hyperbolic plane

Haven't posted in a while, but experimentation goes on. This is a piece based on the hyperbolic plane. If you tile with hexagons, you, of course, get a flat plane. But if you tile with heptagons, you get a hyperbolic plane, which gets rufflier and rufflier as you move outward, like some heads of cabbage. The first one I did was round. I intended it to be a focal piece for a pendant, but it sort of got too 3-dimensional too fast (i.e. it stuck out too far from the wearer's body). I'll try to get a picture of it up in a day or so, but I don't have one now. Anyway I decided I wanted it long and narrow instead, so it would get ruffly, but not TOO ruffly. You could also do this using circles of 7 beads for the heptagons, but I wanted more "there" there, so I made my heptagons out of 7 triangles.
There's another way to get a ruffly structure that starts with a tube instead of a plane (maybe a hyperbolic cylinder? I actually have no idea what I'm talking about here). It comes out looking sort of like a petunia. I made a few of these quite a while ago, and liked them, but never quite figured out what to do with them. I think they should probably be the ends of a sort of a rope necklace, but have never made it. I'll try to get a picture of these too. They're much less open than these plane structures, so they took a long time to do.

new rug

This is the other thing I've been working on recently. It's related, in design, to the one in blues and purples with black and white that I showed a couple of posts ago. That one has small black and white areas along the top left and lower right edges of the S. I wanted to expand those areas and create a space that would separate the foreground S from the background. My original plan was to do this in black and white like the other rug, but at the last moment I decided to make the rug much more muted by using tan and green instead of black and white. I like it, although I'm still partial to the older rug.

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.

tetrahedron in tetrahedron

Back to geometric beadwork. I started this tetrahedron piece a while ago and sort of bogged down in the middle of weaving it. But I really like it now that it's done. I have 2 pictures because it's hard to capture the 3 dimensionalness in a picture (at least with my level of skill at photography). The problem is that the last thing you do is add the little lilac seed beads along the edges and that does alot to firm up the structure because it is a straight piece of monofilament running down each edge. So all the time you're making it it's way too floppy, and there's no way to know till you're done whether it is going to firm up enough to make the whole piece work. I had made a considerably smaller version, but, of course, as you get bigger, you tend to get floppier. Fortunately it did firm up quite nicely, and made a good piece.
I ought to add that the beads are around 15mm long, and the large tetrahedron is around 7" on a side, although it isn't in front of me now, so I can't measure it.

rug designing

Designing with color is so much fun! Last year I did a big dying sequence and got a whole rainbow of colors, which I blogged about at the time. That resulted in 2 rugs, the 1st 2 you see here (also blogged about before). From the really enthusiastic response I got (and, I must admit, from the quick sale of both rugs too) I decided to do another rainbow dying. This one was a bit different, in that my yarn wasn't natural white, but sort of honey colored. On the other hand, in the earlier dying I had cut my colors with a bit of brown or black in each dye stock to keep the colors just a bit muted, so this time I did more or less similar colors, but without the brown dye since the yarn already had a bit of brown. After 2 days of dying I had pretty much what I had planned on.
I decided the first rug would be similar to the blue/purple/black/white one I did a few years ago(#3 pictured above), which I thought was a really great rug. Only instead of the colors just shifting from blue to plum, the outside would go from yellow to blue, and the center figure would go from yellow to red.
That was the plan. But as I looked at the yarn hanging on the fence to dry, I kept being drawn to the blue-turquoise-green tones. This morning I changed the whole plan to one that's much more muted, in those tones plus the honey yarn that I still have alot of. No pictures yet, but I'll post a picture when it's done.

Stellated vessel

Continuing on my stellated object series. I wanted to do a vessel, and this is my 1st one. I'm already scheming my next. When I stellated the sphere I showed in earlier posts, the most disappointing part was that you could no longer see the actual sphere very well. A vessel solves that problem. In this one I used cubes with sides of 2 beads for the actual vessel, but cubes of 1 bead sides for the stellation. That way you can see the vessel better through the stellation, as well as being able to see into it from the top. On the other hand I sort of miss those big fat stellations. Also, the interweaving of the stellations was more apparent in the sphere because of using several colors. Here I used several colors on the vessel itself, but only the darkish blue for the outside.
When I first did it, I just did the rows of stellated triangles, but it seemed to just stop at the top. It seemed to need a finish of some sort for the to edge. So I added a final row that is geometrically quite different, but brings some of the lighter inside colors to the outside and creates a sort of rim. I like that better.
As you can guess, this sort of piece is pretty time consuming. I don't think I would have the patience if I were using the smaller beads that most beaders do. I've come to realize lately that alot of what I do is related to my use of larger, #8 beads. For example someone mentioned that she didn't like using monofilament nylon because it meant doing it without a needle. I can use a needle, because the holes of #8s are big enough that I can do several passes and still pull a needle and 2 thicknesses of monofilament through. Once in a while I'll have to unthread and poke a single strand of monofilament through on the last pass, but not often. And I can use an easy-to-thread, big hole needle, which makes things faster for me. I sometimes miss the color selection that you get with #11s, but there would just be too many things I'd have to rethink if I were to change now.
One more thing just occurred to me--Since I've been talking about size I ought to mention that the size of this vessel is around 5" x5" x5"( it's not in front of me now, so I can't be exact).

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.

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.