Category: Origami

Double Feature: Road Trippin’ *and* Fun With Shapes

Part 2: Fun With Shapes

Now the Origami part of the trip: At the Strong Museum there was a place to play with shapes, and I discovered something interesting. An octahedron made of three regular pentagons and five equilateral triangles. I’ve never seen this shape before and don’t know if it has a name. It will make a nice addition to the Periodic Table of Polyhedra I’m compiling. The goal of that project is to identify every topologically unique combination of edges and vertices for polyhedra (mainly low polyhedra –complete up to Octahedra, as coincidence would have it, and selected interesting ones above that. Variations in angles and edge lengths don’t matter for the purpose of this enumeration.)

So I went ahead and made it out of origami. It has a pretty neat folding sequence and symmetry in the layout. I don’t use Robert Lang’s Reference Finder but instead rely on ratios incumbent in the design to to develop the layout, usually going for maximizing the size of the figure in the paper and still having enough left to make the lock. This one turned out very good in the usage department, although I may have to tweak the lock itself a bit.

This shape has the interesting property that if you replace each pentagon with five equilateral triangles you get an icosahedron. Several other shapes have this property, including pentagonal antiprism and a pentagonal pyramid, so they constitute a set. There’s another with 15 triangles and one pentagon, and yet another still with two pentagons and 10 triangles, but it’s not an antiprism because the pentagons are not parallel.

I’m thinking it’d be fun to do this whole series, especially if I can get the unit edge to be the same size across all the different models. Meanwhile, here is the CP and some pics of the a first (not too neat) version of the model.

Origami USA 2007 Convention

Well it’s that time of year again. I spent the last four days at the OUSA Annual Convention, hanging our with origami people, talking and thinking about origami, and folding late into the night. The OUSA convention attracts some of the best folders from all over the world, including Japan, Europe and South America. I got to catch up with some of my origami friends and colleagues including John Montroll, Marc Kirschenbaum, Robert Lang, Brian Chen, T. J. Norvell, and a good number of others. You know who you are. Shout out to Brian Webb from Indiana.

If you’re into origami, and particularly if you live on the East coast of the United States, you probably already know about it, and may very well have been there. If you’ve never been to one, I encourage you to join us next year. It’s more like a conference that a convention really. There’s an exhibition (amazing!), and classes and seminars, and all-day free folding in the hospitality area. Anyone can exhibit their work or teach a class.

The exhibition was pretty amazing, and featured a great variety of subjects and styles. Highlights for me included Brian Chen’s Totoro Bus and Robert Lang’s American Flag. Satoshi came from Japan as a special guest of the convention, and his stuff is always fantastic. I exhibited some new work including my Armadillo, a few Butterflies, and my Stellated Dodecahedron. I also displayed my UFO, Rocketship, Elephant and Dragon. I’m happy that every year the quality of my exhibit goes up. This year there were a lot of people (over 70) exhibiting, so I selected fewer models to fit in the space, which made the whole thing a bit easier. And Michelle’s cup was in the Origami by Children display.

There’s also a store with books and all kinds of paper and other supplies. This year we bought 2 books. Jeannie got Tom Hull’s new book, Project Origami. Which is rather mathematical in nature and focused on modulars and their geometric properties. I’ve barely glanced at it yet but it looks fascinating, and know Tom, it’s sure to be great.

I bought Marc Kirschenbaum’s Origami Bugs. I’ve been working on origami Lady Bug, based on my butterfly, but after several unsatisfactory attempts I was starting to conclude that the result I was after was different enough that the butterfly base might not be suitable, and was wondering if I could modify the base or if I’d be better off starting over from zero. Then I saw Marc’s Ladybug on the cover of his new book. His has 3 spots per wing, whereas mine will have one, but I’ve found that sometimes it’s good to examine how other folders tackle a subject, even if you have a totally different approach in mind. So I got the book. I started folding it on the train, and so far I can tell you it starts with a bird base and is well over 100 steps. My insect base is derived from a waterbomb.

Saturday Lizzy came with us, and she took a class of modular flowers. She did really well at it and was quite pleased about it, and gave the flowers to Nana, which was very sweet. Jeannie took a couple of classes on modulars and tessellations. I didn’t take many classes myself. Most years I try and take one class if there’s a really nice complex model being taught. This year I wanted to learn Joseph Wu’s Babe the Blue Ox (fantastic!), but it was a morning session, and so I missed it. Up till 3 AM the night before.

I did take John Montroll’s polyhedra class. Most classes teach a single model, but John’s method is that he had lots and lots of models that he’s diagrammed, all of which might someday make it into a book. So he has people fold them and gets their impressions. At this point he has enough polyhedra to potentially make two new books. I spend a fair amount of free-folding time talking with John and folding his polyhedra anyway, since polyhedra from a single sheet is a really interesting design area for me too. I’ve been working on a two colored Tetrahedron Dual (Stella Octangula), and among John’s new stuff was a whole set of interesting and fun-to-fold color-change polyhedra, so I got some ideas from that.

And of course I taught. Normally I do one model in a two-hour class, but this year I did 2 one-hour classes. Each was a relatively simple (for me) model of my own design: my butterfly and my octopus. I invented the butterfly at last year’s convention, and if you’ve been following by blog you know I refined and diagrammed it over the winter and spring. The Octopus is a few years old I never diagrammed it. It always gets a strong response and lots of request to learn it, so I thought I’d do it this year. Both models were rated as intermediate (usually mine are complex) so there was a wider range of skill levels in my classes, but everyone seemed to do pretty well.

Monday is seminar day, where people present topics outside of strictly folding models, things related to origami design, theory, technique or the mathematics behind it. One seminar I went to was by T. J. Norville, who came in last year with some amazing paper airplanes. His seminar was on some simple pleated forms that generate hyperbolic paraboloids. These are negatively-curved surfaces with interesting structural and geometric properties. This gave me and idea for how to do a cool Cuttlefish. (Now that I’ve renewed my interest in the Octopus, I want to hit some of the other Cephalopods.) In another seminar, Toshi from Japan gave a demo of some interesting software here’s developing to take a polygonal 3-D computer model and generate a crease pattern.

Still when all is said and done, the real fun for me is the free-folding, because every year I invent a few new things. This year the major one was a Hot Air Balloon, complete with a gondola hanging underneath. Design-wise it’s related to my Octopus, and also to my Rocketship and UFO. I pretty much nailed it on my first attempt, and then folded a few more trying to refine the curvature of the balloon and the details of the basket. I’ll fold a “final” version soon out of good paper, and it’ll definitely be in next year’s exhibit. Now all I need as a blimp to complete the series.

Then last night, at the closing banquet I was seated next to T. J.’s son, who doesn’t fold but was there to help out his dad and take in the experience. We got to talking and I learned he’s a Star Wars fan. He asked me to fold him an R2 unit, and since I’d been spending the weekend thinking about how to fold dome-shaped things, I was able to come up one fairly quickly. Then a made a golden Protocol Droid to go with it. He seemed quite pleased by the results.

Thanks to everyone at OUSA for putting on another great convention!

Interim Update

Hello all. I’m mainly getting ready for the Origami Conference this week. Folding like a demon in my spare time. Lots of works-in-progress, but no new finished pieces yet. Been trying to finish my ladybug but so far an elegant solution has eluded me. A friend suggested I try and come up with a Moose, so I’ve been looking at the mooses in the books I have. One is by John Montroll and the other by Robert Lang, and their approches couldn’t be more different. John’s is a great example of his classic style, using all 22.5 degree angles and advanced isotopes of the traditional bases.  It’s pretty easy to fold, and works well from plain ol’ 10″ kami. I did one on the train today, starting on the way in and finishing it on the way home. Came out really nice. Robert’s is all box pleating, and I’m about half done, and remembering why I don’t fold box pleated models very much, all that overhead. Still, I’m looking forward to finishing it, and it should be nice. Also made out of 10″ kami to be fair.

My own idea is rather different than both of theirs, particularly with regard to the antlers, which is of course where the action is in a moose. I’m thinking of doing something more sculptural, out of 2 large flaps, rather than hiding all those points deep in the model and opening it out at the end, a feature which both my examples share. So mine basically reduces to an 8 point base. Of course I’m not at the level yet where I can fold a model straight from the concept and nail it every time. No, there’s usually a fair amount of experimentation to get there for me. So we’ll see how it goes. If it works, I’ll also have a suitable base to fold the Great Forest Spirit from the movie Princess Mononoke, kicking off my long awaited Miyazaki series.

In all the excitement, there is one new thing I forget to mention: last week I did a punch-in on the ending of the sax solo for Heat Wave, and produced a slightly-less-rough-mix. Enjoy!

Origami Armadillo

The annual Origami USA convention is coming up in just two weeks, and I’m working on to make some new models for my exhibit this year. Each year I have a few new things and keep some favorites from the years before. Last year the new stuff was Origami From Space, which I will blog about at some point because I’m not done with that line of investigation just yet. More than just a thematic idea, there’s a whole approach to folding in there that I haven’t seen developed elsewhere, and I think is worth pursuing. This year I have a bunch of rather various stuff, including polyhedra, insects and animals. There’s my Butterfly and my Stellated Rhombic Dodecahedron, and now, a brand new Armadillo. I have a bunch more models in the queue, pulling together some threads I’ve been working on for a long time.

I’ve been working on the Armadillo off and on for the better part of a year. Tonight I completed a final version, which I made out of nice paper and it came out really well. The model uses my hex base, which is great for four-legged animals with balanced head and tail, approximately equally long legs, and of course toes. I made a pretty good first attempt a few months ago. The shell and body looked great and the tail and overall proportions were pretty good, and certainly the concept was working. There are some pretty interesting symmetries in the there that I used to develop the shell. The head and neck turnout out to be really tough to get just right. So much of a subject’s identity and attitude is in the head and neck. It seems like I’ll spend as much time on this as the rest of the model. I’ve even made head studies — models of just the head of a subject before. This one in particular had to have big ears and eyebrow ridges in addition to the usual proper posture and pose . The ears were a challenge since the base did not have extra points to use for the purpose, so they basically had to come from nowhere, and it was hard to pull that off and still have an okay looking head. So I’m really pretty happy with the way this one turned out, and it’ll be a keeper in this year’s exhibit fer sure.

I’m tempted to name this model Tarkus, in honor of the classic Emerson Lake and Palmer album with an armored armadillo on the cover. The it would also qualify for membership in the mythical creatures category.

Next up, I have a work-in-progress Ladybug that uses the same base as my Butterfly. It features a black body with a red carapace with 2 black spots, so the double color change is the major interesting thing about it.

Another idea I have is a Dual Tetrahedron. This shape, composed of two intersecting tetrahedra, is equivalent to a stellated octahedron, except that the two tetrahedra would be different colors. I’ve made versions of this shape before out of 4 and 2 sheets of paper, but the single-sheet version is obviously the one to go for.

Third, I want to fold a plant, for this year’s convention challenge. I have an idea for a potted plant, but since the devil is always in the details, I won’t know for sure if it’s a good idea until I have it folded. I have yet to even make a serious attempt yet.

If I get that far, it’s on to the bonus round. An idea I’ve been carrying around for a while for an Oliphaunt. These mythical creatures were featured in the Lord of the Rings films, visualized not just as extra-large elephants, but also having four tusks. The approach I would use would be take my Elephant and modify the base. The side effect of generating more points for the extra tusks would be to have extra paper in the middle of the model. I’ll use this to make a castle on the beast’s back. I figure it’ll make a nice complement to my Dragon.

We’ll see how far I get down this list. The good news is, even though I probably won’t get all of these models made, when I get to the convention, it’s always a really productive and creative folding environment, and I’m sure to make progress as well as come up with some new ideas.

Origami Butteryfly Diagrams

Well it’s been a busy week. We got the tiling and grouting done in our kitchen, so we’re over the hump on that job, and it’s looking really nice. Still have the sealing, caulking and some touch-up painting to do, but each of these tasks is small compared to the work so far. I’ll take some pictures of the completed project and blog about it in a future post.

Meanwhile, the other bit thing is I finally completed diagramming my butterfly. I aim to do a full diagram of one original model a year. Because of the level of work involved, that’s about all I have time for, although I’ve been making more and CP’s of late. I blogged about this model previously, when I posted pictures of it. I mentioned at the time that I mainly developed it at last year’s OUSA. Well, I began diagramming it way back last summer, but then I got busy with work and put it aside for a while, and changed jobs around New Year, and so it took a while to get back to it.

And now here it is. I’d consider this an intermediate level model. I can make a nice looking one from a 6″ square, in about a half hour. The diagrams are only forty-something steps. It does have a rather advanced closed sink. People who don’t like closed sinks might like this one, cuz it doesn’t matter if you do a good job making the inside neat. I posted it online at:

http://www.zingman.com/origami/oriPics/butterfly/butterfly_diagram.swf

The diagrams are done in Flash, using (the current version of) my Foldinator tool. I’ve done a bunch of diagrams in Flash this way and it works pretty well for me. One of the things I like best is that the vector drawings scale up smoothly, so you can get a lot detail into the drawings and it won’t be lost. At some point I’m going improve the Foldinator to include a more generalized representation of the model, animations between frames, and eventually and authoring tool. But for now the next feature will probably be non-sequential access to the steps. In any event, the Foldinator project has taken a back burner for me of late, despite requests from the Origami community. Since I write software all day, and I’d rather spend my origami time making origami than writing more software. Now if I could get a grant or something, that might change the picture…

I submitted this model to this year’s OUSA Annual Collection, so if you want a printed version, look to see; it may appear in there.

Also, soon I will be updating my main origami page to include the Butterfly pics and diagrams, as well as other new models. I’m sort of waiting on that until I have a chance to take some nice pictures, set up with lights and all, rather than just the snapshots I’ve been posting here.

Origami By Children

Every year Origami USA sponsors an exhibit of Origami By Children. You can learn about it here. The deadline for submissions is fast approaching, so last weekend I was able to get my kids to sit down and focus on coming up with something. Lizzy, who is 7 now, started to take an interest in origami 2 years ago, when she invented her first original model, a picture frame.

Last year she did the traditional Lily. It’s more complicated than it looks, but the hardest move in is a squash fold, and she’s good at those. I coached her, showing her the model and encouraging her to take is slow and fold neatly. She did a nice enough job that her model got in the exhibition, and OUSA donated some origami books to her school.

This year she’s had more exposure to folding and knows how to follow diagrams, so I let her decide what to do. She folded a bunch of things out of John Montroll’s Christmas Origami, including the candle, bell, and candy cane. I guess no time of year is the wrong time to think about Christmas when you’re seven. She decided to do the ring from the Twelve Days of Christmas, and put five of them together. Of course it’s not a hard model technically — the folding style is know as “Pureland” meaning it’s only mountain and valley folds, but there’s some art to it in terms of color and composition. I think she did a nice job. I hope she gets in the show again.

Michelle, at three and a half, wants to do everything her big sister does, so she was along for the trip. I tried to teach her the bell, but the reverse fold just blew her mind, and 11 steps is about 4 too many for a 3-year-old to handle. So I scaled back and taught her the classic cup, on which the bell is based, which was just in her range.

Origami Butterfly

A fitting topic for the first day of spring. I had thought I might blog about something else tonight, since origami keeps coming up, and I have been doing other things too, honest. I could say plenty about my new job, but I think I’ll wait until a project goes live. Or I could talk about how I almost made it thru the winter without catching cold this year — until last weekend!

I could talk about my ongoing music work, and how painstaking it is to sequence good drum parts for a jammin’ sounding track. I’ve worked with some really good drummers over the years (you know who you are, Mark, Larry, and Pat), and boy do I miss them. On the other hand, I’m not really set up to mic a drum kit in my little project studio, so it might not come out any good anyway.

I could talk about how I am looking into changing my workout routine, mainly by moving it downstairs. The major reason I’ve been working out upstairs all this time is that I have high ceilings in my living room, and do some exercises where I lift weights over my head. I could do it downstairs, but I’d need to do those sets sitting, which means I need to get a bench. Which has led me to rediscover why I hate shopping along with the fact that modern workout equipment is super-expensive and way more complicated than I need. Like hundreds of dollars just for a bench! When I was in high school I had a bench that came with an exercise machine and I bought the whole system for something like $100. It was really simple, just a board covered with vinyl and foam and some legs. Good for dumbbells and situps. Probably worth $20. I gave it to my brother. I wonder if he still has it…

But I’m not going to blog about any of that stuff tonight. Nope, for now the main topic is origami butterflies. I normally don’t do insects, because that branch of origami has evolved into something like speed metal in music, very focused on one particular dimension — developing lots of points. Not to say it isn’t amazing, cuz it is; but it’s not really my thing. But a butterfly seemed like a good subject because it’s more lyrical than your average bug, and I had an idea for an approach. I’ve seen a bunch of really beautiful butterfly designs, notably Michael LaFosse’s, that are great wings but don’t have legs. I’ve seen others that have legs but are a bit to technical, given the subject. Granted some of these models are from the era where any insect at all was pioneering, but hey. So I wanted to something simple and sculptural, but still complex enough to have legs.

I actually came up with the design midway thru last year’s OUSA convention. Every year I seem to come up with one or two new designs, usually manifesting something I’ve been thinking of for a while but hadn’t had the chance to fold yet. I showed it to a bunch of people and the response was great. It’s based on a waterbomb base, with two of the flaps forming the wings and the other two forming the legs. It’s easily doable from a 6″ square, and only the only hard part is 2 closed sinks in a row. The thing I like best about it is it pretty successfully captures the moment of spreading its wings and taking flight.

I’ve been refining the model over time, an last fall I went to the butterfly tent in the American Museum of Natural History. John Montroll had told me that butterflies really only have 4 legs, the front ones are vestigial and you can’t really see them. Shaw ’nuff he was right. Looking at dozens of butterflies, they all looked like they have four legs. So a redesign is in the offing. Ah well.

Still, I’m happy enough with this design that I’m working on full diagrams for it. Every year I try to diagram one model to donate to the OUSA annual collection. I’m not quite done, but I’ll be sure to post it when I’m done. For now, enjoy this pics and the Crease Pattern for the base.

Origami Sunday

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.

Origami Polyhedra: The Stellated Dodecahedron Part 2

A little while ago I posted some pictures of Stellated Dodecahedra I made in origami. Here the crease patterns for them. You see, in addition to folding origami, I’ve taken an interest in diagramming, and someday I hope to publish a book of my models. But I find diagramming so laborious that I only do one model a year! (Although they do tend to be pretty complex models.) I’ve also been developing crease patterns, which is particularly useful for polyhedra and other complex subjects where there is a lot of prefolding.

I do my diagramming and CP’s in Flash, and I’m not aware of other people doing this. One reason is I use Flash a lot in my day job, so I know it and can work in it quickly. Another is that I can use to make animated diagrams and CP’s. You can see some of them on my main origami page. This is an experimental format which I am refining over time. It had its origin in the Foldinator Project. Foldinator was originally envisioned as a full-on authoring tool for modeling origami and creating printable diagrams. However, to get there is a rather major development effort. So instead I wound up with this little hacker-level tool that I use. I still hope to finish and release Foldinator someday, but I’d need to treat it like a professional software development project and devote something like 6 months to a year of full-time work to it. Ah well, maybe if I’m lucky I can do like Robert Lang and retire young to do origami full-time.

Meanwhile, you can see the various approaches for the Stellated Dodecahedron.

Here is the one made from two squares. As you can see it’s the simplest of the bunch.

Next up is the one folded from a 2:1 rectangle. This one is remarkably efficient in it’s use of paper, to the point where I had to set it into a larger area to have paper to do the joining. It’s also kind of cool because it has a sort of zigzag layout. I plan to publish an animated CP of this one shortly.

Lastly is the “classic” version, from a single square. This is foldable but very difficult. I like the CP a lot because of the way the layout maximizes the root pentagon and underlying square. Vertices of the finishes form touch 3 edges of the paper. This one would be a good for an animated CP as well.