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.
Sorry about the blurry image; no tripod handy. But I think you can see the structure OK. I call this one Gwen's bead, because it was inspired by the paper Gwen Fisher and Blake Mellor wrote about tiling theory and beading. It's in Gwen's blog at beadinfinitum.com. I have to admit I haven't finished reading the article, but I've looked at the diagrams and pictures in it. I particularly liked the hexagonal tiled figure in Fig 28 (on the left). The problem is that as I'm an active rugweaver, when I want to make complex flat patterns, I do it at my loom, and weave a rug. With the beadwork I want to work in 3 dimensions. I started out to turn the flat idea in figure 28 into a truncated octagon, as that's a shape I use alot. But when I realized how big it would get, I switched to a cuboctahedron. Seems like when you use that method in a solid figure, what you end up with is a sort of truncated cuboctahedron. Also it seemed like in the 3-dimensional figure the ratio of the 2 sorts of beads (I think Gwen has a name for them, but I'm too lazy to look it up just now) is different. My piece seems to have lots more silver beads in relation to the copper ones (I think the ratio was 96/32 or 3/1) than her flat figure had. I was also surprised at how firm it was; I was afraid it would be squishy.
I'm not sure just what I'll do with the bead, but I like the lacy openness of it. Anyway it was a fun thing to work on.