stars

On my recent boat trip, I was playing around with  some new ideas.  One of them was stellations.  I made an ornament by making an icosahedron and stellating it by turning each triangle into a tetrahedron.  I liked it, but as it was almost 3" in diameter it wasn't very practical as jewelry.  Then something occurred to me. The icosahedron at the center of it was made up of groups of 5 triangles that formed pentagons coming to a point at the center.  If I took one of those groups of triangles, and made it point inward instead of outward, I'd have a flat side that could lay against the body.  Then I could stellate all the rest of the triangles.  Voila!  Of course, these star forms still extend out quite a ways from the body, but I kind of like that.  I also made a few where the 5 tetrahedrons at the center of the star are made from shorter tubes, and so don't stick out so far, but for the big necklace I decided to stick with the long tubes.

More shapes

Isn't geometry great? After making the bead I showed (badly) in the last post, I wanted to make more. The original one, which is the 1st one in both of these pictures, was based on the cuboctahedron, which has 24 edges. So I wanted to make some shapes based on solids with a fairly similar number of edges, so they could come out similar in size. The 2nd shape in the group is based on the truncated tetrahedron, which has 18 edges. I thought about doing a dodecahedron or icosahedron, but they both have 30 edges, so would be bigger than I thought I wanted. So I went to the list of Johnson solids (Hurray for wikipedia) and found more shapes. I especially like the last 2 that are dome shaped--they're called cupolas on the list--because I'm thinking of making a bracelet with several shapes linked together, and those give a flat side to have on the inside with the "dome" facing out. One of them is basically an icosahedron with the bottom 5 triangles cut off, so it has 25 edges. The smaller one has a hexagon on the bottom and 18 edges. I posted 2 pictures of the shapes so you could see them from the top as well as the side. One thing I've been meaning to do is put together a tutorial and see if anyone's interested in learning how to make one. I might do it with one of these shapes. I don't have a graphics type program, but would do it with lots of photos.

Stellated bowl 2

Just finished another bowl in my series based on the stellated icohedral form I showed a couple of posts ago. This one is more like the sphere, in that the stellations reflect the colors on the inside. I liked that better. The fact that the bowl curves back in at the top gives it firmness, but again makes it harder to see the colors on the inside. A tradeoff. If I made it larger before curving back in I could probably get both the firmness and the good view of the inside, but the thought of making it even bigger is somewhat daunting. This one took forever. It's around 8" in diameter, and 4.5" tall. I must admit I do like it alot, though.

Stellated sphere

I love how ideas just keep growing. My 2nd sphere (last post) was a firmer structure than the 1st one, but that enabled me to make it a bit bigger. The result was that while it was firmer, it still wasn't firm enough. If it sat for a while it would settle out of round just a bit. So I decided to stellate it, Something I've been wanting to do with a sphere anyway. Stellating means that each triangle on the original surface of the sphere becomes the base for a tetrahedron. It's not quite finished, which is why you see some monofilament floating in the picture, but I'm really pleased with the way it's coming out.
So you can get an idea of what it's like I should add that the diameter of the piece is around 5 1/2". Someone told me I should figure out a way to mount it on a base so that it could be a table light. It's probably too much engineering for me, but I do think it would be pretty great.

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.