Sometimes an origami model just doesn’t work out. Here’s a collection of some of my failures.
One thing I’m interested in doing is finding unusual polyhedra, and designing origami around them. This here was meant to be Steffen’s polyhedron, which is a flexible and concave polyhedron. “Flexible” means that it can be deformed even when each of the faces is rigid. “Concave” means that some of its edges are bent inwards instead of outwards. Cauchy’s Rigidity theorem states that convex polyhedra cannot be flexible, and Steffen’s polyhedron is an example of why it doesn’t also apply to concave polyhedra.
Anyway, this is tricky to design because I basically need to make a bunch of triangles of arbitrary sizes, and I need some way to attach them together. At some point, I got the bright idea of making triangle edges rather than triangles. And I didn’t even have to design my own edges, I just took the “Jade” units from Ekaterina Lukasheva, which are designed to be of arbitrary length. I carefully cut the paper to size (which required a bunch of oddly dimensioned rectangles, like 10:17), and started putting pieces together.
But it turns out, the design was fundamentally flawed. The geometry of the jade units doesn’t work out, and you just can’t put arbitrary triangles together with it. Well, back to the drawing board.