I found this interesting design on Galen Pickett’s website, in one of the rather hidden(1) galleries(2) he has full of origami goodies.

It’s a model called “Flammifer” by Peter Budai, who I had never heard of until seeing this model. Here’s a great little writeup by David Lister from a few years back about him.

What I thought was the most interesting thing about this design is that I’ve folded something very similar to this, but with hexagonal instead of triangular square symmetry; but in all other respects it matches the doubling dual-sided pattern exactly.

I had thought about trying to fold this, since I know it’s possible, but I’m very pleased to see that it has been done and solved long ago!

Thank you, Galen, for posting all your wonderful photos online, and sharing some of your origami world with the rest of us.

And thanks also to Peter Budai for the wonderful design. I think this is a natural outgrowth from a very interesting line of origami exploration by Peter- he calls them “Infinite Folds“. this one is just 4 of these “infinite folds” put together. Many of these could no doubt be combined in the same way, and folded to a (theoretical) infinite level of recursion. Fantastic.

edit: fixed the typo. meant to say square instead of triangular. oops.