Category: Origami

Every year Origami USA puts on an origami Holiday Tree at the American Museum of Natural History in New York. It’s always a great attraction full of all kinds of wonderful origami. Ros and Delrosa, who organize the tree, have asked me to contribute a model for the last several years. I look forward to this because they often ask me to come up with something new, so it’s a good design challenge and a chance to show some new work. The tree usually follows a theme that has something to do with the exhibits in the museum. This year Ros and Delrosa asked me to fold a Gila Monster, a poisonous lizard from the American Southwest. They supplied a couple of sheets of great paper for the project.

I used my Lizard a starting point for the Gila Monster model. At first I thought I might just tweak it a bit, but once I started looking at the subject I decided to make a whole new model. Although it uses a hex base similar to the Lizard, there are substantial changes. First the body proportions are altered. The Gila Monster has a longer, fatter body and a shorter, fatter tail than my generic lizard. Second, to make it more realistic, I went with five toes rather then three. As you can imagine, this resulted in a lot more folding toes. Third, I decided to go with a closed back, to show off the excellent paper Ros and Delrosa gave me. These changes added up to a major reworking of my Lizard, to the point where it’s pretty much a new model.

I folded two or three tests to work out the details in the design, particularly for the sculpting once the base is achieved. Once I was satisfied the design would work I started in on the final models. Ros and Delrosa gave me two sheets of paper. One was an 18” square with a black-and orange pattern like lava. It was not even really paper at all but some kind of plastic sheet material, maybe originally intended for wall paper. It was kind of thick and shiny. The other paper was a rectangle of pink and black in a kind of op-art pattern. This was a high-quality paper for folding but on the soft side. Both papers, different as they were, were great choices as far as capturing some aspect of the essence of the subject.

But neither was suitable for an exhibit-quality model as-is. So I took each sheet and laminated to a large sheet of foil, and then colored the reverse side black. This resulted in thick, durable and workable sheets. The black-and-orange plastic one had the look and feel of leather, and the pink-and-black paper resembled tissue foil. I cut the paper rectangle in half and was able to get two 15” squares out it. I ended up folding three models, one orange and two pink. I gave two to the museum and had one to keep.

The origami Holiday Tree is on display from sometime in late November thru the New Year. If you’re in New York during the holiday season be sure to check it out.

Hey guess what? You can now pre-order my book from my publisher’s web site, and also read a most excellent blurb.

http://www.tuttlepublishing.com/authors/szinger-john/origami-animal-sculpture-paperback-with-dvd

Also it looks like they have a cover, and it’s one of the few photos I took myself.

I folded the first three in the series of Penrose tessellations out of good paper for my exhibit for the upcoming OrigaMIT convention October 19 in Cambridge, Mass. The 10-cell is folded from a 6” pentagonal sheet of Marble Wyndstone, the 35-cell from a 12” sheet of Tant, and the 70-cell from a 16” sheet of Wyndstone.

I’ll also be teaching the Penrose tessellations, the 10 and 35 cell versions. I’m giving them precut pentagonal paper to save time. I also finally got around to drawing out the crease patterns. Last year OrigaMIT was a great time, and I’m looking forward to it again.

I’ve also been working on a new butterfly design. More on that soon!

You may recall that I started working on a new Penrose tessellation back in June at the convention. This turned out to be a really interesting challenge for a number of reasons. First, my initial attempts at a pattern for the tessellation were wrong because they didn’t go together according to the rules. There are lots of ways of joining the tiles the look correct at first but really aren’t once you start to grow the pattern. I learned alot about how to join Penrose tiles.

Second, I needed to systematically work out the widths of all the pleats. I discovered they came in at least four different widths. The ratios of the widths are all the golden mean, which I guess is not too surprising. More surprising is that the wide pleats tend to separate groups of tiles into clusters, like avenues, streets and alleys, or maybe branches on a tree. The groups are usually five tiles, sometimes ten, sometimes two or seven, and then these aggregate into larger groups.

In fact the whole pattern is fractal. I made a series of Penrose tessellations with 10, 35 and 70 tiles. For each one, you begin by precreasing the pattern of the previous tessellation and then subdivide it. This happens in an interesting way, since each tile subdivides into approximately 1.6 tiles, with the edge of parent tile forming the diagonal of a new tile.

I worked all this out when I was on vacation last month in Albany and Lake Placid. After that it took me a few weeks to actually fold the models. I’m satisfied that the approach can be taken to an arbitrarily large number of tiles. The next level out would be at least 120 tiles; the further out you go the harder it gets to find a logical stopping point. I might do that eventually, but for now I think I’m going to fold a 70’er out of good paper and declare victory. I suppose I ought to document the crease pattern too. But after that, I’ve been focused on pentagram-symmetry subjects long enough. It’s time to move onto other things.

Like compound polyhedra with a color change!

I’m participating in another origami exhibit. This one is eXtreme Origami and is part of the Origami Heaven convention in Stonybrook, Long Island, and runs thru early August. Go check it out. You can find out more about Origami Heaven here:

http://www.origamiheaven.org/

I’m not sure if I’ll be able to make to check out the exhibit, so if you want to take some pictures I’ll appreciate it.

The theme of my collection of models is single-sheet complex polyhedra. The models I’m contributing are my Stellated Dodecahedron, Great Dodecahedron, and
Tessellated Dodecahedron (a.k.a Penfractal Dodecahedron). All of these
models exhibit pentagonal symmetry, being based on the dodecahedron, which
is composed of twelve regular pentagons. Each of these models is folded from a single, pentagonal sheet of paper.

You’ve seen the Stellated Dodecahedron recently. I still want to fold a second one, but didn’t get done in time, so I sent the one I folded for OUSA. Did manage to make a nice version of the Dodecahedron Tessellation out of Wyndstone paper, and will show that in a future post.

But this post is about the Great Dodecahedron. It’s not exactly all-new; I folded one from a 12” square of Tant a few years back but was never quite satisfied with it. The new one has a refined CP. The main difference is that it’s from a pentagon, so the corners provide nice flaps and the model goes together well and holds its shape quite strongly. I didn’t even need to wetfold it.

The shape itself is a complement to the Stellated Dodecahedron. Both are composed of sixty triangles and form star shapes out of sets of coplanar faces. With the Great Dodecahedron, the coplanar faces form a pentagon with the star rising out of the middle in the negative space.