## Sunday, September 28, 2014

### 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.