Category: Origami

Here are CP’s for the complete set of shapes “Icosahedra with One or More Slices Cut Out of Them, Whose Faces are Composed of Pentagons and Triangles.” I have not yet tried to fold any of these yet, but the layouts all look doable. As luck would have it, I picked a good reference point (half the distance from the edge of the paper to the center) to begin developing the CP for the three-pentagon shape, and can readily develop the other shapes with the same edge length. Four out of the five are remarkably efficient! However the smallest of them, the pentagonal pyramid, wastes a lot of paper. I ought to find a good smaller size sheet to use for that.

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.

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.

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.

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.

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.