Back to geometry

   First of--apologies for the blurry pictures; I didn't haul out the tripod as I should have.
    I've been playing with structures of tetrahedrons again.  Last September I did a post or 2 about some necklaces I made using really long bugle beads to form chains of tetrahedrons (tets).  I liked them but got concerned about the sharpness of the edges of the bugle beads.  Even adding a seed bead at the end of each bugle, I was a bit worried about the fireline fraying.  I decided not to use magnet clasps because I didn't like to be pulling the necklace apart as you do with a magnet clasp, for fear of cutting a thread. 
  Anyway, I started in again, but this time using the oxidized copper tubes I've been using lately.  If you just keep adding tets in the most logical order they make a circle.  I think ( if anyone knows for sure, I'd love corroboration or correction)  that tetrahedrons will tile infinitely in space with no gaps the same way that cubes will.  But they do it in a very curvilinear way.  For example, 20 tets form an icosahedron, which is essentially spherical.  Still, if they'll tile in 3 dimensions, there had to be a chain of tets that would curve  gradually, or even go straight.  But I was having a hard time getting a chain of tets that had a shallow enough curve.  The chain I had used with the 30mm bugles last fall, didn't work with my 22 mm tubes.  The curve was too tight, and I ended up turning it into a bracelet instead of a necklace.
     I spent lots of time coming up with the second structure.  I found a chain of 8 tetrahedrons which didn't bend much.  Then I marked the last tet with a piece of yarn and started adding tets to the chain so that that marked tet was the center of a symmetrical chain of 15 tets.  Then I moved the yarn and extended the 15 tet chain to 29.  I'm sure there are computer designing programs that would figure out something like this for you, but I'll admit I learned alot using this seat of the pants method.  And I got a chain that curved just the right amount.  I've even found a chain that goes straight.  It makes a gentle spiral as it goes, so it's pretty cool.  I don't have a picture of it yet, but I'll post one when I do.  All in all, it was a fun endeavor.