Cages

I've been working on pieces, mostly earrings, where there's a "cage" made from oxidized sterling silver tubes. Then another structure, usually a sphere of sorts floats freely inside that cage.  I've done spheres of 4 mm gemstone beads, but my favorite, and my best selling one is a dodecahedron (sometimes called a Plato bead because it's a Platonic solid) made from 3 mm gold filled beads.  Lately, though, I've wanted to make a shape that wouldn't stay so much inside the cage, but would hang out more.  I thought what I wanted would be a stellated structure with different points hanging out of different triangles in the cage.  But I found I didn't like those.  The problem was using my gold filled tubes to make a stellated structure.  The gold filled tubes are a bit bigger in diameter, around 1.8 mm, and when you make a stellated structure that's small enough for an earring using tubes that fat, it just looks kind of clunky.  I had thought of using just a cube, which doesn't require

so many short tubes and doesn't have such acute angles.  But a cube, since it isn't made from triangles, isn't rigid the way something like a stellated tetrahedron would be.  However, I found that if I made a cube using my stiffest 10 lb test monofilament, and went around each of the square faces an extra time, the cube came out almost as stiff as something made from squares.  And since it's just floating, and so has no strain on it, it turned out to work just fine.  I love the asymmetry it gives to each earring.

Cubes

Ever since I figured out ( post in Sept., 2015) that I could make a rigid cube out of an octahedron and 2 tetrahedrons, by using right triangles instead of equilateral ones, I've been wanting to make a necklace like this.   Not much to say about it, except that I really like it, and I wore it for the first time this week and got several compliments. I think I'll list it on etsy. I'm working on a similar one with 1 cube made from 14 kt gold tubes.  I've been wanting to buy some gold tubing for a while now, and I've finally done it. It's not quite finished, but I love the contrast between the gold and the dark silver.

Math is SO COOL

I had such fun playing with beads/math today.  The other day I was looking at something that was showcasing geometric jewelry.  I'd tell you the source, except that I totally can't find it any more, and I don't know whose work it was that got me started on this.  But anyway, I saw some jewelry that had painted cubes in it.  The cubes faces were 2 colors, with the color change happening on the diagonal of the square.  The way the colors were arranged, you could see that cubes have tetrahedrons embedded in them, but tets that use right triangles instead of equilateral ones.  So I started playing around.  I was using 20mm tubes for the sides of the cubes, so for a hypotenuse I needed around 28 mm.  I used 25mm tubes with a #11 seed bead on either end, and that worked pretty well.  Turns out that you do that and make an octahedron with a tet at either  end.  That's a structure that I've used over and over, but not with right triangles.  When you make either equilateral triangles, of just irregular triangles, you get things like this:

But if you do it with right triangles, you get this:  a cube.  How cool is that? 

I hope you can see it; it's hard to photograph 3D stuff like this.  There's a tet at the top and another at the bottom of the picture.  In between is an oct with hypotenuse edges at top and bottom and side length edges zigzagging around the middle.

  In that cube some of the diagonals line up end to end and some don't.  I realized that I could make them all go line up end to end, and I wondered what the internal structure of a cube like that would be.  I guessed that it might be 5 tets, but I couldn't envision it.  The reason I guessed that it might be 5 tets if that I've learned that when you make an oct, at the time when you've put in 11 of the 12 tubes, and you're getting ready to add the 12th tube, there are 2 possible ways you can orient the 12th tube.  One produces an octahedron and the other produces a cluster of 3 tets.  So I guessed that it would be possible to make a cube out of 5 tets.

Voila!  It turns out that there's an internal equilateral tet made of all hypotenuses.  Then each of the 4 faces of that tet is the base for a tet made of sides of the cube.

You might say this is interesting, but so what.  But for me it could be big.  I really like building things using RAW, but I couldn't use it with the tubes, because the square sides weren't rigid.  Everything could collapse.  So I had to work with tets and octs.  But right angles are so much more intuitive.  We've been stacking blocks since we were kids, and we know how to assemble things using right angles.  60 degree angles and equilateral triangles are much wierder.  So now I can use structures that work with tubes, but still build cubes.  At the moment the cubes I've made are pretty big, but who knows where this will lead?

Live and learn

    I wanted to do something simple and rather stark with my oxidized silver tubes.  Cubic RAW was an obvious choice.  I'd never used it with the tubes, and I didn't really think it would work, but I tried it.
    Over time I've developed a sort of rule of thumb.  With round beads I don't much like structures that use triangles (i e circles of 3 beads) because too much thread shows.  Particularly I don't like to use monofilament  nylon fishing line and have 3-bead circles, because it won't pull tight over such a hard bend, and so lots of it sticks out.  I do occasionally do cuboctahedrons, which are a mix of 3-bead and 4-bead circles, but I tend to avoid them  when I can.  Similarly, with long narrow beads, and particularly with my metal tubes, I mostly only use triangles, because that's the only shape that will stay rigid with long beads.  So I have lots of tetrahedrons and octahedrons, because they're made of triangles.If you tried to make a circle out of 5 tubes, it wouldn't stay round, but could take most any shape.  When I have used 4-bead circles, I've always kept the cross section a triangle, because then, even if the squares turned into parallelograms, it still couldn't completely lose its shape, and it would remain 3 dimensional.
   However, I've come to realize that while a single cube made out of tubes is pretty apt to not stay much like a cube, a series of them will have more stability.  Also, when I was using oxidized copper tubes I used fireline thread, because there wasn't enough room for monofilament, which is fatter.  But the silver tubes, although they're the same size on the outside, seem to have a thinner wall, so there's room inside for more thread.  So here I used monofilament line to support the corners of the cubes better.  The piece moves alot, but it still holds its shape quite well.  It's big, because I wanted it to just go over the head without a clasp, so the pieces that form the long side of each rectangle are around an inch.  Anyway, I enjoyed doing it, and may do more along that line.  One thing I'd like to do just for comparison, is a simple rectangular necklace like this, but made out of a string of octahedrons instead of cubes.  Then I can see whether a much more rigid piece works as well on the body as one, like this, with more give.

Scaffolds and pods

A few posts ago I showed a piece where I alternated strings of interlocked cubes with oxidized copper tube scaffold-like structures.  I had started out to make the necklace entirely of the cubes, but found it was getting too massive and dense.  The areas of copper tubes opened it up and I liked that better.  Even then, though, it was pretty big.  Not something I'd wear myself, although I'm trying to get beyond limiting myself to the sort of jewelry I personally wear.  Anyway, I wanted to do something a bit less massive.  So I made these 3-sided "pods" in shades of purple, blue and gray.  They have right angle corners at each end, so they interlock just the way the cubes do, but they have a narrower profile, so they don't bulk up so much.  Also, I liked the colors of the pods with the almost-black of the oxidized copper.

Rounded corner cubes

   A few posts back, I talked about some necklaces I'd done with interlocked cubes.  I like them alot, but they're pretty slow to do.  One of the things I liked was the transition from the RAW cube modules that make up the big cubes at the bottom (I'm saying "big cube" to distinguish the overall element from the modules that make it up) to the triangular prism modules that make up the "chain" part of the necklace.  By triangular prism I mean that that the sides of each module in that part of the necklace are 8-bead cubes, but there are only 3 sides, so the cross section is a 6-bead equilateral triangle.  It makes that part of the necklace a bit smaller, and quicker to make.  I started wondering if there was a way to make the big cubes using  triangular prisms for the modules.  Turns out you can.  The corner of each big cube is a tetrahedron.  Of course the modules coming off the tetrahedrons don't "want" to make a right angle corner.  They're really at 120 degrees.  But in the same way that you can make a rounded tetrahedron using RAW cube modules, you can make a rounded cube using tatrahedrons at the corners.
  I usually find that an advantage of forcing  beads to do something they don't "want" to do in that way is that it stiffens the piece up.  That didn't really happen here.  I suppose that just the fact that each big cube made this was has a lot fewer beads in it than it would have if made with cube modules, thay came out floppier than I expected (or wanted).  I ended up having to go back and add beads in contrasting colors between the modules on each face to stiffen it up.  I like that, but it at least partly removed the speed advantage I was hoping for.  I'd like to make a whole necklace of interlocked cubes, and, once again, it'll be pretty slow going.
   One more thing.  I don't know if you can see it very well from the picture but when I added the green cube on the left to the gold cube next to it, I goofed, and didn't link it onto the opposite corner on the gold bead, but instead to the opposite corner of the same face of the cube.  Should have been the opposite corner of the opposite face.  However, in the grand artist tradition of deciding that a mistake is really a "design element", I did it again on the other side.  Works for me.