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Solving Cogs Origami Tessellation

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 This is a tessellation by gatheringfolds called 'cogs'. I didn't have any trouble solving the center, but my 16 pleat tester didn't fit the rest of the design.  I decided to just go ahead with a full 32 pleat execution and figure the rest out as I went.  Once I had enough space to work out the rest, it wasn't too difficult. Some plain printer paper stood up pretty well to my final adjustments.  It's a rather large tessellation that doesn't really repeat on a 32 pleat grid. Still, I liked it enough to go ahead with it anyway.  I gave a little thought to how it might repeat in a smaller space. But that's an idea for another day.  The center is a small hex twist with trapezoids emanating from it. Open back triangle twists fill in the gaps of the central module.  To repeat it there are large pyramidal shapes as well as long parallelograms. Personally, I like the pattern on the back (second pic), a little better.  I used ordinary printer paper. The various s

Origami Tessellations: Spiral Staircases

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 This is a modification of a tessellation by Arseniy K called 'Pixelated Chrome'. I changed it up to repeat  on a smaller grid.  The structures are very similar, but the results are different. Mostly because I used paper that backlights really well.  I used the same size rectangles, but smaller, natural triangles.  It's a pretty easy to fold tessellation. I encountered no difficulties with the execution.  I used white, 28 lb printer paper folded into a 32 pleat triangle grid.  The diagram for my version is included at the end of this post.  The crease pattern for his is available on his instagram feed. 

Shy Hexagons Origami Tessellation

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 This is a pretty simple tessellation that has some interesting patterns.  What I wanted to do was tuck some open back hexagons under some straight lines. This is where I arrived with that.  I kinda mostly worked on the reverse side pattern more during the conception than I did the front.  The front has forward facing open back hexagons connected to long parallelograms.  In-between the parallelograms are more hexagons hiding shyly. Hence the name.  On the reverse side are small triangle twists around the prominent hexagons.  You can also see how the shy hexagons are formed.  As I said, it's one of your less intense tessellations. I just used plain printer paper and had no issues.  I believe that I have a crease pattern for this. Will upload it when I find it.  Update: crease pattern added below. 

Origami Tessellations: Quilted Lattice

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  While perusing Instagram, I came across a new tessellation by Aresniy K called 'Wheel of Misfortune'.  As I was working out its construction, it occurred to me that a really beautiful variant was possible.  His is a circular style pattern of long parallelograms tucked into each other.  In my case, I went with a linear weave pattern of the same shapes.  While it's pretty basic from a conceptual standpoint, it yields, what I think, is an impressive finished product.  On the front, it's all parallelograms. They need to be long enough to accommodate tucking the perpendiculars into each other.  On the back side, micro rhombuses are the main component.  I didn't create a a diagram for this one. It wasn't really necessary. It's just the one shape repeatedly tucked into itself at 45 degree angles.  Once you begin folding the front, the small rhombuses on the other side are mostly forthcoming.  I used a 32 pleat triangle grid and that had room for plenty of repetit

Hesitant Helicopters Tessellation

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 I created this tessellation from back to front. The idea for the layout was initially the three open back triangle twists around a small triangle twist.  But as I worked the design and interacted with the paper, the concept shifted in my mind and the front became the back and vice versa.  Interesting how that happens every so often. Planning can only account for so much. Sometimes theory is eclipsed by execution.  The now front side is comprised of open back hexagons and small rectangular twists. When backlit, they almost appear to be spinning.  The other side is the aforementioned sets of triangles.  The trickier ideas will often surprise you, even when you think that you've got it all figured out.  Crease pattern included at the end. 

Origami Tessellations: Unexpected Detours

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This is a layered tessellation that combines rhombuses and trapezoids.  The rhombuses form a circular pattern around an open back hexagon. The next layer is the trapezoids nestled on top of the rhombuses.  The trapezoids are repeated in a triad around an open triangle twist. That then creates the opportunity to repeat more sets of rhombuses around open back hex twists.  It's a somewhat intricate pattern that's best viewed in closeup.  However, it isn't very difficult to fold.  I used tant paper in a pink hue folded to a 32 pleat triangle grid.  For your denser tessellations like this one, it's best to use a sturdier paper.  Interesting thing about tant paper. I actually spilled some coffee on it while in the middle on completing this tessellation.  Figured it was trash, but I wiped it down and waited for it to dry and was able to move forward almost as if the spill had never happened. Pretty impressive that the paper could do that, especially being manipulated so hea

Origami Tessellations: Parallel Parking

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This tessellation looks pretty complex, but it's not that hard to actually fold it.  It features trapezoids rotating around  open back hexagons. Opposite facing trapezoids emerge from the edges of the first set. Those trapezoids then revolve around small offset hexagon twists.  This is an unusual tessellation that has a lot of flexibility in the valley and mountain folds. The way the various shapes interact with each other is such that there are a lot of options regarding what goes up and what goes down.  While this makes it somewhat easier to execute on the face of it, it can be frustrating to actually come up with a cohesive and consistent pattern.  Give it a try and you'll see what I mean.  I have a diagram somewhere. Will add it in the near future.  Update: added diagram below. 

Solving Cubes Tessellation

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 This is a variation on an old image I found on my hard drive. According to the tag in the corner of the original image, it's a Peter Keller design that is untitled.  His design used larger cube modules. on a much larger grid.  I decided to do small cubes so that they could repeat nicely on a smaller grid. Other than that, the concept is the same.  His design used cubes made up of 12 rhombuses each.  I simplified things with cubes made up of only 3 rhombuses each.  The reverse side of the tessellation is comprised of small triangle twists, open back triangle twists and blunt corner triangles.  What I particularly like about this design is how it utilizes space. Leaving those bigger gaps between the groups of rhombuses creates a totally different pattern than what you would get if you kept the same distances between all of them.  My diagram for this tessellation is included at the end. 

Illuminati Origami Tessellation

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 The inspiration for this particular tessellation came from my idea of three trapezoids around a small triangle. The points of the triangle poke into the short tops of the trapezoids.  As a way to further figure out how to repeat that pattern I added open back triangle twists to create another triad of trapezoids.  At that point it all coalesced and the final shape appeared as I repeated the array. A blunt cornered triangle revealed itself to be the last piece of the puzzle.  I actually liked how the back side photographed better than what I originally conceived of as the front. That's shown in the first pic.  But the concept was born of the shapes shown in the second photo. Interesting how that works out sometimes.  This particular orangey color of tant paper really gave me a hard time trying to get nice pictures of it. However, I managed to find a couple of good ones. Just barely.  Yet another aspect to consider when you're creating your own masterpieces.  Every detail matter

Origami Tessellation: Ninja Blades

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 Here's a tessellation that I've not seen done. The idea came from trying to find a new way to repeat right triangles around an open back hexagon. I used some rhombuses and it worked out to be a pretty cool pattern, if I do say so myself.  There are a bunch of triangle twists on the other side that are pretty fussy to fold.  In order to correctly twist the triangles you need to fold a little bit of the paper over on top of the edges of the open back hexes. It's difficult. Use strong paper and do it on a dry day.  There are also small hexagon twists on the back as well.  You could also say that the pattern is alternating right triangles and rhombuses around small hex twists with open back hexes in the gaps.  It's just a matter of perspective.  I do have my crease pattern, but need to take a photo of it. Will add it soon.  Updated to add diagram.

Traffic Jams Origami Tessellation Design

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This tessellation began with the idea of three rhombus twists around a triangle on the other side.  I wanted to find a way to repeat that pattern.  I used open back hexagons to further that goal. From there I was left with large gaps that needed reconciling.  It turned out that a series of seven triangles worked to resolve the void.  Oh, this was an incredibly tedious tessellation to fold. The creases felt never-ending.  Getting all six triangles to work in all the gaps was an arduous task.  At times, I thought to myself, I'll never finish this.  Strong paper and an obsessive personality eventually resulted in the completed tessellation.  You can see from the first photo that I oriented four of the triangles upward.  The second photo shows the other three in the series on the back side.  This type of design has a lot of flexibility.  The shapes can be arranged in different variations of up and down.  Crease pattern diagram included at the end. 

Origami Tessellations: Rocket Science

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 This tessellation is the result of me messing around with repeating linear rhombuses and trapezoids. It kind of looks to me like the rhombuses are launching rockets. Hence the name.  One side is strictly rhombuses and trapezoids.  The other side has quite a few triangles.  These collapsing folds are very versatile. There are so many pattern to be found.  Creating one is often just a matter of putting a few shapes together and filling in the gaps with triangles.  I used pretty flimsy paper, so it's not nearly as perfect as I would like it to be.  Given how obvious the various shapes are, a crease pattern hardly seem necessary, but I'll include one just the same. 

Solving Epicycles Origami Tessellation

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This is a tessellation by gatheringfolds that she called 'Epicycles'.  Every so often, I like to solve someone else's tessellation to give my mind a different perspective on things.  It really does help reset my creative process so that I can come up with new ideas of my own.  It also keeps me sharp in recognizing how to extrapolate the structure of other people's finished designs.  And it's a nice respite from the sometimes arduous process of thinking up and sorting out a completely unknown tessellation from start to finish.  It's an elegant design of open back hexagons and rhombuses.  There are a lot of designs that utilize these two shapes in conjunction with one another. This one is particularly interesting in how the rhombuses twist in a way that almost makes them look as if they're dancing.  The reverse side is exclusively open back triangle twists.  My diagram follows. 

Cotton Candy Origami Tessellation

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This is a tricky little an offset hexagon stars tessellation. The idea is pretty basic. Just the stars and then some rhombuses. Folding it, however, is a little more complicated.  The shapes that fill in the gaps on the reverse side are somewhat unusual. Actually, it's more how you have to twist them rather than the shapes themselves.  I've been messing around with less standard tessellation techniques lately. Really searching for unique ideas and arrangements.  I certainly could've done a better job in my execution. Perhaps a second attempt at another time will yield a more impressive final result.  Still, the idea is intriguing.  Diagram included below. 

Origami Tessellations: Changing Weather

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Some tessellations are obvious and some are not. Some are simple patience. Others are mostly stubbornness. This tessellation falls somewhere in the middle between those extremes.   This builds on the concept of rhombuses around an open back hexagon.  This time the outer edges of the rhombuses are connected to triangles using flagstone style collapse folds.  This creates some interesting shapes in the remaining negative spaces. They are unusual and tricky, but totally foldable.  I used tant paper and 32 pleat triangle grid.  This one needs strong paper.  I have a diagram somewhere. Will upload it at a later date. 

Original Origami Tessellation: Dante's Inferno

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 This is a really interesting tessellation that I found. It has a lot of overlapping layers, which is always cool to find and fold.  I actually came up with the pattern for the back side and later decided I liked the other side better for the front view.  It uses open back hex twists as the beginning point. Some small natural trapezoids emanate from them. Then there are triangles twisted off of the trapezoids.  Everything is rather close together and tightly twisted.  A single module is pretty easy, but tessellating it is exponentially more difficult.  My first attempt with ordinary paper was unsuccessful. I had originally thought to make the repetitions closer together and only realized they wouldn't fit in the midst of that try.  I moved the repeats a pleat further out and was successful using tant paper.  The third photo shows pretty clearly how the trapezoids and triangles twist out from the central hexagons.  It also shows how you need to bisect the folds connected to the tria

Origami Tessellations: Convection Ovens

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This is a flagstone style tessellation using triangles and rectangles.  The center is six triangle twists around a small hex twist on the other side.  The small rectangles connect to the tops of the triangles. It's from there everything repeats.  The negative spaces are blunt corner triangles on the other side.  I may or may not have done this before. It feels familiar, but I couldn't find an older version.  When you've been folding tessellations for as long as often as I have been, you start to lose track.  It's possible I saw someone else's rendition long ago and it laid dormant in the back of my brain until now.  I don't know for sure.  The best way to fold this one is to do the center first. Then twist the outer hexagons on the back. That will make it easier to get the rest of the repeats to fall into place.  I think that I have a crease pattern. Will add it here later if I can find it. But all the shapes are pretty obvious from the view of the front.  It fi