It took a little while to figure out how to get this tessellation to work properly. But I was confident that it could work and I would up hitting upon the solution.  My starting idea was for the center point. The open hexagon with 12 overlapping trapezoids around it. Repeating that was no problem. But the spaces that were left puzzled me for a bit before I realized how to solve it.  On the back side there are three rhombuses. They flank the open triangles seen in the gaps between all the trapezoids on the front.  This is a difficult tessellation . There's a lot of work to be done on both sides of the paper. It combines aspects of flagstone tessellations, tuck and twist styles.  Crease pattern included. Filed under: August 2026 Origami Tessellations

 This is an unusual idea that I had recently. Most origami tessellations either have a linear pattern or a circular one. This one kind of has both and neither at the same time.  When you first look at it, you might think, that's not a tessellation, because it doesn't repeat. But, actually it does. Just in a different way.  The pattern is diagonal, heading off in four different directions from a rhomboid starting point.The sequence spreads outward from each edge of the central rhombus. An infinite array. Rhombus, trapezoid, trapezoid, rhombus and so on and so on. It's hard to see in the finished fold, but is much clearer when you look at the crease pattern, which is at the end of this.  That progression creates gaps which can easily be filled with large hexagons and more rhombuses and trapezoids. Circular arrays butting up against the linear ones. As you move further outward the gaps change and you have to fill them with different sets of shapes. I took it as far as ...

  This is an intermediate level tessellation that I recently folded. The idea is two kinds of triangles twisting around an open hexagon. Not too unusual. It's a little different though because the top corners of the triangles meet and they twist into one another. This is illustrated very clearly in the crease pattern at the end of this post.  In order to repeat the pattern, I used small hex twists and some triangle twists (which are not requited, but I liked them). They could just be left as regular corners.  I used ordinary printer paper because there are a lot of folds which overlap each other. Normally, when you do a hex twist you, just spin each axis in the same direction and they don't interfere with one another. In some cases, like in this tessellation , it's necessary to twist the axes in opposite directions. When that happens, they overlap. When trying to fold overlapping twists, I find it much easier to use thinner paper.  All in all, this paper type worked...

 A new style that I've been tinkering with occasionally is one that combines elements of both linear and rotational patterns. This easy tessellation is my most recent design using that technique.  As you can see there's a diagonal pattern of overlapping trapezoid twists. But there's also a hexagonal pattern that's a little harder to detect.  Twisting around the larger hexagons are both the trapezoids you can see on the front and also rhombuses which appear on the back.  On the back side of the tessellation the rhombuses also appear in a vertical/diagonal spread.  The twist pattern around the hexagons is: trapezoid:trapezoid:rhombus:trapezoid:trapezoid:rhombus. It is much more obvious in the crease pattern included below. 

This is a just a random idea that I had while fiddling around with a small piece of 'gridded' paper. Sometimes, looking for inspiration, I'll fold a small 16 pleat grid on a little square and just screw around with it to see if it takes me anywhere worthwhile. The tessellation that I came up with was an alternating ring of small hexagons and teardrops around a large hexagon. In order to have 12 shapes around the hexagon, instead of the usual 6, it was layered using natural micro trapezoids.  All this information will make a lot more sense upon viewing the crease pattern below.  The back view is rather unremarkable.  What's notable about this particular  origami tessellation , is the fact that I didn't actually fold it as a tessellation. The pattern can absolutely be tessellated. I even went so far as to map it that way on the paper prior to folding.  However, as I was beginning the first of the six repetitions, I realized that the paper I'd chosen combined wit...

This is an origami tessellation idea that I had a while back. Because it seemed so simple, I didn't rush to fold it. It languished for a while waiting for me to become interested.  On a day when I didn't have that much time, I decided to try it.  It's a very simple concept of large hexagons with natural triangles. I add small hexagons at the points of the triangles in order to repeat the pattern.  Some open triangle twists finish off the remaining space.  The diagram included below doesn't really fully illustrate the further finishing touches that I added to it.  Once I had the whole tessellation flattened I did small triangle twists with the corners of the large hexagons. This created kind of pseudo open back hexagons in their place. This led me to then fold their edges inwards, creating the final design.  It's hard to tell from my 32 pleat rendition, but the design is fully repeatable.  Even though it's a very simple concept, it wasn't easy at all ...

I wanted to do a tessellation with a very specific pattern I had in my head. That pattern is rhombus > trapezoid > trapezoid > rhombus.  Which is a very easy pattern to repeat horizontally. Repeating the pattern vertically however, proved somewhat trickier.  It took a  little while, but eventually, I figured a pattern that worked. The unusual thing is that it's both a circular and a linear pattern simultaneously. See the crease pattern below for further clarification.  The circular pattern is asymmetrical. With triangles, rhombuses and trapezoids all rotating around large hexagons.  The linear pattern is symmetrical. Repeating the set of rhombuses and trapezoids evenly and consistently. It's a twist based tessellation that was much easier to fold that it was to conceive.  

 This twist based tessellation is an idea that I had a while back. The first time that I folded it, I spaced things too close together and didn't really like the outcome. So, this time around I went with broader gaps between the shapes.  The shapes are linear rows of rhombuses. Pretty simple stuff. But an interesting thing you can do with this design. Theoretically you could do this with any design that features 90 degree corners.  Anyway, instead of folding flat corners, what you can do, is fold triangle twists at the corners. They twist in opposite directions and that  creates a 3dish sort of curved fold connecting them. My paper was kinda soft for it to really work, but you get the gist.  The back of the tessellation comes out as a series of many parallelograms. Crease pattern included.