Meanwhile. though, I'm still playing with structures. I find the blog is a great way to keep a record of what I'm doing. I use my silver tubes to experiment, but it's too expensive to keep permanent structures made out of handcut and oxidized silver tubes just so that I can get ideas from them. So if I blog about them, then I have pictures and notes, and I can reuse the tubes for actual jewelry.
Ever since I made thebracelet above, I've been fascinated by how an alternating series of right triangle tetrahedra and equilateral ones makes these square structures. I'm making a similar bracelet now, but I kept wondering if I couldn't make the series continue in a straight line instead of turning corners. (This happened at about the time I realized that I didn't have enough 20 mm tubes to finish the bracelet anyway.) So I tried it--and it works!
Doing it just the way I had done the square structures, i.e. alternating 1 right angle tet with 1 equilateral one, I got the top structure, which is flat on the bottom with a zigzag top. But what was more interesting, I thought, was that since the zigzag tubeson top were at fight angles to each other I could make them into right angle tets too and then (bottom picture) I get a structure with a square profile that I can extend as long as I want. Also if I end with an equilateral tet I have a tube at the end whichcould serve as a hinge to join another structure. Actually, just as I write this and look at the pictures, I realize that this is really an octet truss, because if you left out the central tube that is the "hub" shared by 4 tets, you'd have an octahedron. Stay tuned!
I should mention that things don't always turn out that neatly. When I made a chain using only right triangle tets instead of alternating, nothing interesting happened. Also I suspect I could have found out the same thing just by creative use of the Pythagorean theorem, but then I wouldn't have pictures to remind me of what I'd learned.