I recently returned from the 8th #Origami in Science, Math, and Education (8OSME) conference in Melbourne where I presented our work on tessellations of origami wrapping patterns called "flashers"
We showed that you can fill the plane with triangular, square, and hexagonal variants of these fold patterns (and certain combinations of triangles and hexagons) such that closely packed arrangements in the folded state are guaranteed
You can find the paper at morphingspace.stanford.edu/publications