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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

The Wings of Icarus Origami Tessellation

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Nested shapes are a favorite of mine. This tessellation makes grand use of them.  I've explored similar patterns before. In this case, it's alternating trapezoids and triangles around an open back hexagon.  In order to tessellate the pattern, I found that a quadruple set of triangles did the trick.  The other side also has some rhombuses.  There are a lot of multi-corner intersections with which to contend. But patience is the key.   See the pic of the reverse view below for further clarification. A crease pattern diagram is also included at the end.

Origami Tessellations: Winter Wonderland

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This tessellation is a hybrid of flagstone and tuck/collapse techniques. I've been finding a lot of new designs using this combination of folds.  The central component is a rhombus star twist around a small hex twist on the reverse side. There are triangle collapses tucked into the ends of the rhombuses. This kind of makes them look like snowflakes.  It's at the point that I begin to tessellate everything.  What's particularly nice about this tessellation is that the ends land rather fortuitously on my 32 pleat grid. So I was able to create pretty tidy borders.  It looks harder to fold than it actually is.  The reverse side is seven hex twists and a whole lotta triangle twists.  For further assistance see my crease pattern diagram below. 

Hungry Rhombuses 3.0

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 When I was folding this tessellation it did feel familiar, but I couldn't really remember why. So I pressed onward thinking it just reminded me of others, but was different.  Turns out, I've done this one not once, but twice before.  Each time, I created it from scratch in my head not remembering that I had  already done it. I guess that just means that my brain really likes this pattern a lot.  First time was in 2020 and I called it Hungry Rhombuses. I couldn't really get nice photos of it with the phone I had back then.  Second time was in 2021 and I called it Cannibal Rhombuses. I used kraft paper that time and it does not back light well at all.  This time around it came out pretty close to perfect. The pics are very nice. The execution is pretty spot on.  To fold it yourself just do rhombuses around an open back hexagon and repeat.  Be forewarned. Those triple intersections where three rhombus points converge are a tricky fold and there are a lot of them. 

Solved Tessellation: Apline by GatheringFolds

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Folded this one just cause I liked it. I am always impressed with the great patterns that she conceives. They're mostly not overly complicated, yet they are always innovative and inspired.  There wasn't a whole lot of solving going on on my end. The shapes are clearly defined. It was just a matter of ensuring everything landed in the right places.  Repeating rhombus twists combined with trapezoid twists.  A great idea. I don't know if I ever would've thought to combine those two twists if I hadn't seen her do it.  She's the twist expert. I'm more of a collapser when it comes to creating.  Anyway, a fun fold for anyone interested.  Fits nicely on a 32 pleat grid. Works with ordinary paper.  My sketch is at the end. 

Origami Tessellation: Acrobats on the Trapeze

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 This tessellation pattern is similar, yet also different to some others I've done. The central module repeats in six directions from the original starting point. A variant of that same pattern fills in the spaces that exist between them.  It's a lot of shapes, but one of your less intense tessellations to actually fold. Everything just tucks into each other.  The main pattern, which inspired the idea, is alternating rhombuses and trapezoids nestled into each other.  The tertiary arrangement is also trapezoids and rhombuses, they just land in a more twisting circular pattern.  The reverse side is all open back hexagons.  It's helpful to work the back side almost as much as you work the front during the folding process. Although, that's probably true for most origami tessellations.  A crease pattern diagram is included at the end for those that want it.