles on the square grid for a while now.  Used what I learned from this tessellation as a jumping off point since the triangles are really just half diamonds and the flat side is the same as a single side of a square.  It came together rather uneventfully.  It needs a lot of small diagonal folds in both directions. A little bit tedious in the prep work.  The actual collapse is pretty simple. However, it does overlap some on the backside. As you get closer to finishing the collapse you'll need to tuck certain folds under others. The specifics  will become apparent as you approach completion.  I do have a rough crease pattern that I haven't yet photographed. Will add it at a later date.  Update: Adding crease pattern....

Puzzle Pieces

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 This tessellation was inspired by the way in which a small hexagon can be folded offset from the grid creating triangles very closely surrounding it. Like in the ninja stars tessellation . I figured why not see how it works out if I turn those triangles into rhombuses. Sounds logical, right? It worked out pretty nicely.  A very straightforward construction. Completely non-irritating to fold.  Still you wind up with a pretty picture for your not so hard work. The negative spaces are a larger version of the shape seen in the ringing bells tessellation . If there's a name for this shape, I don't know it. I guess it's a trapezoid variant of sorts.  I went with two pleats between where the rhombuses meet each other. You could go only one pleat. That's how I drew the crease pattern included below. I'm pretty sure you could even go no pleat and wind up with an even more compact version of the pseudo-trapezoid in the negative space. 

Natural Miniature Just Rhombii Tessellation

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  This is an idea that I had a while back, but it seemed next to impossible to actually execute.  While it's not a very clean fold, it's satisfying to have done it. Slightly better paper might have yielded a somewhat neater finished product.  It's a very small, very densely structured design.  It's rhombus flowers, like the classic just rhombii flower flagstone . However, it's the tiny rhombuses natural to the grid.  Collapsed hexagons are at the center of each 'flower'. Small triangles negotiate the spaces in-between. Crease pattern is included below.  . 

Origami Tessellation: Spinning Turbines

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So I came upon an interesting tessellation someone had created and I went about reverse engineering it. I thought from the single module I had come up with that I had it all figured, but I missed a few details which later revealed themselves as I went ahead and folded the larger incarnation.  Upon realizing, I returned to the original photo and figured out the steps I'd missed. A fold for another day.  My 'mistake' actually resulted in a pretty nice finished design. Pictured here first front, then back.  Central small hexagonal twists have double length rhombuses two pleats off of their axes. Repeat. Very large triangles form on the reverse side. They bisect three of the grid's tiny rhombuses.  It's an uncomplicated and relaxing fold. For what it's worth, those seem to be the sort that yield the most brilliant photos.  I have a very messy crease pattern photo. There are other ideas in the background, but the red lines still adequately illustrate the design. 

Joel Cooper's Rhombus Stars and Hexagons Flagstone Origami Tessellation

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  This is a Joel Cooper flagstone tessellation that I'd seen before, but for some reason, I had not really paid much attention to it. Until now.  It's his rhombus stars and open back hexes repeating. Fairly straight forward design once you're familiar with the structure of flagstone tessellations.  He does a video tutorial for it at his website. But video tutorials feel slow and frustrating to me.  He doesn't pre-crease beyond the standard grid. Which boggles my mind. My paper just doesn't behave that way. He also folds it in stages. One shape at a time. My paper doesn't do that either.  I always have to ease everything into place as a whole. End result, pretty much the same.  It was easy enough to map it out on a triangle grid and follow the crease pattern.  I used slightly better than crappy paper and it was a pretty fuss free fold.  Crease pattern is included below for those that want it. 

Rhombuses with Good Intentions

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  In further exploring what shapes and configurations might work in an origami tessellation with a central six triangle twist core, I arrived at this result.  It's not a terribly elegant or clean tessellation. Although on paper and in theory it works, it's a bit fussy and messy to fold.  The first time I tried to do it I used flimsy paper and while I was able to complete it, it was sloppy and poorly constructed.  I tried again, with slightly better paper. It did work out nicer (as shown) but still not entirely as I had envisioned.  Really sturdy paper, I avoided, since I figured it would never allow all the overlapping and too close together folds required. But perhaps, patience and sturdy paper are actually what this tessellation requires. But I'm not up for fold it a third time to find out.  Crease pattern is at the bottom. 

Big Wheels and Little Wheels Origami Flagstone Tessellation

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  I had seen a pic of a tessellation someone had done that was the classic circle of flagstoned triangles surrounded by large blunt pyramids. This led me to wonder what other shapes might possibly be able to tessellate around that familiar circle of triangle twists.  That is how I arrived at this configuration.  It begins with the familiar flagstone circle of triangles emanating off of a small hexagonal twist on the reverse side. It's from there that I wondered how open back hexes would work as the next layer. It turns out that they work out quite nicely. Oddly offset parallelograms form on the back to reconcile the shapes on the front.  I had been fumbling around with ideas for flagstone open back hexes for a while and not really finding anything useful when this idea came quite suddenly. It all just coalesced pretty rapidly.  I used kraft paper thinking its sturdiness would be helpful, but it was actually really difficult to fold a true flagstone using such thick paper. I suspect

Parallel Perfection Origami Tessellation

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This is a pretty simple design that I stumbled upon quite accidentally. I was messing around with more complicated folds and not really succeeding, when this idea just jumped out at me. So I went with it.  Collapsed hexagons in one direction and elongated rhombuses in the other. Both the rhombuses and the hexes are natural to the triangle grid.  Some offset triangles result in the spaces between.  It's a pretty simple design. Fairly easy to fold. Any old paper will do. I have included a basic crease pattern for those that want it.

Pattern Searches Origami Tessellation

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 This is a variation on the open back hex twist and natural triangle tessellation . Instead of repeating the the hexes, they are half hexes, also referred to as trapezoids.  In order to repeat, you just use a mirror half hex off of each of the center hexes. Easy peasy.  This was my idea. Of course, it may have, probably, has been done before. But I've not encountered it.  It's not hard to fold. It is however, hard to keep track of the directions on the folds. Many of them are bidirectional.  So finishing a cohesive pattern kind of results in a lot of trying to keep track of which fold went which way and trying to determine what makes a sensible pattern to you. Circular or linear or something else altogether.  Using a 32 pleat grid further clouds the process since there are no full repetitions.  It's an interesting idea from which other interesting ideas might be gleaned. Make of that what you will. 

The Devil's Tessellation

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 I was going through some crease patterns that I'd saved from the internet many moons ago. I came across a few that seemed interesting. Little did I know how diabolical this one would turn out to be. Truly diabolical  I used good paper or else it would've been a complete loss.  Even the good paper took quite a beating in the process.  There were multiple times when I thought it simply was a theoretically accurate tessellation that wasn't actually foldable in real life.  However, I saw glimmers of it being possible as I stubbornly persisted in coaxing and cajoling the increasingly mangled paper into the shapes I desired.  Several hours later, it did bend to my will. I was stunned to have finally succeeded.  I don't remember where I found it. I don't know to whom it belongs. It was just sitting ide in my google photos when I rediscovered it. I almost wish I hadn't. But I'm glad I did.  I cannot stress this enough. A truly diabolical fold. Next to impossible. K

Mystery Crease Pattern

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 I found the crease pattern for this tessellation sitting in google photos. I'd saved it a long while ago and then forgotten about it. I don't remember where I found it. I don't know to whom it belongs or from what site it originated. I'd be happy to credit the designer if I could.  What I do know is that I was able to fold it. Which was no mean feat. This was truly one of those agonizing folds where you know it can be completed, but it's just really, really, really difficult to do so.  Maybe it was because I used pretty crappy paper. It looked like it would be simple. So I thought cheap paper would do. I was very wrong. And then wrong again and again.  Maybe it really is just one of those painstakingly tedious tessellation to fold that I both love and hate.  Perhaps, a little of both.  At any rate, it's a pretty neat result.  Left side is the crease pattern for the finished fold above.  Again. Not my crease pattern. Don't know whose it is. All credit to the

Paper Jaws

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I've been struggling to find a new flat fold design, but I did land on a three dimensional fold that I really like. Three dimensional tessellations aren't my usual modus operandi, but I do occasionally fold them. This is one such instance. The idea is simple. Open back hexagons are surrounded by triangles.  Normally they'd be situated in a twist or flagstone style that allows for flat folding. In this case they kind of bang into each other creating a pretty interesting end result.  No crease pattern is really needed. It's just open back hexagons and the triangles point at the flat edges. Repeat as often as the grid allows. Both the hexagons and the triangles face up to the front of the paper. On the back side the triangles have little 'flaps' almost folding over on each edge that can't quite be flattened. 'Bridges form between the triangles' shared edges.  It's a pretty easy fold. Finished model looks like it was way more difficult than it was. .

Syncopation Origami Tessellation

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I've been playing with certain shapes lately and how they fit together using a few different techniques for nesting folds. This is another variation on combining different shapes around hexagons using the classic flagstone method of nestling shapes closely together so they almost touch.  I've put this model up for sale on etsy. See the listing I started out using some flimsy paper and quickly aborted.  I've done many similar tessellations with not too thick, not too thin printer paper. So it's definitely possible. It simply can't be too thin.  However, since I recently acquired a bit of kraft paper I decided to see how that would do. It actually made it somewhat more difficult to fold, but resulted in a much cleaner/crisper completed model.  Folding the reverse side of these types of tessellations is sort of tricky. Once you get into the thick of the process it becomes quite clear what needs to happen.  A crease pattern was drawn and photographed. It should illustra