Uses offset square twists in the back to make the open squares in the front.
As mentioned on the flickr page- Where did I first see this? Is it yours? I have seen it many places, but I can’t seem to recall (or find) the first one I ever saw.
If you have folded this, and have a copy online, would you consider posting a link to it in the comments for this blog post? Or if you don’t wish to do that, I’d also be happy to hear from you via email- you can reach me at origomi@mac.com.
-Eric Gjerde
I first saw the square weave years ago on what I have bookmarked as “Helena’s Origami Index Page”. The site looks to be dead, but I found the page on archive.org’s wayback machine here: http://web.archive.org/web/20010512021737/hverrill.net/pages~helena/origami/tessellations/orites8.html
I spent many hours reverse-engineering these folds from this and Alex Bateman’s site – Good times!
I’ve never talked with Helena Verrill, but a lot of the first tessellation stuff I saw online was of hers. I wish it had been easier to find and understand, it would have saved me some time when I was trying to figure it all out the hard way…
Thanks for the links!
Hey Eric!
I first saw this tessellation in a math paper by Kawasaki and Yoshida. (Yoshida is a well-known mathematician, whereas Kawasaki is a mathematician and an origamist. So I think it’s safe to say that Kawasaki came up with it, since they don’t credit it to anyone else.) The article came out in 1988. Here’s the reference.
Kawasaki, Toshikazu and Masaaki Yoshida, Crystallographic flat origamis, Memoirs of the Faculty of Science, Kyushu University, Series A, Vol. 42, No. 2 (1988), 153-157.
It’s pretty hard to find, hard to read, and the math is (honestly) no great shakes either. But it does have crease patterns for 4 origami tessellations. One is a standard square twist tessellation. Another is the classic triangle twist tessellation. A third is the one in this blog post, and the fourth is an offset square twist variation that is iso-area.
Surely here on flickr, the first to discover this pattern was Ryan, you can see his first approach to this kind of design here:
http://www.flickr.com/photos/infinite-origami/87641014/
🙂
The first recorded example of this square weave tessellation I can find is from Shuzo Fujimoto, see page 157 of “Sojo Suru Origami Asobi e No Shotai” his 1982 book. It is shown in figures 271 and 272. In this case it is the closed back version rather than the open backed one above.