This is a triad based flagstone tessellation that I recently created.  The starting point is an open back hexagon with alternating trapezoids and rhombuses  collapsed around it.  From there that pattern can be repeated by adding an opposite facing trapezoid off of each central one.  That, however, leaves a lot of empty space to reconcile.  I did so using a series of additional rhombuses as well as a few triangle collapses.  It's all just a matter of making the space work for you.  The reverse side, as you would expect of a flagstone tessellation, is a vast array of triangles.  It's somewhat different from any tessellations I've seen before. It's an interesting study in how far you can go in manipulating the paper if you're able to discern what combination of shapes will rectify the gaps in your ideas.  A starting idea is a wonderful thing, but working out how to take it all the way to completion is where the real magic is done....

This is a pretty easy tessellation if you're looking to get a feel for the process.  Open back hexagons have trapezoids collapsed around them. It's a really easy starting point.  Then we just add some rhombuses tucked into the points of the trapezoids.  At that point, the pattern can be repeated.  Large pyramid shapes fill out the remaining gaps.  If you're looking for an easy tessellation to get yourself familiar with some basic techniques of the genre, this one would be a good place to start.  I did draw a crease pattern. I haven't taken a pic of it yet. Will add it later on.  Update: added crease pattern at the end.  But all the shapes are right there in plain sight. There are no tricks or secret sneaky folds. It's a very straightforward tessellation. It shouldn't be too hard for even a beginner to figure out.  If you decide to fold this, leave a comment and let me know!

 This is a fun little tessellation that I came up with in an effort to be able to fold something new during high humidity.  I talk about humidity a lot in regards to folding various tessellations. The paper absorbs the moisture in the air and becomes soft and difficult to fold. Particularly for your more intricate patterns. Simpler designs, however, are still perfectly executable under most any weather conditions.  This tessellation is a prime example.  I used ordinary 20 lb copy paper on a drizzly day and it turned out very nicely.  The premise is rhombuses twisted around a small central hexagon. From there some small triangles twist off of them. Then just repeat.  This tessellation is actually a variant of another tess I did not too long ago called Flowers in the Garden Tessellation . Both begin the same, but diverge slightly in how they repeat.  On the reverse side there is just an array of open back hex twists.  So, not so simple as to be bori...

This is a tessellation that I did not that long ago. I called it cotton candy because I had used pink paper and it made me think of that.  I came up with the crease pattern again without realizing that I already had. And then proceeded to fold it again before finally noticing it was a previous design.  The first time I folded it, it didn't turn out as nice as I would've liked. This time around though, it came out much neater and looking more like I expected it to when I conceived of it.  It's an unusual design that puts together several different shapes in a way that isn't typically used.  To access the diagram refer to my first fold/post of this tessellation called cotton candy .  There are also additional details in that post about the nuances of executing this particular design.  If you happen to fold it yourself let me know in the comments.

 This tessellation combines offset rhombus star twists with collapsing trapezoids to create a unique pattern.  The other main aspect of the tessellation is a series of six trapezoids rotating around a small hex twist on the other side.  Initially, the trapezoids emerge from the central star by tucking over the edges of the rhombuses.  It's from there that they twist around the small hexes and collapse upon one another.  This a hybrid fold utilizing flagstone, collapse and twist techniques.  It's a medium difficultly tessellation.  The hardest aspect is the spaces where the trapezoids meet at their long edges. There are narrow rectangles that are a little tricky to fold. Everything else is pretty straightforward.  The second photo, of the reverse side, shows the long rectangles between the trapezoids.  For further details on how to execute this tessellation, consult the diagram included below. 

 This tessellation is kind of different from my usual modus operandi. We have tall isosceles triangles that wrap around six sided polygons.  My ' Fireworks Display Tessellation ' uses the same triangle shape in a much denser configuration.  I actually came up with this tessellation before I did that one. I had simply forgotten to take a photo of the diagram, so I was waiting on that to post this. In fact, it was this tessellation that led me to that one.  It's pretty common for one configuration of shapes to inspire something similar, yet entirely different.  This one is far simpler and easier to execute. The end result is a pretty neat pattern though.  Crease pattern included below.

 It took me a little while to solve the 'emergent triangles' tessellation by gathering folds. I was kind of stuck on the idea that it was a group of six triangles and then another group of six rhombuses. When that kept leading me to dead ends, eventually, I tried a different approach.  Instead, I solved for the set of three rhombuses around the large hexagons. It was from that starting point that I finally worked out that the triangles  and rhombuses had to alternate.  It was definitely a eureka moment.  It's a wonderful design. Another one of her trademark mirror image tessellations. Each side is a mirror of the other.  I do have a diagram, but I haven't taken a pic of it yet. Hope to add it soon.  Update: diagram added. 

 This is a tessellation that I was really thrilled to have created. The pattern utilizes a different triangle shape that I've not worked with much at all. It's a taller triangle than what you'll typically find in origami tessellations. Also known as an isosceles triangle. Two sides are equal and the bottom is smaller.   The longer sides of the triangles are 1.5 pleats long. While the bottoms are a single pleat.  I created a rotation of six of them around a classic small triangle collapse. They alternate forward and back as they go around the center point.  In order to repeat the pattern, there are natural triangle twists on their outer edges. Three of the isosceles rotate around those.  At that point, the repetitions can keep going ad infinitum.  All in all, not too difficult to execute, but a pretty remarkable end result.  I used tant paper folded into a 32 pleat triangle grid.  As with all origami tessellations, this is folded from a sin...