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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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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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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

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

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.

Herringbone Tessellation

Messing around with rhombuses yielded this interesting pattern. It utilizes reverse rabbit ear folds to create triangular points which connect the running rows of rhombus twists. The triangles form in the spaces between the rhombuses. Then there are mirror triangles to facilitate the the next row. It kinda looks and folds like a square grid tessellation even though it's done using a triangle grid. It's a fairly easy fold. I do have a crease pattern. Just need to take a pic and upload it. Update: photo of crease pattern added below.

Origami Tessellation: Galactic Centers

Here's a new origami flagstone tessellation that might be somewhat original. I've seen similar designs, but not this particular configuration. It begins with a classic ring of triangle twists around a hexagonal twist on the back. Then there are those odd polygons which alternate between following the grid and bisecting it. I've included a photo of my crease pattern and a view of the backside below.

Ruffled Rings Origami Tessellation

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.

Mysteries of the Triangle Grid

I discovered this elongated rhombus shape at the gatheringfolds website. I can't believe it never occured to me before. It seems so obvious after the fact. It's basically just two rhombuses stacked on top of each other. That shape led to this configuration. A central small hex twist on the rear with the elongated rhombuses spinning off from it. Some double wide triangle twists between the repetitions. It's a very simple design, but I really like it. For this one, I did keep the crease pattern. So if you're just looking to fold without having to figure it out, you can do that.

Angles of Trust Origami Tessellation

Fiddling around with triangle twists and shapes that might complement them is how I wound up with this particular configuration. It turned out to backlight really cool. I was inspired by someone else's tessellation that I had previously recreated. Their idea just set me off on the path to this one. It came together rather quickly. When unlit appears as flagstone type small hexagons around larger hexagons. Triangle twists to make it all work. Backlit, you can see it's actually natural rhombuses. It's a pretty straightforward fold. Not too difficult at all. I did draw a single module crease pattern. If I can find it, I will upload it and it will make everything pretty clear, if it isn't already. Update: adding crease pattern

Escher Steps Origami Tessellation

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.

Hungry Rhombuses Origami Tessellation

There's a variation on classic flagstones that doesn't use triangle twists on the rear. Instead, it's a tucking in of the space around the foreground shapes. I've folded several examples of this technique in models originally designed by others. It's a pretty difficult way to fold, but it does open up a new array of design possibilities This design uses that technique to closely nestle rhombuses in rings around open back hex twists. The hexagons and the rhombuses are the only two shapes. No triangle twists are required on the backside. Super hard to fold on average weight paper that isn't very large. I wasn't really confident I would actually be able to complete the model, but in the end it did finally come to fruition. When folding in this style you'll benefit a lot from a blunt, yet pointy tool of some sort to tuck the paper under itself. I use a metal nail file.

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