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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

Twelve Sided Cogs Origami Tessellation

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So I finally bought some kraft paper to see what that's like for tessellations. It certainly made the folding process less intensive.  On the one hand, it made folding the grid slower. I'm not sure why. However, once I had all the folds in place, the actual collapsing took no time at all.  I'm not sure how I feel about that.  The tedious process of slowly coaxing all the shapes into place is both my favorite part and my least favorite part. .  This is dodecagons and rectangles. I originally wanted to do open back hex twists with the same rectangles, but it didn't work with the grid. The main round shape follows the same pattern as the bullet shape I've done previously. One cross grid, one with grid until a circle is formed. Both shapes are connected by flagstone style arms.  The reverse side generates a weird trapezoid type shape. I didn't pre-crease the reverse folds. I figured the front would sort of force them to behave. That proved true for the most part.  T

One Way Streets Origami Tessellation

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 I've been kind of short on origami tessellation ideas lately. I've done so many tessellations over the years that the well begins to run dry. Creativity is part of it. But geometry imposes its own limits.  I know there are many variations that simply don't occur to me. I discover it all the time in the work of others.  A single mind has its limits. Especially mine. There might be thousands or more undiscovered possibilities, but I can only ever hope to ever find a small fraction of them.  Still I persist and found this one.  A bullet shape that forms around hexagons. Some rectangles were required to make it work. Although not a true flagstone, it is folded in the same sort of way. All the shapes are connected by those angular arms that allow them to nestle closely together.  In order to fold it successfully you'll need to work both the front and the back simultaneously. Still, overall, it's not super difficult for an experienced folder.  I don't have a crease p

Bullet Rings Origami Tessellation

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 I'm still obsessed with variations on 'encapsulated' triangles.  This pattern is interesting in that it contains a shape that is partially rhombic, yet rectangular on its other end.  This results in a pattern where some of the triangles are dominant and others are submissive.  It's just an interesting set of shapes that naturally coalesce on the grid.  It's an intermediate difficulty fold on medium grade paper. Crease pattern is fairly obvious, but I have included it below.  Reverse side does require a little finesse to make it work. It fits perfectly on a 32 pleat grid.   

Hawaiian Leis Origami Tessellation

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Building off of some other recent configurations, I came up with this one. You've got the classic rhombus, the triangle and also an elongated rhombus. They alternate to form circular hexagonal shapes.  The back side is a little tricky. There is some freeform diagonal cross creasing required. Nothing super complicated. It's not something you would want to pre-crease. It's easier to just pinch into place as you work.  I was very conscious of trying to fit my idea into my typical 32 pleat grid as my previous idea did not.  Been toying around with the idea of using kraft paper. This seems to be the most economical and sturdy choice for tessellators.  The shapes in this tess are folded in the Scholz style. The points are pushed into and under the cross grid pleats of the adjacent shapes. It's a pretty popular and well documented technique.  Reverse side folding is important and critical to effective completion of the model.  I didn't save a crease pattern, but you can ea

Rhombus Circus Origami Tessellation

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So I came up with this tessellation pattern that I really like. I haven't seen it before. That always excites me. Unfortunately it just misses fitting on a 32 pleat grid with any full repetitions. I tried using a 48 pleat grid, but my paper just wasn't sturdy enough. I mapped it all out, but was only able to do the 32 pleat version with the paper that I currently have. .  Some fancy elephant hide paper might be in my future. Depends on how much I obsess about it.  It would also be really cool to see someone else fold it. If some industrious folder were so inclined.  It's a pretty cool design. It's tricky to execute and a somewhat complicated pattern.  The idea started with this single module. It came together rather easily.  How to repeat it didn't come as quickly, but I eventually found it hiding there in the grid and was able to map it all out in detail.  It was really disappointing however, to discover that I wouldn't be able to fold it in all its full repeat

The Wall Flagstone

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I screw around with variations on classic shapes and techniques. This is one such result. Close knit rectangles. Similar to the wall of rhombuses flagstone I did recently. Same idea. Different shape. It's good practice for honing your folding technique.  It's a pretty simple design that illustrates another way in which shapes on the grid naturally coalesce.  It's a 32 pleat triangle grid. You might think square grid for rectangles, but no.  I'm back to flat folds after a brief flirtation with the 3D variety.  I can't imagine too many would need it, but there is a crease pattern included below. 

Joel Cooper's Sunflower Tessellation

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  This is a reverse engineer of Joel Cooper's Sunflower Tessellation that I found in his flickr albums. It's old. 2006 old. But it was new to me. Not super complicated to figure, unlike the stuff he does nowadays. It's a slightly unusual approach to rhombus and hex twists.  As far as the actual execution is concerned, it was of intermediate difficulty. Neither easy nor crazy difficult.  It does backlight very nicely, which is always a pleasant surprise.  Joel doesn't tend to upload crease patterns for his folds, but I did save mine. So if you're looking to just fold it without figuring it, you can do that.  I just used slightly better than average printer paper. Nothing fancy. It was quite adequate. 

Ruffled Rings Origami Tessellation

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 I'm pretty sure that I tried to do this one a little while back and didn't quite achieve success. Didn't quite figure the reverse side the first time around. This time I got it quite easily. At least the concept and architecture anyway. The actual execution was another story.  It started out really difficult working from the front side of the paper. However, once I moved to the rear it became a lot easier. Not easy really, but less frustration, more just folding.    Folding the back side really is the key. Alternating triangles and rhombuses. The rhombus points are 'eaten' by the triangles flat sides.  Similar technique to that used in Scholz's Triphilia tessellation.  I did save a crease pattern sketch. It's not terribly detailed, but it should be helpful if you're interested.

Origami Framed Stars Tessellation

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  Lately, I've been coming up with tessellation ideas that don't truly fit the grid and therefore don't result in a flat fold. Three dimensional origami tessellations are nothing new to the world at large, but they are still kind of new to me.  I've done a few. This is my latest. It turned out pretty nice.  It combines flagstone and 3D.  Unfortunately I was using discarded paper with a print out on it. So that distorted my photo of the bottom shape a little.  For a long time I took the approach that  going 3D was a cop out. If I couldn't find new shapes and patterns in the paper that naturally flattened, then I wasn't really succeeding.  But, after having stumbled into a few 3D folds, I kind of came around to the idea that they're something new and exciting. A different sort of challenge.  Rather than grind on the same old same old, why not embrace a new experience and explore its possibilities. . 

Razor Wire Origami Tessellation

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I saw someone's tessellation somewhere on the internet. Don't remember to whom it belonged. Went looking for it, but did not find it again.  Had previously downloaded the photo and decided to try to replicate it. Once I zoomed in on the pic it became mostly obvious how it was constructed.  Their fold was much neater than mine. My paper simply wasn't up to the task. But I was able to complete the tessellation. It's just a little janky, but still legit.  I actually like the backside a little better than the front. Which is why I made that the first photo.  It's a small hex twist on the back, then do some rhombus twists one small natural rhombus off of the center. Triangle twists off of the rhombuses. Some half offset triangle twists form in the gaps. If you've ever folded that triangle twist between small and two pleat, it's that, but only half of it.  A unique and interesting flagstone for sure.   

Escher Steps Origami Tessellation

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 I came up with this odd shape that I really haven't seen before in other origami tessellations. It's not ground breaking. It follows the same basic principles as other grid shapes. It's a flagstone fold for sure.  It was new to me, so I just went with straight up repetitions. But it seems perfectly logical that it could be combined with triangles and other shapes in various configurations.  It was a pretty hassle free fold. Although, working the back side was definitely required.  It helped a lot to go to the back and tease those folds.  The opposite side takes an interesting picture too. An unusual tiling.  I do have a crease pattern sketch, though it's a fairly uncomplicated to figure without any assistance.