Another Icosahedron

Here's another of my spheres that I call offset icosahedrons. It's a bit bigger, 3.5" in diameter, where the 1st one was around 3". Also I made the change I was talking about earlier. The end faces (8 beads) of each strip of cubes is a side face in one of the other, different colored strips, so they share a whole face. Each strip is added on to the adjoining ones as if the whole thing were a flat piece. It's just when you pull 5 strips together into a pentagon that you force a curve into the shape. Doing it this way made the piece firmer, so I could make it bigger. Each strip of cubes is 8 cubes long, where the other sphere used strips of 6 cubes.
One thing I forgot to mention that worked out really well, in both balls, was that I found that if I used 5 colors I could arrange them so that I never had 2 of the same color next to one another.
Seems like now I have to do something asymmetrical. Every time I try to work my way out of symmetry, I find myself coming back to it. Actually I like symmetry too, and I think you probably have to work out the symmetry of a structure before you can play around with it, and do something asymmetrical.

Offset Icosahedron

I figured out a way to firm up my new sphere, and while I was at it, took a better picture. I've added a #6 bead between each face of each pentagon (i.e. 5 beads in each pentagon). They're a bit hard to see because they're matte black, but with those there I can run a thread around each pentagon and pull it tight, firming things up alot.
I tried to reply to some of your comments on the piece, but once again my computer won't let me post a comment, even on my own blog. I'm pretty sure it's linked to changes in settings that my husband made in an attempt to avoid the new paywall at the New York Times, so we probably deserve what we get, but If I can remember how I fixed the problem before, I'll take care of it. Meanwhile, someone asked about what beads and thread I use. I use almost exclusively #8 beads, and that is what this piece is made of. I think it was Gwen who suggested adding some #15 beads, but I confess I don't own any, and I suspect I never will. I don't even use #11s. Life's too short. For thread I mostly use monofilament nylon fishing line for the extra body it gives a piece.I sometimes use Fireline, though, mostly with stone beads because the holes are smaller on them. This piece uses the monofilament.

Offset Icosohedron

Here's a new piece that I owe to Gwen Fisher, although indirectly. On her blog there's a link to lots of mathematical art from the Bridges exhibits. I was amazed by the spherical pieces by George Hart. At the very bottom of the page on http://www.georgehart.com/sculpture/sculpture.html there's a piece that's alot simpler than all the rest, and it was the basis for this piece. It's based on the icosahedron, but instead of each set of 5 triangles meeting at a point, they're offset so they meet at a pentagon. Only problem is that it's a bit too soft, but I've already figured out how to make the next one firmer. In the pentagonal areas, each side shares only 1 edge (2 beads) with the adjoining side. In the next one they'll share an edge (8 beads) and that will firm it up. Also when I made the first section, and made it 6 squares long, I had no idea what the size of the sphere it would generate would be. I think I'd like it to be a bit bigger. This one is around the size of a tennis ball. Of course, in beading, the bigger it is the more it tends toward squishiness, so I hope the added size doesn't undo the gains I get from changing the structure.

Pythagorus pendant

Great comment,Gwen, about adding the cube in the middle to indicate the right angle. The thought had crossed my mind, but I was afraid of detracting too much from the jewelry side in favor of the math side. But based on the comment I decided to try it, and I kind of like it. Thanks.

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.