The last week before the start of a semester is always a good time to mess about. While I've spent some time reading about buildings and apartments and chambers (Tits Systems and Coxeter Systems and such), I also did some origami. I've done the 5 interlocking tetrahedra before, but it wasn't very nice (I used pieces of paper that were too long). This one's a bit better, with color and all (trying to use up my color paper). Plus this gives me a chance to see how blogger does pictures. Gotta have some excuse to play with stuff, right? If you're looking to make your own, I used the plans from Thomas Hull's 'Project Origami' book, but they are also in the book I got that started my hobby: 'The Origami Handbook' by Rick Beech. In fact, Dr. Hull has the plans online.
What I'd really like to do next is an origami trefoil knot, using the Phizz units, along the lines of the torus. Now, I'm not very bright, and have never done an origami model without the plans sitting in front of me. So I asked my friend google to tell me about possible models. The only thing I've found so far is this paper (.doc, ewww), which does have plans for the trefoil. In fact, I really enjoyed the paper, and learned some things from it (the counting bits at the end). But the plans seem to lack the 3-fold symmetry I expect is possible. Perhaps I just don't know enough (any) of the geometry involved, but I figure there should be a fundamental domain that is a third of the model. Or perhaps the three things go together, but each one is 120 degrees rotated (along the meridian) to get the appropriate twisting. So, if you know of such a model, and can send me a link, it'd be much appreciated. If you know a reason such a model can't exist, please do tell me about it. Otherwise, one of these days, I may start folding some more units. That sounds productive.
Actually, now that I think about future origami plans, hot on the heals of this five tetraheda model, there's another large project I've been wanting to do. The five tetrahedra made from penultimate units. I've sat down to do it before, but you have to cut paper to specific sizes. And not something like '1.5in x 4in', but 'a 4x3 rectangle whose width is 2.58 inches'. Right. Perhaps I'm missing something (besides a functional brain).