This is an appendix to my series about symmetry in origami. Here I will provide a proof that my construction of symmetrical colorings works.
While I try to make the series accessible to people who do not know much about math, I don’t think there’s much point in trying to make this proof broadly accessible. This is intended as a reference for people with some experience with group theory. (You need to know about cosets at the very least.)
Cube Tessellation, designed and folded by me.
This model is a sendoff of my Ph.D. It’s folded from a poster about my research, created while I was writing my dissertation. It’s really big, about 25 inches (63 cm) across. It’s the third tessellation I’ve made from one of my science posters, thus the title of this piece is “A Deconstruction of My Research 3”.
For this third model, I wanted to do something special, so I tried designing my own tessellation completely from scratch. I was inspired by the Rhombille tiling, which looks a bit like a wall of cubes. So I tried making a wall of cubes. And after a long design process, I was able to perfect it.
Below the fold, I have diagrams and prototypes to document the design process.