more right angle explorations

I haven't blogged in a while; sometimes life gets in the way.  My husband and I have been in the sailboat business for 40 years, and we've just closed our store ( which was also my main studio) and are trying to figure out the future plan.  I've now sold all my looms, and the jewelry work is quite portable, but it still creates complications.  Right now I'm cutting tubes at a workbench in a storage locker we've rented, as we live in a townhouse, and the room I've set aside as my workplace is carpeted, and not conducive to sawing metal.  My plan is to cut tubes in larger batches so that I don't mind going to the storage place to do it, but I'm also looking at the possibility of an outside workbench here that won't look too industrial and irritate the neighbors.
   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 which

could 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.