This tessellation builds off the concept of using a small hex twist on bisected axes.  A conventional hexagonal twist is turned on the axes that follow a triangle grid. However, you can also twist them offset from the grid.  Doing this opens up new options with what shapes you can combine them with and how.  In this case, I did rhombus twists around the hex.  What happens next is pretty cool.  We add open back hexagons off of the points of the rhombuses.  Once you get that first set of central rhombuses in place, it's not too difficult from there.  On the reverse side of the tessellations are the offset hex twists and some parallelograms.  Crease pattern is included below. 

  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 alternated the valley and mountain connections of the double rhombuses in order to create consistent patterns for the outer repetitions.  The second photo shows all the triangles on the reverse side of the tessellation. I've also included some closeups of each side with less back lighting.  I have a diagram. Will add it soon. Diagram added.    

 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 might repeat in a smaller space. But that's an idea for another day.  The center is a small hex twist with trapezoids emanating from it. Open back triangle twists fill in the gaps of the central module.  To repeat it there are large pyramidal shapes as well as long parallelograms. Personally, I like the pattern on the back (second pic), a little better.  I used ordinary printer paper. The va...

 This is a modification of a tessellation by Arseniy K called 'Pixelated Chrome'. I changed it up to repeat  on a smaller grid.  The structures are very similar, but the results are different. Mostly because I used paper that backlights really well.  I used the same size rectangles, but smaller, natural triangles.  It's a pretty easy to fold tessellation. I encountered no difficulties with the execution.  I used white, 28 lb printer paper folded into a 32 pleat triangle grid.  The diagram for my version is included at the end of this post.  The crease pattern for his is available on his instagram feed. 

 This is a pretty simple tessellation that has some interesting patterns.  What I wanted to do was tuck some open back hexagons under some straight lines. This is where I arrived with that.  I kinda mostly worked on the reverse side pattern more during the conception than I did the front.  The front has forward facing open back hexagons connected to long parallelograms.  In-between the parallelograms are more hexagons hiding shyly. Hence the name.  On the reverse side are small triangle twists around the prominent hexagons.  You can also see how the shy hexagons are formed.  As I said, it's one of your less intense tessellations. I just used plain printer paper and had no issues.  I believe that I have a crease pattern for this. Will upload it when I find it.  Update: crease pattern added below. 

  While perusing Instagram, I came across a new tessellation by Aresniy K called 'Wheel of Misfortune'.  As I was working out its construction, it occurred to me that a really beautiful variant was possible.  His is a circular style pattern of long parallelograms tucked into each other.  In my case, I went with a linear weave pattern of the same shapes.  While it's pretty basic from a conceptual standpoint, it yields, what I think, is an impressive finished product.  On the front, it's all parallelograms. They need to be long enough to accommodate tucking the perpendiculars into each other.  On the back side, micro rhombuses are the main component.  I didn't create a a diagram for this one. It wasn't really necessary. It's just the one shape repeatedly tucked into itself at 45 degree angles.  Once you begin folding the front, the small rhombuses on the other side are mostly forthcoming.  I used a 32 pleat triangle grid and that had room ...

 I created this tessellation from back to front. The idea for the layout was initially the three open back triangle twists around a small triangle twist.  But as I worked the design and interacted with the paper, the concept shifted in my mind and the front became the back and vice versa.  Interesting how that happens every so often. Planning can only account for so much. Sometimes theory is eclipsed by execution.  The now front side is comprised of open back hexagons and small rectangular twists. When backlit, they almost appear to be spinning.  The other side is the aforementioned sets of triangles.  The trickier ideas will often surprise you, even when you think that you've got it all figured out.  Crease pattern included at the end.