Stellated Dodecahedron in Origami

As mentioned previously, I had a great OUSA convention this year. If you’re interested there are lots of pics online here. One of the things that made it great for me is I had a lot of new models: Timber the Dog, Sophie the Cat, my Giant Squid, Cuttlefish, a new rendition of my Zeppelin, my Penfractal Dodecahedron Tessellation, and my Stellated Dodecahedron. I hope to say something about each of these, starting with the Stellated Dodecahedron.

Most people make origami polyhedra using the modular approach, putting together lots of triangles or whatever to create a shape. To me this is not very interesting since the assembly dominates the folding, and in my view it misses the essence of doing origami. Much more challenging is to fold a polyhedron from a single sheet. In fact it’s so challenging I only know three artists who work in this area: John Montroll, T.J. Norvell, and myself. John has written several books on the subject and has made it challenging indeed to find terra incognita in this space.

My Stellated Dodecahedron is the result of a long and arduous quest, one of a handful of advanced polyhedra I’ve been working on for the last few years. Now I can finally cross it off my list. In case you don’t know, the stellated dodecahedron is a shape based on the regular dodecahedron, which is a platonic solid composed of twelve (“dodec” means two and ten) regular pentagons. The stellated version replaces each face with a five-sided pyramid, resulting in a star-like shape (“stellated” means starlike) composed of sixty triangles.

I made several attempts at it a few years back, but it was beyond my skill at the time, and I only barely managed to make one out of a giant sheet of foil, and it didn’t hold together too well. This year I was determined to finally make an exhibit-quality one for the convention. I’d been working feverishly on Zeppelins (more on that in another post) but found the time to create this as well. In the process I think I leveled up as a folder.

The hard part of doing this model was closing it all off at the end. My previous version was made out of a square, and this created the problem of having all the flaps being different shapes and very difficult to deal with. For the new attempt I began with a pentagon sheet of paper rather than a square. The first step was to fold a pentagon out of a square anyway, so I just cut off the leftover bits rather than fold them under. Now when I got to the end I had a nice array of identical flaps that made perfect tabs, and I was able to use a twist-lock to finish the model.

I folded the Stellated Dodecahedron from a 50 cm regular pentagon of Marble Wyndstone (a.k.a. Elephant Hide) paper. It took me five sessions of several hours each, and this after I made a study out of draft paper. The first two were just to do the precreasing (you can see the CP below). The next one was to fold the bulk of the model, up to the close. At this point it became clear that I would not be able to close my study model because the paper was too soft, and I’d have to just go for it. Wyndstone is thicker and I’d precreased everything strongly with a bone folder, so it looked like it would have enough “pop”.

Once I got it got it collapsed there was some springiness that wanted to push the model apart from within. I applied a drop of water to every concave vertex, the ones where six triangles come together. Then I wrapped the whole thing tight with tape and string and let it dry overnight. Next morning – the day of convention – I unwrapped it, not knowing how the wetfolding had worked. To my delight it came out perfectly. The final model was tight and strong like a soccer ball. In fact I like it so much this model has now taken the spot on top of my piano previously occupied by the only modular I’ve ever liked well enough to actually fold – Tom Hull’s Five Intersecting Tetrahedra.

I want to fold another one of these soon, for an upcoming exhibit on Long Island. Between doing this and the Zeppelins, I’m now seriously considering getting a KNK Zing or a Craft Robo. Having a machine pre-score my paper from a .eps file would seriously reduce the amount of time I have to spend prefolding, plus it would guarantee everything to come out as precise as can be.

It’s All About Lizzy

June has come and gone in a blur. Yesterday we had a party for Lizzy’s 8th grade graduation. It was a bit low key with no one staying really late, partly cuz I’d been sick the night before. But still it was lots of fun and I’m glad so many people could make it. A good time was had by all. Finally today is a day to hang around a relax and catch up with stuff.

Way back at the beginning of June, we had the carnival at the kid’s school. Lots of fun that. I helped out at the Father’s Club tent, making burgers and dogs for the concession stand, and also running some of the carnival games. This year I played three games and won three prizes. One was a dart toss, another was dropping golf balls down a ramp to try and get a high or low number. I explained to Michelle the secret of winning that one and she played a perfect game with a score of six, the lowest possible.

Then it was the kids’ show of the Wizard of Oz, in which Lizzy played Glinda and rocked the house. Here’s picture of her from the local paper. Also Jeannie took a picture of Lizzy on her last day of school, in the same spot as her first day of pre-k all those years ago. How the time flies.

Then it was the graduation dance, and then the graduation itself, all fun if somewhat poignant occasions. Lizzy graduated with first honors and is in the honors track in her new high school. She placed out of ninth grade math, but she’ll have to take Latin. She doesn’t mind so much since that’s the language they use to cast spells in Harry Potter (the school doesn’t offer Elvish). Michelle will be at the grammar/middle school for a few more years, so it wasn’t really such a big goodbye for us, although some families that have become good friends are moving on. Hopefully we’ll be able to stay in touch. Earlier this week Lizzy had her orientation at her new high school, so it’s really moving forward into a new phase of life. So congratulations Lizzy!

Lastly we had the origami convention. This year was a really good one. I had lots of new stuff. In the middle of, Jeannie and bopped out to Long Island for her cousin’s wedding on Saturday night, and another good time. More on the origami stuff in a future post.

Busy Season

Lots and lots going on here these days. It’s the end of the school year for the kids. Last week they had their spring show for their theatre group YAA. It was a The Wizard of Oz. It was a really good production. Michelle was a Munchkin and Lizzy was Glinda, the good witch of the north. She was really perfect in the role, and I think her singing and acting has improved even since February. Either that or they had better sound reinforcement at this place. Jeannie taped the big Munchkinland production number. I’ll try and post a bit of it. As an added bonus Lizzy and Michelle have been singing songs from TWoO and Wicked around the house. They sound pretty good; they can actually harmonize. And I practically have the Munchkinland number memorized at this point. I’m thinking it’d be fun to get the sheet music and learn it, and somewhere down the line record it interpreted as a prog metal epic. Maybe rename it “Monsterland” and use low growly voices instead of high squeaky ones.

This week Lizzy sat for her algebra final. If she does well she’ll get to skip a year of math in high school. Meanwhile Michelle has been getting me to watch a bunch of math-oriented youTube videos, about things like the Fibonacci series and plant growth, fractals and other fun stuff. This began when she told me she got a book of graph paper and began making fractal doodles in it. The girl is definitely one of mine! The one on plant growth, even though it mainly contained material I already knew, explained it in such a way that I got a new idea for how to make origami pinecones, pineapples, and other forms in way that’s more realistic and naturalistic than anything that’s been done before. (Yes, we’re still talking about pineapples!)

But right now I’m busy with other folding projects. I’ve been working on a pair of Zeppelins, one for this upcoming exhibit and the other for myself. This is probably my most labor-intensive model. I’ve been at it for over a week. I only ever folded one and that was few years back, at the end of a long road of attempts. Now it’s a fair amount of experimentation and reverse engineering. Today I had to make a study of how the nose went into 3-D cuz I couldn’t remember. Tonite I finally got them more-or-less made into full 3-D form. I still have to do the final sculpting and finishing. These models will be wet-folded for sure, and probably (don’t tell anyone!) have a few paperclips and bits of tape on the inside to keep them from spreading apart over time. Once that’s done I still have to make a stand (sometimes in life you just gotta make a stand) and a road-worthy container. One that’s done it’s back to working on fractal polyhedra, which was going to be my Big New Thing this year. Oh yeah, I’ve also been asked to contribute an Armadillo for the exhibit. Ah well, there’s still a week to go, and I’m taking a couple of days off.

I’ve also been busy because now that my book is soon to be released, my publisher wants me to get my “social media” presence up. I created an author page on Amazon, and an artist page for my Origami on facebook. Not much there yet, but it’s a start. I also created a Buzzy Tonic page on Amazon, and checked in fb to see the one there needs some attention. Yet todo is iTunes. My feeling about all this alternates between thinking that its pretty cool and it’s just a big time suck. I’m looking to get the whole thing driven by feeds when I post to my blog with certain tags or categories. I suppose if it make some sales its worth it.

The music thing will have to wait until July, after the origami convention and some travel. I’m close to finishing two songs, Black Swan and Is It Safe?. Last thing I did in recordingland was to lay down sax parts for Is It Safe?. Martin’s original parts were out of tune on the high E’s and F#’s. I got those notes, but had a lot of trouble with the high B’s. Anyway, closing in. When I’m done I’m gonna take what I have and organize it into a logical EP, and go back master what I have so far. I also have a concept for a logo and some album art, but I need time to draw it nicely. When that’s all in place I think it’ll be time to form or join a live band. That’ll be a whole nuther adventure. I’m continuing to develop a set of covers and my own tunes. More on that soon, but probably after the origami convention.

Penfractal Dodecahedron Tessellation in Origami

Here’s my prototype of a Penfractal Dodecahedron Tessellation. It’s a 3-D evolution my Penfractal Tessellation. Each face of the dodecahedron is subdivided into six smaller pentagons. The model also makes a reasonable representation of the dodecahedral analog of the tesseract, albeit in 3-d hyperbolic space rather than true 4-d space (trust me on this; I looked it up). Now that my proof of concept is done, I want make another version that’s more ball shaped by making the tessellated sub-faces bulge out. And you should know that although I almost always work with a square sheet, I’m considering using a pentagon for this one, so I don’t have to deal with all different ways to handle the unused paper in the corners. I think the subject may justifiy this.

I’ve been folding lots of other stuff too. I’ve perfected my dog and cat and made a whole bunch over the weekend. A few are to give away, and others are for my exhibit and the convention model menu. Soon as I get around to it I’ll take some pictures with the good camera. I’ve also been invited to contribute a model to an upcoming exhibit. More on that soon. The model they want is my Zeppelin. This is one of my hardest models. In fact I’ve only really successfully folded one. I’ve been meaning to fold one out of better paper for a long time. So now I’m making two, one for me and one for the exhibit. Luckily I diagrammed the first half of the model (the precreasing part) so I don’t have to work that out.

If I get that done in time, my next model will be a new attempt at a one-sheet Stellated Dodecahedron, since it uses the same base as the Dodecahedron Tessellation.