## Thursday, July 8, 2010

### Sierpinski spheres

This is a bit more on my Sierpinski-ish structures. The blue ball I showed before isn't a Sierpinski one because the small units are dodecahedrons and the overall ball is a buckyball. You could, of course make each of the small ball units buckyballs, but that would take more work than I wanted to do. I did try to go the other way and use small dodecahedron balls as units to make a large dodecahedron. I couldn't do it. The small goldish hemisphere was my attempt. The problem is that 5 dodecahedrons don't really want to make a circle. I don't know enough trig (or, for that matter any trig) to know what the angles are, but when you make it you have to pull it together some to get a circle out of 5 spheres. It wants to be 5 and some fraction spheres. You can do it fine for the first (bottom) circle, and the 5 circles that adjoin it, but after that it's too far off. The only way I could create that sort of structure was to link the adjoining balls with a small 5-sided "tube" of beads to give me a little wiggle room. That's the red and black structure, red dodecahedrons joined together by black tubes. Some of the tubes, as needed, have 2-bead edges on the inside and 3-bead ones on the outside. On the blue buckyball from the earlier post, the 5-ball circles are separated by 6-ball circles, and that gives you the same sort of wiggle room.
When I had done the red and black structure, I found that I actually liked the look of separating the small balls, so I did the same with a buckyball, the multicolored one. I really like the fact that it's a more open structure, and you can see what's happening better. Also it's larger (around 4" diameter.