another redo

 I didn't intend for these redos to become a "thing."  But I did another one and I was so pleased with the results I decided to post it.
This was not a case of not liking the original piece; I actually liked it a lot.  My intent when I made it was to use it as a jury shot, as it was rather big and dramatic.  But I absolutely could not get it to photograph well (and I took a million pics).  The top pic is the best I got, and the gold doesn't stand out against the black well at all.  Also, photographing it straight on like that you don't get a good sense of the 3D-ness and it's hard to judge the size. So even though I liked the piece a lot, it wasn't doing what I wanted it to do.

That wouldn't have caused me to redo it, except for one thing.  I realized after looking at it for a

while that it would have been more pinwheel-ish if I had put the arms that extend out right at the points of the hexagon that is the central structure of the necklace instead of in the middle of each face of the hex.  Then it occurred to me that the best way to do it would have been to make a tetrahelix that would be part of the central part of the necklace and then continue into the extending arm.  That would be a true pinwheel. And I rearranged the gold tubes to highlight the spiral better.  Also I'm putting together an application for an exhibit of mathematical art and that would be a much purer mathematical structure. 

So I redid it, and was quite pleased with the results.But that still left the photography problem.  I took lots of pics, basically redoing all the mistakes I had made with the original necklace.  Photographing it on the black form was the best way to get a sense of the size and dimensionality. But for some reason that I fail to understand, whenever I did that, even in the same room and under the same light conditions as the other shots, I got a picture that waymore washed out.  Finally, I turned out all the lights, so I only had indirect light from the window, and dialed back the exposure to make it even darker--and it worked.  I think it shows off the piece quite well.  No idea why.

Shapes of toruses

   After spending a lot of time working with my tube beads, I spent some time this week going back to my molecular shapes.  My idea was to make several long narrow toruses (I suppose it's actually "tori", but I can't bring myself to say that) that I would join together, probably with metal tube structures. I found I couldn't make what I wanted, so I took some time to just try and figure out how shaping these structures works.
  The basic idea is that if you build a tube out of hexagons ( 6-bead circles serve as hexagons), it will be just that--a straight tube.  If you want it to curve, you add  heptagons on the inside and  pentagons on the outside of the curve.  It takes 12 heptagons on the inside and 12 pentagons on the outside to make a full  rotation and create a torus.  Actually, you can do it with 10 and 10, and that's what many of the toruses in the beaded molecules blog do, but to get it all around without having to force it you need 12.  Often you get a firmer structure by making it do something it doesn't quite "want" to do, but here I was trying to not do that.
  What I've come to realize, after making a jillion of the things, is that what you really need is just to add 12 extra beads on the inside and a corresponding number left out on the outside, and you can do that in any configuration.  The easiest, and one I had done before, is to use 6 octagons on the inside and 6 squares on the outside. The picture here is taken from one of my very first posts, and shows  a hexagonal torus done that way on the right of the piece.  It's easy to see because the octagons are green, the squares blue and the rest red-brown. The big square and triangle of the necklace were made by trying to stretch those same octagons into ever tighter angles, and show how much I didn't know what I was doing back then.  On the other hand, it's nice to read that post and see that I've actually learned something since then.
  The 6 octagon/6 square torus makes for a very blocky shape that I don't much like, so I haven't used it often.  But now I can see that there are lots of ways to add 12 extra beads on the inside of the circle, the number 12 being divisible in so many ways.

The first torus in this picture was made by making the center out of 4 circles of 9 beads.  That way each circle has 3 extra beads for a total of 12 extra. It's a bit odd because 9 is an odd number, so sometimes you're adding more to the back and sometimes to the front, so it doesn't lie quite flat.  But you get a sort of 4-cornered torus. The center is actally a short fat diamond on 1 side and a tall skinny one on the other, so it's a bit odd. The second torus uses 3 circles of 10 beads each, and so makes a triangle.  And the last one uses 2 circles of 12 beads each, and makes a sort of long skinny shape.  I can now see that if I had added some hexagons (6-bead circles) between the 12-bead ones, I'd have gotten a longer torus, which was what I was originally looking for.  But by then I was into exploring torus shapes.Actually in any of these configurations, you could make the donut hole larger by just putting 6-bead circles between the larger circles.

  Having gotten  handle on the inside of the torus, I started playing with the outside.  I liked the triangular center best, so I used a center of 3 10-bead circles in each of these.  On the outside you need to take 12 beads away from your structure of hexagons.  You can do that with 12 pentagons, or with 6 squares, or with a combination of the 2.  Using all squares ( the 1st one) makes the hardest angles.  Using some or all pentagons makes the curves gentler, which I prefer.  Also it makes a difference whether you put the smaller circles near the points of the triangle or along the flat sides.  If you could space your small circles evenly around the torus, you'd get a circular outside with a triangular hole in the center.  I couldn't quite figure out how to do that. but I came close in #2.  It has 6 5-bead circles and 3 4-bead ones.  There are 2 pentagons on each flat side and a square at each point of the triangle.  The last 2 are both done with 12 pentagons, so they have nice, gentle curves.  #3 has 4 pentagons at each point of the triangle, so it maintains it's triangular shape. #4 has 2 pentagons at each point and 2 on each flat side.
  I have no idea if anyone is still reading, or if this makes any sense at all.  But I do like being able to talk out my ideas, even if no one is listening.  And if you actually are reading this and have questions, be sure and ask.

Hamiltonian path

I'm so proud of this dodecahedron! If you're like me, and I know some of you are, you've made jillions of dodecahedra, so what's so special about this one? It was made using what the beaded molecule people call the Hamiltonian path, which means that each bead has only 2 passes of thread through it. (Actually don't look too closely at the picture, because I didn't take the time to photograph the actual one, but since I wanted a picture for the post I just used the photo from one of my dodecahedron earrings--but, trust me, I actually made the real thing.) I read about this Hamiltonian path on the blog a few days ago, and my first thought was "that's impossible". Since each bead is in 2 circles, I knew you'd need 2 passes, one for each circle. But you need a third pass to get your thread into position for the next circle. Today, while I was away from the computer, I was composing a comment to the blog, asking them to explain. I was going to say that I knew you'd have only 2 passes through each bead if each circle was a separate piece of thread. Also you could do the same using 1 thread for each 2 circles, by making figure 8s out of 2 circles and then joining them together. A few hours later, while I was doing something entirely unrelated, it occurred to me that if you could make a figure 8 (2 circles) you could extend that and make a 3 circle version. If that was so there must be a way to extend that to 12 circles in such a way as to have a dodecahedron. That led to much staring at diagrams of dodecahhedra, and eventually I figured it out. Actually it turns out that if you use the 2-needle technique--that is, a length of thread with a needle at each end--it's not hard to do. But it took me a while to realize that. I don't much like the 2-needle thing, because it makes it hard to maintain tension, but it simplifies things because you don't have to figure out a way to get the thread back to the beginning of the structure. Essentially you're bringing the beginning and end of the thread along with you. Anyway, I made it, and it was great mental exercise. Now I'll go back to making things the usual way. By the way, does anyone know who Hamilton was/is?

I've been fscinated by lots of mathematically inclined bead blog posts I've seen lately, so I thought I'd post a few of mine. The first one is just a simple pendant style necklace, but it's the diagram you always see illustrating the Pythagoran Theorum, with a 3/4/5 right triangle.
The one I've worked alot on, though is the ping pong ball bowl in pictures 2 & 3. 3 is, of course, the view from the top. It's based on the variation of the buckyball structure that uses 120 beads instead of 90, and so is just a bit bigger. But what stumped me for a while was the fact that if you stop halfway through to make a bowl instead of a whole sphere, the edge has no stiffness. I tried all sorts of things to stiffen it, but without much luck. Then I thought about the idea from the Beaded Molecules blog where you use heptagons instead of hexagons and that makes the shape flare out. So I added a row of heptagons and then tied the flared rim down to the bowl body, and voila! a stiff bowl. There's an exhibit coming up at our local art center called "Art for the Senses" and it's art that can be appreciated by people who are visually, or otherwise, impaired. Since this has lots of texture and is now sturdy enough to be handled I'll enter it.