This is a difficult tessellation that contains an interesting array of interconnected shapes.  I conceived of it by mapping rhombuses twisting from three corners of a natural blunt pyramid. From there, I had to work out how to repeat it in a way that naturally flattened.  When you create tessellations like this one that only use a third of the six rotations available on a hexagonal grid, it can be tricky to accurately rotate the shapes. I've found that the easiest way is to have a separate drawing of the main idea that you can rotate. You can use this to easily orient the design so that you don't get frustrated trying to map the full 360 degrees.  Once you have a full six point rotation, you can then work out what might work filling in the remaining spaces.  I discovered that a collapsed hexagon worked for the remainder.  I was so obsessed with the rhombuses and pyramids that I didn't even notice what shapes might be created on the other side.  T...

My first official tessellation post of 2025. This difficult tessellation is a little bit over the top. I kind of tried to see how many triangles I could squeeze together in conjunction with some small hexagonal twists. Every shape is extremely close to the others.  It's not a particularly beautiful tessellation , but I was compelled to do it simply to see if I could get everything to work.  I'm a fan of three triangles tucked into each other and this tessellation is a reflection of that. I would've liked to get all the triangle points tucked more neatly into their partners, but they just kept popping up again every time I tried.  Perhaps if I had utilized a different type of paper I might've been able to do that. But I chose thin paper because it works well with such a dense array of triangle twists. If the paper had been thicker, I'm not sure I'd have been able to flatten everything as well as I did.  The backside is pretty interesting too.  I think that I hav...

 Here's a fairly simple tessellation. It's rhombuses twisting around a small triangle. They twist around it in a different orientation than i usually employ. Even though it's very basic, I kinda like how the wings of the rhombus twists are visible. I thought that was in interesting variation.  As the tessellation pattern is repeated they rotate around large hexagons.  The back view is interesting and a little weird when photographed.  An easy tessellation to practice your folding skills without taxing your mind too much.    Crease pattern included. Filed under: December 2024 Tessellations

This is a fun one. Probably an intermediate level tessellation . It uses open back hex twists and small hex twists. The triangle twists off of the open back hexagons are evenly spaced. The triangles off of the small hexagons alternate between 2 pleats and 1 pleat away.  The concept reminds me of some tessellations that I have done by gatheringfolds, but  I do believe this is different and an original tessellation .  I'm always fascinated by how the back sides of twists turn out. I have trouble deciding which I like more, the front or the back.  But I like the title revolving doors and that only makes sense for the front. If I had to name it by the reverse side, I think that I would call it Multiverse. A nice title in its own right.  I do have my crease pattern all ready to go.  Filed under: December 2024 Tessellations

This tessellation is based on a collapsed hexagon. I then use the flaps that result to make some overlapping triangle twists around it.  Repeating it was just a matter of adding enough space between the repetitions. As I repeated the central set of triangles around the hexes, I found that a larger hex collapse was needed in the gaps between the repeats. I still used the same pattern. Three are the same as the center and three are a larger version of  it. That all being dependent upon how I spaced the second set of repeats.  Looking at my diagram, I think it could have been spaced one pleat closer together for a different result, but it was tricky enough the way it is.  I feel like I may have done this in the past, but I went looking for it and could not find a previous version.  It can be hard to find a specific tessellation that you might have done before when you've done so many.  It's also entirely possible that I thought of it in the past, but wasn'...

created by  solvingorigamitessellations.com  This origami tessellation is one that I just stumbled into as I was messing around with possible triangle twists revolving around collapsed hexagons.  I don't think that I've done it before, but I am not entirely certain. It does feel somewhat familiar. I couldn't find it in old posts. But sometimes the previous version is there and I just can't find it. I don't know whether or not it's been done by others. Very likely.  solvingorigamitessellations.com But for all intents and purposes, it was new to me when I came up with the diagram.  It's an uncomplicated design. Collapsed hexagons have 12 triangle twists around them. Half the triangles overlap each other and the other half abut each other. Then just leave a small gap and repeat.  This is an intermediate level tessellation . It's a little fussy getting all the triangle twists to fold nicely given that everything is so close together.  The reverse side i...

Breaking Infinity by solvingorigamitessellations.com  This tessellation was inspired by one by Peter Keller. His design was large cubes formed by  rhombuses.  In my case, I did a series of six diamonds formed by rhombuses. I used the idea I learned from his design to separate the 'shapes' of the flagstone by leaving a larger gap in the appropriate places.  I would call it a flagstone tessellation even though the larger gaps technically disqualify it. The overall concept still fits the category.  created by solvingorigamitessellations.com The reverse side is just as interesting as the front. Featuring linear rows of rhombus wings with six triangle twists between each of them.  The first time I did this, I mapped the central point incorrectly. I used that mistake to help me determine the right way to do it.  The second time around, it all worked out quite nicely as can be seen here.  This is a difficult tessellation, as are all flagstones. I might...

solvingorigamitessellations.com  Here's a simple tessellation that yields a pretty interesting result. I was intrigued by it because I don't recall having seen it before. Which kind of seemed strange. Also because I couldn't recall having done it myself either, even though it felt so obvious once I found it.  Maybe others have thought of it and just felt that it was too simple.  It's doubtful that it's truly an original tessellation , but it was new to me. I figured, why not. It didn't take up much of my time.  It's just open back hexagons connected to each other by natural triangles. That's it.  Once you complete it, you wind up with an array of overlapping hexagons that all tuck neatly into each other's various edges. It would make a cool pattern for flooring in a mansion or a museum.  solvingorigamitessellations.com It's a very easy to execute design. Perfect for beginners.  The name is an homage to Fujimoto's Crowding Butterflies des...

solvingorigamitessellations.com   This tessellation is kind of a funny story. I thought to myself, let me do something with repeating rhombus cubes. Meaning, three rhombuses around a triangle and then repeat that pattern with another shape or two.  I worked with it for a bit. Trying alternating it with open back hexagons.  Eventually coming to the conclusion that open back hexagons were the answer just in a different pattern.  That's how I wound up with this tessellation.  I changed up the edges to make a neater finish.  The funny part is that I later discovered I had actually done this tessellations years ago in 2018 and that it was originally created by Robin Scholz. And I had folded it from his crease pattern all those years ago.  solvingorigamitessellations.com I was a little disappointed to realize that it was not really my original creation even though I had dreamt it up without remembering that I'd already done it.  That happens sometime...

  created by solvingorigamitessellations.com When I created my ' Circling the Crown' tessellation I mentioned that I wanted to try to find a way to repeat the central pattern.  I struggled with it for a while. Trying to do it as full flagstone.  When that kept leading me to dead ends, I finally had the idea to do it as a hybrid of flagstone and standard collapses.  That's how I eventually came up with this original tessellation design that worked to create the pattern I wanted.  The center point that repeats is a triangle surrounded by three trapezoids and three more triangles.  In order to successfully repeat this central cluster I added open back hexagons tucked into the outer edges of the trapezoids. From there, it was just repeating the patterns and adding an additional triangle in the spaces remaining between them.  created by solvingorigamitessellations.com The reverse side just has a multitude of triangles surrounding the hexagons. I was caref...

  solvingorigamitessellations.com This tessellation is another in my series of experiments in how close together you can successfully layer twists.  This is a good one. It's achievable and it's also difficult . Which are the best kind.  I recommend a heavier weight paper. I used thin paper and while I was able to pull it off, it was a bit of a struggle.  I was kind of lazy and didn't pre-crease everything. As I worked the one side, I kind of let circumstance help me fold the rest. This technique works best with thinner paper.  solvingorigamitessellations.com It's quite a densely packed design. I conceived of it via the back side (second photo). Which is rhombus twists tucked closely into open back hexagons. But the beauty of the pattern happens on the opposite side of the paper (first pic) where all the layers converge.  This is a difficult tessellation because everything is tight and layered on top of each other.  Will add a crease pattern soon. Upd...

  solvingorigamitessellations.com Here is a new flagstone tessellation that I recently created and folded. The starting point is trapezoids and triangles around a central triangle. From there I just expand outward using the shapes that work with the space.  Because it starts from a triangle, everything repeats 3 x 3 instead of x 6. So 3 sides are a pattern and the alternating 3 sides are a different pattern. The pattern of shapes changes as the design expands outwards because there is more and more space to fill.  solvingorigamitessellations.com Because this is a flagstone, it is a difficult tessellation to fold. The reverse side is full of triangle twists.  As far as I know, this is an original origami tessellation . I've not seen it done before.  It occurred to me after I had completed this that the central module can probably be repeated if I flip the trapezoids of the second generation. I started to work that out on some grid paper, but haven't finaliz...