This is a tessellation that I came up with after having done a very similar one. That first one (Controlled Chaos Origami Tessellation) had exceedingly small rectangles, which made it nearly impossible to execute cleanly on both sides.  In this case, I made the rectangles bigger and it became infinitely more manageable.  I'm pretty sure that I've seen this one before. I think that I've seen it done by  Daniel Kwan as a crease pattern posted to his flickr account.  I was not using that crease pattern while conceiving of this, though I did have some recollection o ..read more

 This one has a bunch of shapes in it, all working together to form the whole.  When creating a tessellation, I usually just start with one shape that interests me at the moment.  From there, I choose whether it'll be a six axis or a three axis rotational repeat. In other words, will I try to repeat it around some form of triangle or some form of hexagon.  Once I have a starting point, I mess around with additional shapes which may help me to further create repetitions.  The last step is just to figure how to fill in any gaps that are created.  In the case ..read more

 This is tessellation is interesting because I actually messed up the pattern that I had created. It still looks really cool, but it is asymmetrical.  My original diagram called for all the repetitions to match each other.  This is also another difficult to execute to design. Regardless of whether you follow the pattern precisely or you accidentally. deviate from it as I did, it's pretty intense to fold.  My tant paper actually tore a little bit in one spot from all the stress.  The center is easy enough to get situated, but after that all bets are off.  ..read more

 This is an interesting one. It's nicely layered. I always find tessellations with layers intriguing.  Trapezoids rotate off of a small offset hex twist on the other side. Then I tucked some small triangle collapses into the outer edges of the trapezoids.  I repeated the trapezoid shapes off from the other points of the small triangles. Thereby repeating the hex/trapezoid unit from the center.  From there I found that a pair of open back triangle twists perfectly filled in the remaining gaps.  A triangle collapse differs a lot from a classic triangle twist.  ..read more

 This tessellation was pretty ambitious undertaking. When I plotted it out on some grid paper, I knew that it would be kind of crazy, but I loved the design too much to not try.  At the center point is an open back hexagon. From there I add three trapezoids and three triangle collapses.  Then I add another layer of trapezoids.  This in turn, creates the opportunity to add a whole bunch more small triangle collapses. Ten total per third edge.  It is ridiculously difficult to get all those triangles to work together while also making them behave nicely with the rep ..read more

 Here's a fun little tessellation that utilizes just a few not too difficult techniques to create a moderately intricate pattern.  Rhombuses twist off from offset hexagons on their reverse.  Then on the outer edges of the rhombuses we add some open back hexagons.  At that point, the pattern can be easily repeated.  It's relatively simple compared to a lot of the tessellations that I've done in recent years.  It's a great exercise in some basic ideas that can lead to many other interesting configurations.  It also concisely demonstrates the close rel ..read more

 This is a tough one. Right triangles around an offset hex twist. When you go to repeat the pattern these very tiny rectangles are in the spaces between the points of the triangles. It's doable, but you probably need really thick paper in order to end up with a neat reverse side.  My tant paper worked for the front, but on the back I was only able to get some of the rectangles to land neatly.  In the diagram below they show up as micro rhombuses, but when you twist them they form very small rectangles.  Either kraft paper or elephant hide would be your best option for g ..read more

 Here's an unusual tessellation that uses a few different techniques.  It begins with a small hexagonal twist. Pretty typical.  Next, we have trapezoids spinning off from it. They are situated to twist the hex on bisected axes rather than the natural ones.  I call this an offset hex twist. Instead of using the grid lines to twist the hexagon, you create folds that bisect them and twist the hexagon that way.  The trapezoids have open back triangles in the spaces between them.  These open back triangle twists are not symmetrical three ways. They connect sligh ..read more

  If you're in the mood for a tessellation that looks complicated, but actually isn't, this one might interest you.  The pattern begins as open back hexagons with rhombuses collapsed along their edges.  From there, rather than a straight up repeat of the pattern, I added an additional rhombus before moving on to the next iteration.  Open back triangle twists fill in the gaps where six rhombuses converge. .  There are also small triangle twists on the back in the areas where two rhombuses connect along the edges of the hexagons.  In the center module, I alt ..read more

 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 ..read more