Four Linked Triangles, designed by me
This is an original design that I made in 2019. The instructions are lost to time. I usually at least have some messy digital sketches, but I got nothing here.
Well, I recall a bit from memory. This is one of those designs that follows a fairly braindead design pattern: throw lots of pieces of paper at it. Each triangle? Six separate sheets of paper. I’m sure part of the reason I didn’t preserve instructions is that I was not so impressed with the design. If I gave it another shot, I’m sure I could do better than that.
How did I think of linking four triangles? Well, that’s nothing new. There’s a very famous origami model called Four Intersecting Triangles by Tung Ken Lam. (That model only uses three sheets per triangle.) So, I just have a hole in each triangle. It’s neat to assemble, because when you only have three linked triangles, they lie flat, and have a valknut topology. Once you put in the fourth triangle, it is forced into a 3D configuration.
I later took this design, and made a 10 intersecting triangle version. That design… was not terrific. Maybe I’ll show it at some point.
Interlinked triangular frames (and their extension, interlinked polyhedral frames) have a fun and extensive history in the origami world. The (non-origami) concept was explored in the book “Orderly Tangles” by Alan Holden; the “holotype” for the polyhedral concept is Thomas Hull’s iconic “Five Intersecting Tetrahedra.” I did an analysis of the concept (G**gle for “Polypolyhedra” to see those; I’ll note there were a few holes in my enumeration that got plugged by Tom and others, many thanks). Looks like your design concept has a lot of potential for those other structures as well (but by golly, that’s gonna be a lot of squares!).
I don’t remember whether this model was actively inspired by polypolyhedra, but I was certainly aware of polypolyhedra at the time that I made it!