This is one of those tessellations where I pack an absurd amount of triangle twists into a small space and see what the result is. More often than not, you'll get a pretty interesting design on the opposite side.  This tessellation starts its life with an open back hexagon. From there, it's pretty much a chaos of triangle and rhombus twists. Not really chaos, but it kinda looks that way when you see the other side.  My grid wasn't large enough to actually repeat the center, but I think it can be done if you have more pleats to keep going.  I did this one quite some time ago, so I don't really remember how it came to be exactly. Although, I do remember that I was kind of fixated on folding the edges of open back hexagons in on the center.  My crease pattern is below. I think I remember that I made a small mistake when tracing it. I believe there's a missing triangle in the right mid edge section.  I like to fold twist based tessellations using thinner pap...

 I've been meaning to add this particular origami tessellation for at least several weeks now. I just had a lot of trouble getting a good photo of it. It's still not a great pic, but it was the best that I could get.  I had hoped using thinner paper would allow for a nice backlight pic, but it didn't work out that way. So, I just went with a standard photo instead.  It's kind of an unusual pattern for me. There's a large natural triangle at the center with three small triangle twists rotating around it. Then on the other side there are three sets of three triangles twisting around it.  I repeated the center three times and then filled in the other three areas with a different collection of triangle twists.  It's a fully twist based tessellation.  I can't really decide if I like the front of the back better. Although, I do remember that the design the the center of the back was my original inspiration. Interesting how things evolved so much from there....

 This is an odd one. It's kind of like multiple patterns mixed into one. I really don't know why I did it this way other than just experimenting. Thinking about it, I would probably like to take the multiple patterns and do a few different tessellations with them in the future.  For now, this is what I have.   I'm sure that if one had a large enough grid and took the time to work it out that it could easily become a truly tessellating design in and of itself. It's both random and intentional. Kind of interesting in that way.  What I really like about simpler twist based tessellations like this is that you can do them successfully regardless of what paper you use. And the weather doesn't matter much either. They are a great way to teach yourself how the shapes rotate on the angles of the grid. As well as how the various shapes can and cannot interact with each other.  Crease pattern included. 

 This origami tessellation uses the fact that trapezoids can create overhang in order connect to the next set of shapes. That's one of the things that I find so interesting about them. You can arrange them in ways that a lot of other shapes simply can't do.  In this particular tessellation, I did alternating trapezoids and rhombuses around open back hexagons. The gaps between them left space open for me to add opposite facing trapezoids. Which allowed me to repeat that molecule.  The repeating process created the more standard six trapezoids around a hexagon in the other spaces.  It's a nice, fluid design that highlights the versatility of the trapezoid shape in tessellating.  If you're a fan of flagstone tessellations , this is a pretty cool one.  Crease pattern below. Created the pattern last week. Just fold it the other day.  Filed under: April 2026 Origami Tessellations

 This is a twist based origami tessellation using trapezoids and hexagons. I think that I created it two weeks ago and just gto to folding it about a week ago.  The most notable thing about it, is that even though it uses hexagonal twists, it's actually a linear configuration.  This was achieved by connecting the hexagons to each other rather than just repeating the trapezoids all around them.  This happens pretty naturally when you connect the trapezoids vertically and look for a way to repeat the design horizontally.  It's also a mirror symmetry design. Each side is a mirror image of the other.  It's a pretty easy tessellation to fold. Any ordinary paper will work fine.  My diagram is below.