Cube Tessellation, designed by me
Back in 2017, I designed this tessellation based on the rhombile tiling, and I blogged about it here. More recently, someone asked my permission to teach it in an origami convention. I said, “Sure, but I only have crease patterns, no instructions. Can you figure it out from there?” This being an expert origamist, he figured it out alright, but he said it was very challenging. I tried it myself, and I had to agree!
The challenge can be part of the fun, but I still wanted to make it a bit easier. So I revisited the model to see what I could do. I finally made some step-by-step instructions! Very difficult to make instructions for tessellations, because every step involves multiple simultaneous folds. I also added some steps to clean up the “edges” of the tessellation. The result is what you see above.
2024 was a very artistically productive year for me. I folded about 10 original designs, revisited my cube tessellation design, and made two group theory infographics. This is in addition to folding dozens of other people’s designs. It helps a lot that I returned to origami meetups this year, which I had stopped attending during the pandemic.
Looks nice! Now, can you do a version with seamless faces?
@bugfolder
I think it should be possible! You could put the front-side seams along the edges of the faces rather than cutting across the faces. I think you’d have to sacrifice some efficiency though–this design is maximally efficient or very close. And a major consideration is that the seams tend to pull apart. Here, I felt that the vertical seams were actually the more problematic ones, as the diagonal seams could be more easily secured.
I think a fruitful avenue of exploration is to borrow some ideas from universal hinge patterns. I’ve been eyeing that “arctan(1/2) gadget” for a while but haven’t worked it into a model yet.