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Triple Trapezoids Origami Tessellation

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  This is an intermediate level tessellation that I recently created. It's a kooky kind of pattern that starts off very simply.  The center point is a small offset hexagon with rhombuses around it.  Next I add some open back hexagons and sets of three trapezoids.  Some rhombuses take up the remaining spaces.  This pattern repeats six times around the center.  At that point, I was getting close to the edge of the paper.  The open back hexagons repeat again. Then I just filled in the remaining space with more trapezoids and rhombuses. That third level has its own pattern. If you had larger paper and were to go for a forth level, that would need a slightly different pattern yet.  It's a little different from a traditional origami tessellation which repeats the same pattern infinitely. I'd  call it a progressive tessellation.  As you move outward the pattern changes slightly, but it can keep going and going for as long as you want. It's just a matter of reconciling the spac

Chasing Infinity Origami Tessellation

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 So, I decided to buy some fancy tissue foil paper from France. I had this tessellation idea that I wanted to do, but I couldn't quite get it done using any of my usual papers.  From what I had read online, tissue foil is supposed to be really great for tessellations because it's both thin and resilient.  This tessellation is my first time using it.  While, I did find it to be very sturdy against repeated folding, I also found it too soft. It didn't offer any push back. It didn't really hold onto creases. This made it quite tedious for me to put all the shapes in their proper places.  Admittedly, this is a very difficult tessellation, but honestly I was expecting more from the paper.  While I was able to finish the fold, it was incredibly difficult. The paper fought me every step of the way. I had planned to rearrange some of the orientations of the folds after the collapse was complete, in order to create a more cohesive pattern, but the paper was again, too soft.  So

Origami Tessellations: Double Parking

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 This little tessellation is unique for me in that I didn't really plan it. I just folded a 32 pleat triangle gird and mapped it out right on there. No fiddling. No testing. Just draw and fold. I'm not really sure what came over me, but it worked out well.  I even used ordinary 20 lb printer paper. Nothing fancy at all.  Guess I was just in the origami zone that day.  The center point is an open back hexagon with rhombuses circulating around it.  From there I stuck some triangles into the outer edges of the rhombuses.  At that point I got a little funky with it. Three of the triangles have double trapezoids off of them and the other three have double rhombuses. Both the trapezoids and the rhombuses follow the same pattern of reflecting outward in both directions away from their triangle beginnings. There is another ring of open back hexagons as well as some rhombuses on the back side.   At the point, I just fit in the shapes that would fill out the little bit of grid I had on t

Origami Tessellations: Into the Wind

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 Here's an easy tessellation that looks really cool when finished.  I have the nagging feeling that I've done this one before, but if so, I haven't been able to find the previous version.  It uses just one shape for its foundation. I'm not sure if there is an official geometric name for this shape. I was pretty good at geometry and I don't recall anything like that.  It's a six sided and triangle like shape. Obviously it's not a triangle, as those have only three sides. But when you look at it, it makes you think of a triangle.  I just took that shape and used the cross-grid edges to connect them to each other. In doing so, some large hexagons formed on the other side.  That's it. That's all there is to it.  My crease pattern is included below if you'd like to fold it. 

Scattered Dreams Tessellation

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This tessellation is all rhombuses on the front. It starts with a small hexagonal twist with rhombuses around it. From there it progresses by adding additional rhombuses  until I'm able to also add some open back hexagons. The pattern of repeating the open back hexagons and rhombuses can then continue repeating.  When you break it down to it's components, it's essentially two base ideas combined into a single design.  You've got the small hex with rhombuses offset around it and then you have the larger hexes with the small rhombus spiral going around them. I just added enough extra rhombuses to transition between the two.  It's an intermediate level origami tessellation. Nothing too crazy.  I found it particularly interesting because I was able to do all rhombuses on the front and almost all hexagons on the back. There are some rhombuses on the back too. But there are no triangles at all. Which is a little unusual.  I do have my diagram that I used to create it. I&#

Stairway to Heaven Origami Tessellation

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 This is an interesting little flagstone tessellation that I designed. It's a linear style of alternating trapezoids. I also used some regular rhombuses as well as double length rhombuses to help the pattern repeat nicely.  It's not a design I've seen before, which is always nice to find.  It repeats very nicely on a 32 pleat triangle grid.  I used tant paper. I'm pretty positive it would also work with any somewhat thicker printer paper.  This is an idea that I've had for a while, but I kept thinking that it was too simple and I wasn't motivated to actually fold it.  It also took a little fiddling before I realized how it would tessellate neatly.  Eventually, I worked it all out and was quite pleased with the end result.  It's a little difficult to fold, as are most flagstones. But with sturdy paper it is a mostly pleasant experience.  My crease pattern is included below for those that might wish to attempt it.  It's worth noting that when you fold a te

Origami Tessellations: On the Dance Floor

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 This is a triad based flagstone tessellation that I recently created.  The starting point is an open back hexagon with alternating trapezoids and rhombuses  collapsed around it.  From there that pattern can be repeated by adding an opposite facing trapezoid off of each central one.  That, however, leaves a lot of empty space to reconcile.  I did so using a series of additional rhombuses as well as a few triangle collapses.  It's all just a matter of making the space work for you.  The reverse side, as you would expect of a flagstone tessellation, is a vast array of triangles.  It's somewhat different from any tessellations I've seen before. It's an interesting study in how far you can go in manipulating the paper if you're able to discern what combination of shapes will rectify the gaps in your ideas.  A starting idea is a wonderful thing, but working out how to take it all the way to completion is where the real magic is done.  This ability comes mostly from pract

Origami Tessellation: Power Fluctuations

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This is a pretty easy tessellation if you're looking to get a feel for the process.  Open back hexagons have trapezoids collapsed around them. It's a really easy starting point.  Then we just add some rhombuses tucked into the points of the trapezoids.  At that point, the pattern can be repeated.  Large pyramid shapes fill out the remaining gaps.  If you're looking for an easy tessellation to get yourself familiar with some basic techniques of the genre, this one would be a good place to start.  I did draw a crease pattern. I haven't taken a pic of it yet. Will add it later on.  Update: added crease pattern at the end.  But all the shapes are right there in plain sight. There are no tricks or secret sneaky folds. It's a very straightforward tessellation. It shouldn't be too hard for even a beginner to figure out.  If you decide to fold this, leave a comment and let me know!

Origami Tessellations: Whirling Dervishes

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 This is a fun little tessellation that I came up with in an effort to be able to fold something new during high humidity.  I talk about humidity a lot in regards to folding various tessellations. The paper absorbs the moisture in the air and becomes soft and difficult to fold. Particularly for your more intricate patterns. Simpler designs, however, are still perfectly executable under most any weather conditions.  This tessellation is a prime example.  I used ordinary 20 lb copy paper on a drizzly day and it turned out very nicely.  The premise is rhombuses twisted around a small central hexagon. From there some small triangles twist off of them. Then just repeat.  This tessellation is actually a variant of another tess I did not too long ago called Flowers in the Garden Tessellation . Both begin the same, but diverge slightly in how they repeat.  On the reverse side there is just an array of open back hex twists.  So, not so simple as to be boring, but not so difficult as to be a pro

Cotton Candy Tessellation 2.0

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This is a tessellation that I did not that long ago. I called it cotton candy because I had used pink paper and it made me think of that.  I came up with the crease pattern again without realizing that I already had. And then proceeded to fold it again before finally noticing it was a previous design.  The first time I folded it, it didn't turn out as nice as I would've liked. This time around though, it came out much neater and looking more like I expected it to when I conceived of it.  It's an unusual design that puts together several different shapes in a way that isn't typically used.  To access the diagram refer to my first fold/post of this tessellation called cotton candy .  There are also additional details in that post about the nuances of executing this particular design.  If you happen to fold it yourself let me know in the comments.

Caged Stars Tess

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 This tessellation combines offset rhombus star twists with collapsing trapezoids to create a unique pattern.  The other main aspect of the tessellation is a series of six trapezoids rotating around a small hex twist on the other side.  Initially, the trapezoids emerge from the central star by tucking over the edges of the rhombuses.  It's from there that they twist around the small hexes and collapse upon one another.  This a hybrid fold utilizing flagstone, collapse and twist techniques.  It's a medium difficultly tessellation.  The hardest aspect is the spaces where the trapezoids meet at their long edges. There are narrow rectangles that are a little tricky to fold. Everything else is pretty straightforward.  The second photo, of the reverse side, shows the long rectangles between the trapezoids.  For further details on how to execute this tessellation, consult the diagram included below. 

Origami Tessellations: Hungry Pythons

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 This tessellation is kind of different from my usual modus operandi. We have tall isosceles triangles that wrap around six sided polygons.  My ' Fireworks Display Tessellation ' uses the same triangle shape in a much denser configuration.  I actually came up with this tessellation before I did that one. I had simply forgotten to take a photo of the diagram, so I was waiting on that to post this. In fact, it was this tessellation that led me to that one.  It's pretty common for one configuration of shapes to inspire something similar, yet entirely different.  This one is far simpler and easier to execute. The end result is a pretty neat pattern though.  Crease pattern included below.

Solving Emergent Triangles Tessellation

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 It took me a little while to solve the 'emergent triangles' tessellation by gathering folds. I was kind of stuck on the idea that it was a group of six triangles and then another group of six rhombuses. When that kept leading me to dead ends, eventually, I tried a different approach.  Instead, I solved for the set of three rhombuses around the large hexagons. It was from that starting point that I finally worked out that the triangles  and rhombuses had to alternate.  It was definitely a eureka moment.  It's a wonderful design. Another one of her trademark mirror image tessellations. Each side is a mirror of the other.  I do have a diagram, but I haven't taken a pic of it yet. Hope to add it soon.  Update: diagram added. 

Origami Tessellations: Fireworks Display

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 This is a tessellation that I was really thrilled to have created. The pattern utilizes a different triangle shape that I've not worked with much at all. It's a taller triangle than what you'll typically find in origami tessellations. Also known as an isosceles triangle. Two sides are equal and the bottom is smaller.   The longer sides of the triangles are 1.5 pleats long. While the bottoms are a single pleat.  I created a rotation of six of them around a classic small triangle collapse. They alternate forward and back as they go around the center point.  In order to repeat the pattern, there are natural triangle twists on their outer edges. Three of the isosceles rotate around those.  At that point, the repetitions can keep going ad infinitum.  All in all, not too difficult to execute, but a pretty remarkable end result.  I used tant paper folded into a 32 pleat triangle grid.  As with all origami tessellations, this is folded from a single sheet of paper. The paper wa

Infinite Sprockets

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  This is a tessellation that I came up with after having done a very similar one. That first one ( Controlled Chaos Origami Tessellation ) had exceedingly small rectangles, which made it nearly impossible to execute cleanly on both sides.  In this case, I made the rectangles bigger and it became infinitely more manageable.  I'm pretty sure that I've seen this one before. I think that I've seen it done by  Daniel Kwan as a crease pattern posted to his flickr account.  I was not using that crease pattern while conceiving of this, though I did have some recollection of having seen it in the past.  The front is all right triangles.  The back side is small offset hex twists, the aforementioned rectangles and small triangle twists.  Even with the larger rectangles, it's still a difficult to fold tessellation. The triangles and rectangles overlap each other.  My crease pattern diagram is at the end of this post. 

Partners in Crime Tessellation

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 This one has a bunch of shapes in it, all working together to form the whole.  When creating a tessellation, I usually just start with one shape that interests me at the moment.  From there, I choose whether it'll be a six axis or a three axis rotational repeat. In other words, will I try to repeat it around some form of triangle or some form of hexagon.  Once I have a starting point, I mess around with additional shapes which may help me to further create repetitions.  The last step is just to figure how to fill in any gaps that are created.  In the case of this tessellation, I started with natural triangle twists off of the six edged pyramids shown in the first photo.  At the point, I added an open back triangle twist to repeat the natural triangles. Rhombuses were the final puzzle piece needed.  On the reverse side I wound up with some rhombus based cubes and two different sizes of negative space triangles.  This tessellation is not difficult. I was able to execute it using ord