Category: Origami

Yesterday I taught at a Special Folding Session with the Origami Society at the American Museum of Natural History. I taught my Turtle, and diagrammed the crease pattern just for the occasion. It’s a model I like alot, and it makes good use of my Hexagon Base. I’ve gotten a fair amount of request for diagrams over time, and one of the organizers of the session asked for this model. One reason I never diagrammed or taught it is that shortly after I finished it, Robert Lang’s Origami Design Secrets came out, and his Western Pond Turtle is not unlike mine in appearance. My model, however, uses a very different folding sequence that is both much easier and roughly twice as efficient in its use of paper. Like many of my models from my Elephant to my UFO, it follows a sort of “upside-down-bowl-with legs” approach, with the greater part of model being only a single layer of paper thick, and the bulk of the paper going to form the legs, head and tail, with the rest gathered near the edges and providing strength.

The Museum is such a great, fun place, and it’s a happy circumstance of history that OUSA is based there. My class was pretty small, 8 people, but 3 or 4 were teenage boys and one in particular was really annoying in a mostly funny kind of way. They’re origami geeks, all into debating which model out there is the “hardest”, and asserting “Satoshi rules!” and that sort of thing, plus a lot of, uh, less mature banter. I didn’t know any origami people when I was growing up, but if I did, I’d have probably been like that.

The model went over well, but all those toes took a long time to fold, so I didn’t get to spend as much time as I’d have liked on the sculpting at the end. It’s pretty advanced model, so not everyone could pull it off with enough precision, but most did pretty well. A fair amount of sculpting can’t really be diagrammed anyway, it’s up to the expressiveness of the artist. It was a fun time, and I think I’ll teach one of these sessions again.

Jeannie and the girls came, and Lizzy stayed and folded while I taught, to the delight of the ladies who like to make ornaments and boxes — she made a bunch of that kind of stuff. Jeannie and Michelle took in the museum, and at the end we had a whirlwind tour of the dinosaur lobby and main African hall. Didn’t make it to the whale room, but otherwise a great day.

And, as a bonus, as I was putting together the CP, I came up with an armadillo, using my hexagon base. I had been thinking of a way to fold an armadillo since last summerwhen we were in Florida and they were in the yard of the house, living uder the hot tub. I had a concept that was similar, but using 45 degree symmetry, that I made from a (rectangle) Animal Kingdom map, but when I got home and tried to reproduce it I couldn’t get it to work. Don’t know why I didn’t think of the hex base sooner; it’s perfect for animals with equal-length legs, and toes. So the approach was solid although the first attempt was not prefect. Made a 2nd attempt with refined proportions, head and tail. It’s pretty close, I probably need one more try, mainly to fine-tune the head. So watch this space.

As long as I can remember I’ve liked geometry.

I’ve been doing origami polyhedra for quite some time, and you can see some of the ones I’ve designed on my Origami Page. My approach is mainly from single sheet, in contrast the more common modular approach. When I first started, I thought that it was new, largely unexplored territory, and I could do something really interesting. Soon I could see it was a rich area of endeavor, but also very challenging. Around that time I met John Montroll, and he was way ahead of me down this path. In fact he was about to release a book on origami polyhedra, and was working on a second one. This was great for me, because he was eager to have people test his diagrams, and was very generous with his ideas, and I learned a lot from our discussions. On the other hand, he pretty much had the basics covered and then some, like several versions of the platonic solids, and some prisms and Archimedean solids and other shapes. So I had to go a good deal further to get into original territory.

One of my all-time favorite shapes has always been the Stellated Dodecahedron, which is the 3-D analog of the pentagram. (Which, BTW is the 4D analog of the Tetrahedron, but since no one folds 4-D origami, that’s a bit outside the scope of this discussion.) I’ve designed and attempted to fold various versions of this shape over time.

Here is a design from a single square. I actually succeeded in folding one, from a giant (24″) sheet of foil paper. It worked, but I would not call the result great in terms of the level of craft. I tried another from a smaller (14″ or so) piece of thickish (for origami) paper, but never completed it. The problem is that once you get towards the end, there are many flaps of extra paper to deal with, and the model wants to spring apart. This, combined with the limitation of having only two hands, makes it very tricky to close. I may give this design another try, but I’ve been exploring other avenues.

Last summer at the OUSA Annual Convention I was playing around with ideas for this shape again, and it occurred to me to try it from a 2:1 rectangle. It was still a single sheet, but provide more edge relative to the paper’s area, so it ought to reduce the problem of extra flaps of paper to hide. I have a design for a 2:1 icosahedron which is really efficient and easy to fold, and it didn’t take too long to come up with a regular dodecahedron, which is the base for the stellated version. When I went ahead and folded it, it realized it was so efficient that there was not enough paper to make a lock, so I’d need to go back and modify my design be setting it into a slightly larger rectangle. So I tried again. Still making the model close was a bit of a challenge. Doable, but requiring some effort.

Then over Christmas vacation, I finally had some origami time again, and this time I went for a version made from 2 squares, each of which comprise half the finished model. This is much easier to fold because you can reach inside each half as you’re making it, and the leftover flaps of paper become tabs that fit into the opposite half, nicely solving the problem of what to do with the leftover bits. At the end, the two halves lock together tightly and securely. The resulting model is quite attractive, because it’s much easier not to crush it as you’re putting it together. The examples below are made from (2 sheets each of) 6″ foil paper and 8.5″ photocopy paper.

Which brings up the question: Origami purists like to only work for a single square sheet. Which is more of a “cheat”: to use two squares or one rectangle?

Coming Soon: crease patterns for the 3 methods for Stellated Dodecahedra.