Any paper that concerns origami and extending its reach is of interest to the Project. Central to our thinking on this is the work of Kôdi Husimi (sometimes anglicized as Koji Fushimi).
Origami was originally constrained in the folds that were allowed and it is a special quest of moderns to figure new folds, still within the tradition.
For instance, instead of edge to edge and corner to corner, a challenge is to use crossing of folds to create points to use as targets. In theory, many more ratios can be leveraged; the strict square only allows even integers and the square root of 2. A holy grail of sorts is the so-called quasisymmetries, those that use 5 and 7 sided units for instance.
Huzita shows a method here of folding 7 and 9 sided polygons. It isn’t what we need, which is a vocabulary of folded structures that use these symmetries, but it is interesting. The method also seems less formal than we need, but it is within the scope of our interest.
The Relationship to Kutachi
We likely will develop a user interface that will leverage hand movements and folds from origami. But it needs to be able to mimic some of what we expect will be complex symmetries from the categories used. Quasisymmetries could help.
Links
Kôdi Husimi paper. (not yet online)
The Kutachi essay on Origami. (not yet online)