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Origami Tessellations: Single Sheet Geometric Paper Art

It's amazing what you can create from a single sheet of paper. No scissors. Just folding. Exploring origami tessellations and the art of paper folding. Reverse engineering tessellations of others found on the internet, folding shared crease patterns and sharing my own origami tessellation creations.

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Showing posts from June, 2018

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Rhombic Star Swarm Origami Tessellation

Posted by softermaniac on June 18, 2018

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Keller Flagstone Tessellation

Posted by softermaniac on June 17, 2018

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Triangles and Hexagons Tessellation

Posted by softermaniac on June 04, 2018

origami tessellations

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About

Origami tessellations are the art of using a single sheet of uncut paper to fold intricate repeating designs.

They begin with a square or a hexagon. Everything else is pretty much geometric magic.

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Snowflake Treasure Tessellation

I was googling for new origami tessellation ideas and came across Ben Parker's snowflake design. I was going to attempt that, when a related image caught my eye. I think he called it "Hidden Treasure". It was a little more complex and really piqued my interest. Second only to coming up with my own tesses, one of my favorite past times is trying to figure out how to fold those of others. This one wasn't too difficult to determine. The front shapes were obvious. Some hexagons at the center of the 'snowflakes'. I thought at first, triangles on the back for the negative space. As I began putting it all together it became obvious that it was not triangles. It was that blunted corner triangle that follows the grid. The same shape featured in this tessellation . Those shapes land on the rear of the paper to create the negative space triangles on the front and make everything else synchronize nicely into a flat fold tessellation. It's a beautiful design. Wish I

Natural Rhombus Herringbone Tessellation

This is in keeping with my exploration of non-hexagonal twists repeating. It's just a dizzying array of rhombuses all linked to one another. It employs an up/down repetition pattern. The rhombus shapes are different from traditional rhombus twists as they follow the natural grid lines. This crease pattern is a natural flow of the same single shape ad infinitum. It takes advantage of the natural folds of a triangle grid to create an easy to fold collapse that results in a complex structure of repetitions. It's difficult and a little confusing trying to get all the collapses to flow in the same direction. Especailly at the edges where the shapes get truncated. You could potentially alternate directions as well. Or come up with other patterns. The folds go forward or back at your discretion. I often find it frustrating to see a folded tessellation and no crease pattern to accompany it. Depending on how the photo was taken, the lighting and the clarity, it can so

Waterbomb Tessellation

When you google origami tessellation crease patterns something called the waterbomb flagstone tessellation comes up in the top results. It looked pretty simple, but I found it rather fussy. I really need to start working with better paper. Unlike your typical flagstone, which has triangle twists on the rear, this has little rectangles. It's a familiar pattern that still proved quite difficult. The front is offset hexagons and natural triangles. The back side is the rectangles. It feels almost like it's not meant to lay flat. But it also feels like it could flatten with a stronger paper. I didn't bother to flatten it with weights or books. All the time I spent working the folds were enough to create the intended pattern. It seemed like if I tried to make it entirely flat, it would be ruined. You can see the rectangles in the rear view. I've fiddled with rectangles and hexes before. But this was a whole new level.

Natural Rhombus Flowers Tessellation

I recently did a tessellation that used the smallest natural rhombuses in a triangle grid. I can't believe this hasn't occurred to me sooner. If you're familiar with triangle grids you know that two triangles form a rhombus natural to the grid. These are the rhombuses that were used in this design. There are small hexes on the rear center of the rhombuses. There are also small hexes on the front surrounding the rhombuses. Some triangles on the rear as well to make it all work. It was moderately difficult to execute. Mostly just because it caused the paper to curl up a lot. The folds weren't difficult, but seeing what you were folding was. When I search for tessellations and crease patterns I don't come across ones like this. It's similar to a flagstone with a less complicated rear. Everything on the front flows together without much issue other than the fact that there is a lot of overlap in the background. Some people must have come across this pos

Narrow Bridges Origami Tessellation

Combining open back hexagons with regular heagon twists has been something that I've wanted to do. This tessellation uses a lot of offset folds to achieve that. It's just a bizarre crease pattern that was not easy to fold. The first time didn't work out. The second try did. It backlights very nicely. There's a lot going on in there. You can see the open back hexes dominating the front of the design. There are large triangles right off of those. The regular hex twists land on the rear. As do some triangles which are natural to the grid. I didn't see those triangles at first. When I finally did, it all came together. My first attempt was unsuccessful. The paper was a little weak for the task. I kept that for the crease pattern and tried again. Overall, the second attempt was pretty successful. I got frustrated with the edges. Those are always a pain when they result in partial folds. It's tough to get them to comply. Still, I'm pleased with des

Ninja Stars Origami Tessellation

It's about time I added a new origami tessellation. This one was as frustrating as it was satisfying. My paper was not cooperating, but I persevered. I've explored similar designs. This one took it a step further. It uses the smallest rhombuses natural to the grid to connect an array of stars that are formed from offset hexagons and the resulting triangles. When you fold an offset small hex twist small triangles naturally form. This creates the stars. A typical hex twist follows the normal grid lines of a triangle grid. These hex twists fold bisecting the grid lines. However, unlike traditional open-back hexes, they are the smallest hex available on the grid. The hex shape itself does follow the grid. It's only the twist that is offset. I actually have a crease pattern from my planning stage which I haven't yet photographed. That would probably explain it better than words can. I'll hopefully upload it soon. There are also larger triangles on the rever

Intersecting Arrows and Octagons Behind

So, I found the crease pattern for this on google. Whose it is, I'm not certain. I was drawn to it because it seemed pretty straight-forward, but it was actually really difficult to fold. I'm sure my paper didn't make it any easier. It was probably too small and probably not the best density. The first time I folded this, it was good on the front, but terrible on the back. At that point, I felt that I understood it well enough to do a much better version. The second attempt did come out much better, but really wasn't much easier. I really like this pattern. Pointed rectangles on the front. Octagons on the back. It's simple in theory, but complex to execute. Very elegant. All those fiddly little diagonals seem to wreak havoc on my paper. Honestly, I think it just needs bigger paper. That would probably make all the difference. Or a much sturdier paper. But I pressed onward and was able to complete a second attempt with a pretty good result.

Window Panes Tessellaton

I had found a tessellation and crease pattern on flickr that I was curious to fold. I did fold it. Twice. This isn't it. More on that next time. This is the pattern it inspired me to create. It's probably nothing new. It's pretty obvious to the grid. Nevertheless, it was new to me. It's full on winter weather here in the northeast, so my photos are not lit the way I would like, but next springtime is distant dream. So we persevere. For a change of pace, I've been working with a square grid rather than my favored triangle grid. I find square grid tessellations of any real complexity more difficult to fold. Everything seems to happen in a much smaller space and is nestled so close together. And they always seem to need way more preceases. Even with a clear and perfectly feasible plan, there's quite a lot of struggle to get the paper to do what I want it to do. Maybe that's just my inexperience with square grid tessellations. This one, however, is

Woven Hexes

This is a classic weave pattern. Open back hexes and small triangle twists are just one pleat apart. This results in the woven pattern on the other side. I think I've tried to do this before. It seems familiar. But I couldn't find any pictures of such a tessellation in my personal archive. I suspect I may have attempted it and failed before. On this occasion, I was able to complete the project. It's a fairly simple pattern, but because everything is so close together it's a little tricky to execute. You can see from the crease pattern pictured further down that the triangles are only one pleat off of the axes of the hexagons. This makes everything fit together rather tightly. There's a lot of overlap. After completing the center, it gets temperamental. You can partially fold sections, but everything is interdependent for the most part. Good preceases are a necessity.

Embracing the Triangles

I've been screwing around with the natural folds of a triangle grid. It's a little less intense than flagstones, but has a similar feel and result. This one is all triangles. Which, up until this point, I had not realized was a natural fold. I don't know how I've spent so many hours folding tessellations without coming across this sooner. It's just natural triangles on the front and hex twists on the rear. When I got to the edge I went with rhombuses as that made more sense. The folds on the back overlap a lot, but it's nothing unmanageable.

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