Octahedron shapes.

   I've been playing around with the different shapes I can get in octahedrons.  I started thinking about how I don't get a firm shape using RAW with tube beads because a square isn't rigid the way a triangle is.  But on the other hand right angles are just so "freindly" to work with.  We're surrounded by them, and we know how they work.  So I started imagining  octahedrons (octs)that were more or less square in overall shape. I wanted the piece to be not too deep, i.e. not sticking up too far off the body (as lots of my pieces do).  So with a relatively flat oct I could just use Pythagorus to figure out how long to make the "waist" beads--here the gold beads-- so that you'd have a right triangle, and that would make a square shaped oct.  The cross-wise and length-wise tubes are 20mm long, so a 28mm gold tube would be about right.  Actually, though, I decided to use 25mm cold tubes instead, so the octs aren't quite square, but zigzag a bit.  Partly that was because I thought a bit of a zigzag was more interesting, and partly because I prefer using more or less stock lengths rather than cutting tubes just for a single design.  If I use stock lengths (5, 10, 15, 20 and 25mm), I have more flexibility in the design.  If I cut custom pieces ahead of time, I have to have it all figured out before I do it, and I like to sort of make it up as I go along, even if I have the general idea figured out at the start.  Also there would be lots of times that I would cut lots of, say 28mm tubes and then discover that to get the right curve, I really needed them to be 27.5 or 29mm or whatever. 
   Here, when I got to the back and needed to make it curve, I had to use shorter tubes on the inside triangles than on the outside ones.  The ideal length for the inside tubes would have been around 18mm, so I just alternated between 15mm tubes in 1 oct and 20mm ones in the next.  One of these days I'd like to skip the curve and do a piece that would look sort of like a tic-tac-toe grid.  

dangles redone; learning about structures

   Well, I redid my dangles, as I mentioned in my last post, and they do indeed dangle more freely now.
    The thing I probably should have talked more about concerning this necklace is the tube itself.  It took several tries to get it right.  The nice thing about doing more random structures is that when you need it to curve, you can just start throwing in a few short tubes on one side and longer ones on the other side till you get the amount of curve you need,  But with a piece like this, where you keep repeating a structural shape, you have to get the shape right so that it will produce the curve you need.  My initial plan was that my tube would be octahedrons ( I call them octahedrons because they're made of 8 triangles, but, of course, they're not equilateral triangles as they would be in a true octahedron).  The cross-section triangle would be all short (15mm) tubes .  The tubes running more or less lengthwise would be 20 mm, except that to get the curve I wanted the triangle on the outside would have 25mm tubes.  I'm trying to use tubes of 5, 10, 15, 20 and 25 mm and make that work without cutting special lengths for a particular piece.  Anyway, it didn't work--the curve was too tight.  I tried 2 more variations before I came up with this one, where the cross-sectional triangle alternates between a 15mm equilateral one and an isosceles one.  That made a curve that was just a bit too shallow, but I had a few longer tubes (28-ish mm) so I could put them in the 2 outside triangles at the very center, i.e. bottom of the necklace and get a sharper curve just there.
  This brings up a whole new idea--that I have to move from thinking of a piece as a chain of units, and think more about the overall piece as a unit.  I came up against this same issue some years ago in a sphere I made and posted about at the very start of this blog.  My idea was to take the basic dodecahedron ( Plato bead in

some publications) and think of it as a bead to use in building a bigger sphere, a truncated icosahedron ( or Archimedes bead).  That's what I did here (sort of--Actually there are 60 small spheres, not 90, but anyway...).  I built it adding on 1 sphere after another, and when I got to the last 4 or 5 spheres it was really hard to get the needle in and out as the big sphere closed up.  After I was done I realized it would have gone much easier if after I had gotten, say, 2/3 done I had switched my viewpoint to the whole sphere.  Then I could have built the whole inside of the rest of the sphere, the very dark blue beads, then the whole middle layer, the clear beads, and finished with the outer cobalt blue layer.

    Now I'm have the same issue with my tube necklaces. Here's one in particular.  I've been using a chain of tetrahedrons to make either a bracelet or a necklace.  Mostly the only way I could make the structure go from making a bracelet to making a necklace was to make all the tetrahedrons bigger. 

  But then I rethought, and realized there are sort of 3 parts to the structure.  The last picture shows it (I hope) with bugle beads.  First there's a series of triangles at the top of the structure, which will be the inside of the curve.

In this example they're a sort of light iridescent gray, and you can see them by themselves on the left.  By playing with the size of these triangles you can vary the height of the piece.  I have tended so far to make it tall  and sort of dog collar-ish.  Then there are the tubes (here dark gray and spirally) that turn those original triangles into tetrahedrons, so that the dog collar becomes a spiked dog collar, as in the center.  Actually you could leave the piece like this, and one of these days I probably will. 
   Finally, you have the zigzagging tubes on the outside edge of the curve.  Here I have just 2 bright silver ones on the far right.  It turns out that the length of these tubes determines the shape of the curve.  Here I've used tubes that are shorter than the other ones.  By using shorter tubes (20mm instead of 30mm) you almost eliminate the curve in the structure.  The longer the tube the tighter the curve.  So now I understand the structure and will have much more control over what I build with it.

  This has been pretty windy, but spelling it out helps me get it into my head, so if you've gotten this far, my apologies for the length.  Also the paragraphing got real weird at the end and I don't have the energy to go back and fix it.  Happy New Year.