Redoing things

 Since there's not a lot happening just now by way of sales (galleries mostly closed, shows cancelled) I've been spending some time redoing some older pieces.  Sometimes there'll be a piece that I almost like but something seems a bit wrong.  Often it takes me a while to decide just what it is that I don't like, or, once I figure that out, how best to fix it.  Sometimes it just takes a small tweak and sometimes a major redo.  Here is one of each:

When I made this pendant I had just figured out the square and circle (hexagon actually) shapes, and I've used them several times since.  So I liked the shapes, but I didn't quite like the shape of the pendant--too wide and flat, sticking out way beyond the chain. 

One of the recurring problems I have is that I make individual units, often not knowing just how I'll arrange them till after I've made several.  Then when I've decided I have to attach some sort of rings in the proper places as attachment points.  I could do this easily with open rings, i.e. ones that  aren't welded shut. But since I have thread at each joint, my worry is that a thread will find its way through the inevitable space where the 2 ends of the ring meet.  So I always want a closed ring.  But a closed ring has to be put in place as you're building the structure, and you often don't know where you'll want the

join to be.  In the first iteration I joined the shapes by putting a pair of tetrahedrons between them.  But that meant I had to join them at the places where the edge of the shape was a crosswise tube, not a point.  And that made the overall shape of the piece so long and wide. For the second version I came up with a way to join a point on the square to a crosswise tube on each circle and I like that better.

The second redo was a complete rethinking. I've always liked the colored piece shown first.  But it had some problems.  The colored tubes, which are anodised aluminum, are quite a bit bigger in diameter than the silver ones, and I've always felt that those bigger openings at the end of each tube were a problem.  Early on, my solution was to put a seed bead at the end of each tube and treat the bead-tube-bead as a single unit.  However, that triples the joints, and creates that many more places where if the thread tension is just a bit off the piece gets looser.  In general that method tends to make the structure much less firm.This piece has been around for a few years, and there were starting to be places where you could see thread between ajacent beads in a way I didn't like.The other problem is the structure puts a lot of  "stuff" at the back of your neck.  I used to be quite rigid about maintaining a structure all the way around the back, which can make them harder to wear, especially when, as here, the structure is relatively wide and flat.  A rounder shape going around the back works better.

The problem I had, though, is is that without the seed beads at each end,the colored tubes were too short to make octs that wouldn't zigzag, and I wanted them to run straight.  And I can no longer get those aluminum tubes, so I couldn't cut longer ones.  I could have cut a whole set of silver tubes in custom lengths to make the existing colored tubes work.  Instead I redid the whole thing in RAW and eliminated the color.  While I was at it I made the arrow heads more pronounced, added an extra arrow, and made the necklace one unit narrower and the back more wearable.  I like it  a lot, but I still miss the color, and I'm working on a way to do the new design in octahedrons with color.  More on that later.

Developing an idea

 I've been making lots of pieces like the first one here: repeats of a structure like an oct, separated by biggish stone beads.  And I've varied it by using different structures, but always a repeat of the same one.  I've wanted to do 2 things--eliminate the beads and vary the structures.  Leaving out the beads means you don't have the color limitation, i. e. you're not limited to wearing it with an outfit that goes with red. There are 2 ways to do this.  One would be to put a closed ring between the octs (or whatever structures) Or they could interlink directly with one another.  Here I interlinked them. It means that you need to build more structures, as they overlap, but it makes the design tighter. I like this one, and I think pretty soon I'll make another one with the pentagonal shapes done in gold filled beads.
   As with most of my ideas, I start out being rigidly symmetrical, and then later I play with the idea in a freer, asymmetrical way.  Picture 3 shows me doing this design in that way.  I think its my best one so far.  I also think adding the gold makes the piece more interesting, without limiting the colors you can wear it with.  Now I'd like to extend that more asymmetrical, more random approach to some of my very structural pieces.

octahedra and pearls

  Recently I bought some pearls with holes big enough to slide them over my tubes.  I decided I wanted to make a neckpiece that was a simple series of octs, ornamented by the pearls.  I had made a similar structure using bright silver and colored aluminum tubes a few years ago, and wanted to repeat that structure.  So I went to my handy blog, where I keep track of my structures.  Here's what I found, from August, 2014:  "It's a simple chain of octahedrons.  But a chain of octahedrons would normally form a straight line.  In order to get the curve you need for a necklace I had to make the triangle on the outside edge longer than the triangle on the inside edge.
Here's where some trig would have come in handy in figuring out just how much longer, but I managed to figure it out with "lesser" math, and it came out right."
  It would have been really handy if I had written down just what the lesser math had given me so that I could have reproduced the shape.  That, after all, is one of the main reasons I write this blog.  Since I didn't do that I started and ripped apart the new piece over and over trying to get the curve I wanted.  As you can see I didn't get the same curve as last time; it's a little pointier at the bottom and straighter across at the back but I like it OK.  It's also just a bit shorter.  That's only because I was running out of 25 mm tubes, so I did just 20 octs instead of 22.  Then I made the 2 tets at the back by the clasp longer.  Also I now make my own hooks and they're longer than the one I used in the earlier piece.  So the overall piece probably isn't that much shorter, but I do think it's a bit shorter.
  So as not to make the same mistake twice I'll put down the plan for the curve.  The outside triangles are mostly equilateral 25mm triangles.  To get more curve I used 28/28/25 mm isosceles triangles at position 1 (at the center), 3, 9 and 10.  On the inside the triangles are either 20mm equilateral or, at inits 1, 2, 3 and 6, to tighten the curve, 20/20/25 isosceles.  It actually doesn't change things all that much.  If I didn't want it to be so pointy at the bottom I could have spread them out more.  Also triangle 6 is an equilateral 25mm oct.  I CHANGED SOME OF THIS AND WROTE ABOUT IT IN THE NEXT POST.

more right angle explorations

I haven't blogged in a while; sometimes life gets in the way.  My husband and I have been in the sailboat business for 40 years, and we've just closed our store ( which was also my main studio) and are trying to figure out the future plan.  I've now sold all my looms, and the jewelry work is quite portable, but it still creates complications.  Right now I'm cutting tubes at a workbench in a storage locker we've rented, as we live in a townhouse, and the room I've set aside as my workplace is carpeted, and not conducive to sawing metal.  My plan is to cut tubes in larger batches so that I don't mind going to the storage place to do it, but I'm also looking at the possibility of an outside workbench here that won't look too industrial and irritate the neighbors.
   Meanwhile. though, I'm still playing with structures.  I find the blog is a great way to keep a record of what I'm doing.  I use my silver tubes to experiment, but it's too expensive to keep permanent structures made out of handcut and oxidized silver tubes just so that I can get ideas from them.  So if I blog about them, then I have pictures and notes, and I can reuse the tubes for actual jewelry.

    Ever since I made thebracelet above, I've been fascinated by how an alternating series of right triangle tetrahedra and equilateral ones makes these square structures.  I'm making a similar bracelet now, but I kept wondering if I couldn't make the series continue in a straight line instead of turning corners.  (This happened at about the time I realized that I didn't have enough 20 mm tubes to finish the bracelet anyway.)  So I tried it--and it works!

  Doing it just the way I had done the square structures, i.e. alternating 1 right angle tet with 1 equilateral one, I got the top  structure, which is flat on the bottom with a zigzag top.  But what was more interesting, I thought, was that since the zigzag tubeson top were at fight angles to each other I could make them into right angle tets too and then (bottom picture) I get a structure with a square profile that I can extend as long as I want.  Also if I end with an equilateral tet I have a tube at the end which

could serve as a hinge to join another structure. Actually, just as I write this and look at the pictures, I realize that this is really an octet truss, because if you left out the central tube that is the "hub" shared by 4 tets, you'd have an octahedron.  Stay tuned!
   I should mention that things don't always turn out that neatly.  When I made a chain using only right triangle tets instead of alternating, nothing interesting happened.  Also I suspect I could have found out the same thing just by creative use of the Pythagorean theorem, but then I wouldn't have pictures to remind me of what I'd learned.

a redo

I've been quiet for a while, but not for lack of making jewelry.   Partly, I've been on another canal boat trip in England, but, of course, I took plenty of silver tubes with me.  But since I've been back I've been spending some time redoing som pieces I was never quite happy with.  This is one example.  The picture on top is the original piece.  It's a chain of octahedra and tetrahedra made from a mix of oxidized silver and gold-filled tubes.  While I was making it I thought it was going to be great (I usually do).  But when I got it finished I didn't like it as well as I had expected.  I've stared at it off and on for a few months, trying to figure out what I didn't like. One thing I decided was that the "corner" on the left side wasn't sharp enough and didn't provide enough contrast with the curve on the

right, so I figured out how to make it pointier.  But then I decided that the real problem was that the piece sort of had 2 focal points, the change in shape on the left and the change in color on the right.  You couldn't quite tell where you were supposed to look.  So I redid it, eliminating the corner altogether.  I also changed from gold-filled tubes to red anodised aluminum ones.  I did this because I'm starting to make some pieces with accents of 14 kt gold  tubes, so it seems too confusing to have gold-filled ones as well.

Cubes

Ever since I figured out ( post in Sept., 2015) that I could make a rigid cube out of an octahedron and 2 tetrahedrons, by using right triangles instead of equilateral ones, I've been wanting to make a necklace like this.   Not much to say about it, except that I really like it, and I wore it for the first time this week and got several compliments. I think I'll list it on etsy. I'm working on a similar one with 1 cube made from 14 kt gold tubes.  I've been wanting to buy some gold tubing for a while now, and I've finally done it. It's not quite finished, but I love the contrast between the gold and the dark silver.

What a difference 8 beads (tubes) makes

 Yesterday was a good day.  I feel like I improved a necklace.  The top pic is a piece I made a few months ago. I wanted it to be sort of special, because I don't do too many pieces in bright silver  (don't want to spend time worrying about tarnishing). I had high hopes for it, but when I was finished, I wasn't quite happy with it.  I wasn't sure why.  But yesterday I was scrolling through my pictures, and stopped at that one.  It occurred to me that what I didn't quite like was the extreme pointiness of it, sort of like an icicle about to fall on you.  I also noticed that there were a pair of triangles on either side of the bottom point that could be turned into 2 faces of either an octahedron or a double tetrhedron.  I chose the double tet, cut some beads and added them on and I like the "new"

necklace, the one on the bottom, better.
That is both one of the upsides and one of the downsides of beadweaving versus the rug weaving that I used to do.  When  rug came off the loom it was done.  Nothing more to think about, because you couldn't change anything.  Now I find myself tinkering with pieces.  Mostly I like that, although sometimes it's nice to just say it is what it is.

Some math, some design

 In some earlier posts, I've talked about some necklaces I've made out of octahedrons, where a long tube, often a colored aluminum one, acts as a hypotenuse to create octs that can stack in a way similar to the cubes in RAW.  This works well for necklaces, where it's nice to have the structures lying somewhat flat, but it doesn't work so well in a bracelet, where you would generally want them to stand up.  I needed a way to join 2 standing up octs so they'd be at an angle to each other.  After some trial and error, I  came up with a solution.  If I made an oct so that the triangle on the top used tubes that were half as long as the tubes on the bottom, I'd get an oct that if you looked at it from the top would look like one of the pictures
below, with the little triangle in the middle being the top of the oct and the bigger outside one being the bottom.  And the triangle "walls" that connected them would be perpendicular to the top and bottom ones ( actually there are  are 6 triangles connecting them and every other one is perpendicular.  If I used the pattern on the left to join 2 of my squarish octs, they'd be at right angles to one another; if I used the other, equilateral one they'd have a 60 degree angle.  That's what I used, and started to make the bracelet  shown below.  I was pleased

 with it from a structural standpoint, but it didn't seem to have enough color, and the aluminum tubes seemed to sort of get lost in all the dark sterling.  I decided that the problem was that the joining octs didn't have any colored tubes, and also that the colored tubes on the inside of the bracelet were kind of lost.  So I took it apart  and moved all the tubes to the outer wall of the bracelet, using them in both the squarish octs and the joining octs.  Both the bracekets are incomplete because I was gradually taking apart the first one to build the second one.  But I hope  they're complete enough that you can get the idea

of what they look like.

new tet structure

I've been working on a few pieces based on a new structure built of tetrahedra (tets).  A lot of my necklaces are more or less chains of either octahedra or tetrahedra.  A chain of octs is relatively straightforward, because octs have opposite sides that are parallel to one another, so you can line them up end to end.  The trick there is to get the chain to curve, so as to make a necklace.  But with tets it's more difficult,  Because no side is parallel to another.  Still, I've managed to come up with 2 different chains of tets that create curves that can become necklaces.  But, I wanted something that was more complex than a simple chain.  
The question is whether you can tile tets in 3 dimensions.  The simplest is a group of 5 tets forming a sort of pentagonal circle (how's that for inexact terminology?), i.e. the shape pictured here.  It seems to work, and I'm sure I read that Archimedes, or one of the other big-time Greek mathematicians,

thought that it worked.  Actually, it doesn't quite work; if you make 5 perfect tets sharing a single central edge, there will still be just a bit of space left over.  But as we know, in beadwork, close is often good enough, hence the structure here.  The trouble is that that little bit that's off tends to build as you extend a structure.  If the structure on the left actually worked, you could also make an icosahedron out of 20 tets.  I've done it, but you can tell that all the internal spokes are just a hair too long and tend to bunch up at the center.  Still, I thought I could make the idea work for just a couple of layers before the slight errors built up too far.  So I built this necklace. I like the way it goes from being a chain of single tets on the sides to a more complex structure at the bottom. I broke up the open structure of tets

with cubes made of freshwater pearls, and I was pleased with it.  As I looked at it, though, I noticed that there was a line of tubes going more or less straight from the point at the center bottom of the piece all the way up to the back on each side, and that might be another way to accent the piece. 
 I thought about buying some gold tubes, but decided to do the first experiment with colored aluminum ones.  The aluminum tubes are much bigger in diameter than the silver ones, so I always use seed beads to close off the ends.  I decided to use them at the ends of the silver tubes too.  That made the 25mm tubes effectively 28mm, and so made the necklace a bit bigger, whch I liked.  
The one pictured here is actually my 2nd try.  

The first time I tried making the line of colored tubes go around the color wheel from red at the bottom thru rose, purple, blue, green etc.  But I found that the blues and greens didn't stand out enough from the dark silver, and so you lost the continuity.  So I stuck with just red.  I also added a second row of red tubes, going crossways at the bottom and then up to meet the long line.  This is actually a pretty lousy picture.  You can't see, for one thing, that the  crossways line is actually a different red from the long vee line.  Also, although I really like the way that black form shows off the shape of the piece, it makes the silver tubes look much lighter than they are.  However that's a problem for another day.

Math is SO COOL

I had such fun playing with beads/math today.  The other day I was looking at something that was showcasing geometric jewelry.  I'd tell you the source, except that I totally can't find it any more, and I don't know whose work it was that got me started on this.  But anyway, I saw some jewelry that had painted cubes in it.  The cubes faces were 2 colors, with the color change happening on the diagonal of the square.  The way the colors were arranged, you could see that cubes have tetrahedrons embedded in them, but tets that use right triangles instead of equilateral ones.  So I started playing around.  I was using 20mm tubes for the sides of the cubes, so for a hypotenuse I needed around 28 mm.  I used 25mm tubes with a #11 seed bead on either end, and that worked pretty well.  Turns out that you do that and make an octahedron with a tet at either  end.  That's a structure that I've used over and over, but not with right triangles.  When you make either equilateral triangles, of just irregular triangles, you get things like this:

But if you do it with right triangles, you get this:  a cube.  How cool is that? 

I hope you can see it; it's hard to photograph 3D stuff like this.  There's a tet at the top and another at the bottom of the picture.  In between is an oct with hypotenuse edges at top and bottom and side length edges zigzagging around the middle.

  In that cube some of the diagonals line up end to end and some don't.  I realized that I could make them all go line up end to end, and I wondered what the internal structure of a cube like that would be.  I guessed that it might be 5 tets, but I couldn't envision it.  The reason I guessed that it might be 5 tets if that I've learned that when you make an oct, at the time when you've put in 11 of the 12 tubes, and you're getting ready to add the 12th tube, there are 2 possible ways you can orient the 12th tube.  One produces an octahedron and the other produces a cluster of 3 tets.  So I guessed that it would be possible to make a cube out of 5 tets.

Voila!  It turns out that there's an internal equilateral tet made of all hypotenuses.  Then each of the 4 faces of that tet is the base for a tet made of sides of the cube.

You might say this is interesting, but so what.  But for me it could be big.  I really like building things using RAW, but I couldn't use it with the tubes, because the square sides weren't rigid.  Everything could collapse.  So I had to work with tets and octs.  But right angles are so much more intuitive.  We've been stacking blocks since we were kids, and we know how to assemble things using right angles.  60 degree angles and equilateral triangles are much wierder.  So now I can use structures that work with tubes, but still build cubes.  At the moment the cubes I've made are pretty big, but who knows where this will lead?

Playing with an idea

Still playing with my chains of squarish octahedrons.  The last one I did, and posted about, was not as deep (that is, not as 3 dimensional, not standing up as far off the body) as most of my work.  The tubes to give it depth were 10 mm long.  Here I used more or less the same structure, but with tubes of 15 mm. They changed the geometry enough that once again the octs zigzag a bit, but that was fine here.
   It had occurred to me that you could also use those tubes as hinges and join rows of octs just at those hinges.  So that was what I did here.
   Then I started thinking of other beads I could use for the "waist" beads.  A while ago I had gotten strings and strings of marble beads on sale, and hadn't done a lot with them.  So I thought I'd try those.
  I had 2 sizes, 35mm long and 30 mm long.  I tried the larger ones first and got the structure you see here.  The ends of the marble beads were pretty wide, so I added a bronze colored bead to give a narrower end.  It came out quite zigzaggy, which I liked.  But the 35mm beads were awfully heavy, a

and I was afraid if I made a whole necklace like that it would be uncomfortable.
   I tried using the 30mm marble beads, and to keep more or less the same proportions, I changed the silver tubes from 25mm to 20mm.  The next picture shows that one.  I liked it, but somehow didn't decide to do a whole necklace like that.  But I thought that  single one made a great pendant, so I just finished off the one, and I'm putting that on etsy.










  What I finally ended up with was using the smaller (30mm) marble beads, and 25mm silver tubes.  That made each oct more

square, so I changed the 2 tubes on each outside face  to 20mm ones, and got just enough curve.  It's not quite finished, but here's a preview.  Each 2-oct structure is 2" long, so I'll have 9 of them hinged together.
  The fun part of all this is to take an idea and watch it evolve, and see what you can do with it.

New octahedron piece

This is sort of a follow up on a post I did in January.  In that post I showed and talked about a necklace I had made in which I built octahedrons sized so that adjoining faces were almost at right angles to one another.  Each oct had a "waist" made of 2 short ( 10mm) tubes and 2 long gold filled tubes.  The angles weren't quite right angles because the 25mm gold filled tubes weren't quite long enough to be hypotenuses.  That would have required tubes of about 27mm, and I like to use stock sizes where I can.  So  on the sides of the piece the octs zigzagged a bit.
  In that post I mentioned wanting to use this idea to make a piece that was something on the order of a tic-tac-toe grid.  When I started to do it with the zigzagging rows of octs, I found that the intersecting rows weren't quite at right angles to one another.  To get that, I really did need octs that had right angles between their faces, so using the same 20 mm beads on the non-waist edges, I really did need 27mm waist tubes.
  It turns out the perfect solution was to use a 25mm tube with  a #11 seed bead at each end.  I wanted to use my anodised aluminum tubes instead of the gold filled ones, so that each chain of octs would have a different color, and I've found that with the aluminum tubes I'm pretty much always happier if I put a seed bead at each end of the tube.  That's because the aluminum tubes are quite a bit fatter than the silver ones, and so the open hole at each end of the tube is unattractive.  The addition of the seed beads solved both problems.

Octahedron shapes.

   I've been playing around with the different shapes I can get in octahedrons.  I started thinking about how I don't get a firm shape using RAW with tube beads because a square isn't rigid the way a triangle is.  But on the other hand right angles are just so "freindly" to work with.  We're surrounded by them, and we know how they work.  So I started imagining  octahedrons (octs)that were more or less square in overall shape. I wanted the piece to be not too deep, i.e. not sticking up too far off the body (as lots of my pieces do).  So with a relatively flat oct I could just use Pythagorus to figure out how long to make the "waist" beads--here the gold beads-- so that you'd have a right triangle, and that would make a square shaped oct.  The cross-wise and length-wise tubes are 20mm long, so a 28mm gold tube would be about right.  Actually, though, I decided to use 25mm cold tubes instead, so the octs aren't quite square, but zigzag a bit.  Partly that was because I thought a bit of a zigzag was more interesting, and partly because I prefer using more or less stock lengths rather than cutting tubes just for a single design.  If I use stock lengths (5, 10, 15, 20 and 25mm), I have more flexibility in the design.  If I cut custom pieces ahead of time, I have to have it all figured out before I do it, and I like to sort of make it up as I go along, even if I have the general idea figured out at the start.  Also there would be lots of times that I would cut lots of, say 28mm tubes and then discover that to get the right curve, I really needed them to be 27.5 or 29mm or whatever. 
   Here, when I got to the back and needed to make it curve, I had to use shorter tubes on the inside triangles than on the outside ones.  The ideal length for the inside tubes would have been around 18mm, so I just alternated between 15mm tubes in 1 oct and 20mm ones in the next.  One of these days I'd like to skip the curve and do a piece that would look sort of like a tic-tac-toe grid.  

sterling silver tubes

 Buying and cutting those colored aluminum tubes that I've talked about in the last few posts has started me off on a tear.  I've thought for a while about using oxidized sterling silver instead of oxidized copper, but was put off by having to cut the tubes myself.  At the same time I knew that there were things I couldn't do with the copper tube lengths I had, that I could do if I could control the length myself.  So as soon as I had worked a bit with the aluminum tubes, I found myself buying silver tubes and cutting them up too.
  As a practical matter, the price difference between copper and silver isn't so very great because the necklaces don't actually have that much metal in them. They're light as a feather.  In fact, that may be a problem in some pieces down the road.  On many of my copper pieces I used some 18mm melon shaped beads, mostly to add a little weight to make the piece hang better.  But those same beads in silver are pretty pricey because they have a lot of silver in them.  For now, the time it takes to cut and, more importantly, de-burr the cut tubes adds more to the cost of the work than the difference in metal prices.  And I think silver has more customer appeal than copper.
   The piece on top, with the tetrahelixes, was my first one with oxidized sterling.  I find it doesn't oxidize as dark as the copper does, at least using liver of sulphur.  There may be other chemicals that make it darker if I decide I want that.  For now this is OK.  I felt I needed seed beads at the ends of the aluminum tubes, so I used them at the ends of the
silver tubes too.  On the second piece, below, I used them just on the aluminum, not on the silver.  As I was cutting the silver, I found I was seduced by how pretty the bright silver was, so for the second piece, I left it bright (also the dark blue and purple show up better against the bright silver).  However, as a practical matter, I don't want to spend a lot of time trying to clean silver, so I think I'll mostly darken it.  I've looked at a lot of Flora Book's work with silver tubes, and it's so beautiful it tempts me to do more with bright silver. I'll just have to see as I go along.
  On the bottom piece you can see the advantage of cutting my own tubes.  It's a simple chain of octahedrons.  But a chain of octahedrons would normally form a straight line.  In order to get the curve you need for a necklace I had to make the triangle on the outside edge longer than the triangle on the inside edge.
Here's where some trig would have come in handy in figuring out just how much longer, but I managed to figure it out with "lesser" math, and it came out right.

evolution of a design

I've been trying to get into better shows with my beadwork, and while I'm improving, I'm still not getting into some of the shows I want to ( as if that isn't always the case).  Part of my problem is that for years I've been applying to shows, with the rugs, in the fiber category, which is generally one of the less competitive categories; now I'm applying in jewelry, which is always one of the most competitive.  Anyway, I've been using the oxidized copper tube pieces, because I think they're the most uniquely my work.  But I wanted another piece with some color, and since some of my pieces are rather irregular, I wanted one that was more controlled.  Hence the top piece.
  I like the piece, but, for a jury shot, I thought maybe I had moved too much in the direction of repetition.  I wanted a piece that was controlled, but

not quite so predictable.  Also, although I had color, still it had a lot of browns and neutrals.   I decided  I wanted to make 3 changes:  more color, copper tube pieces that were octahedra like the ones in the first piece, but irregular octahedra, and more interesting shapes than the ovoid ones in the first
piece.
     The second pic shows me playing around with shapes till I got one I liked, sort of a fat crescent.  Incorporating the other changes gave me more the sort of piece I was looking for, controlled, but just s bit unpredictable.  I still have to work on getting a better picture of the new necklace--it's really brighter than this pic makes it appear.

keggin and keggin-ish structures

    I'm on a 2-week break, since the store that my husband and I own is closed for the holidays.  Just when I had lots of free time, the beaded molecules folks (thebeadedmolecules.blogspot.com) posted a set of pictures that set me off on another structural journey.
The structure is called a keggin structure and wikipedia says it's the form of certain acid molecules.  I confess to not being much interested in the chemistry of it, but only in the geometry.  Geometrically. the structure is made of groups of 3 octahedrons that serve as the triangles in a larger structure.  The top  picture shows one such unit.  You can see on one edge (the top in this pic) there's a big triangle, and on the other edge (bottom) there are 3 small triangles that meet at a point in the center.   4 of these units, with the 1-triangle side on the outside and the 3-triangle side to the cente, form a  tetrahedron-ish thing.
    In thebeaded molecules site they showed 5 versions of this structure, identified by Greek letters that I don't have the font to write.  Picture 2 is the alpha version.  Till I made it, I couldn't tell how the others differed.  Turns out that in the alpha version, the triangles on the outside all line up with edges parallel to one another.  In the beta version one of them is point-to-edge.  Each of the others has 1 more triangle arranged point-to-edge till all 4 are that way.  But I had to see it in front of me before I understood it.  It's really hard to show a 3 dimensional structure like this well in a flat picture.  Even more so for me because I don't have 2 colors of bugle beads in the same length just now.
  Anyway, that's it for the Keggin structure.  But for me, since I'm dealing with it just as a geometric structure, not as a chemical thing, it seemed that the next logical step would be to take 8 of these triangle-ish units and make an octahedral version of the structure. So that's picture 3.  Then I took the 8 triangle version and made all the triangles point-to-edge instead of edge-to-edge.  That's the last picture.  I also improved things in that one by making the seed bead accents on the outside a different color from those on the inside of the structure, so that it's easier to read what's going on.
     A person just a little crazier than I  could also take 20 of the 3-octahedron units and make an icosahedron, but I think I've just about exhausted my interest in this.

Oxidized copper and stick pearls

This was a fun piece to make.  I did a necklace a while ago that had some stick pearls in it in place of the oxidized copper tubes.  But I used dark gray pearls and I only had 10 or 12 of them, so they didn't have as much impact as I'd hoped for. This one came out more the way I intended.  I've found that if I alternate 1 or 2 octahedrons with  what I guess you'd call a triangular prism, you get a blend of firmness ( from the octahedrons, since they're all triangles) and flexibility (from the prisms, since they have squares for the sides with a triangular cross section) that works pretty well.  Anyway, I enjoyed making this. 

Cage pieces 2.0

 I find that when I'm trying out a new idea, I usually start out with a very regular, often symmetrical, piece.  Sort of like what they sometimes call a "proof of concept".  As I get more comfortable with the idea, the pieces lose a bit of that.  In mid-June I showed some new work I called cage pieces, with a bead structure loose inside a cage which was an octahedron made from tube beads. I wanted to make 3 changes for my 2nd version of the idea.  First I wanted the inside structures to be brighter, for more contrast with the dark gray cages.  Second, I wanted the cages to be less regular.  And, third, I wanted to eliminate the cages st the back, because they poke into your neck just a bit.     My first try at this was the picture on top.  Mostly it achieved what I wanted.  However, in making the cages irregular, I also made them smaller.  That is

because the original cages, which were regular octahedrons, were made entirely from 1" tubes.  In order to make the cages irregular I substituted 2 or 3 short (1/2") tubes in each cage, which inevitably made the overall structure smaller.  More importantly, though, the 1st piece used 1/2" tubes between the cages, and I forgot that and used 1" tubes in the 2nd one.  So the new cages were both smaller, and more widely spaced.  I didn't really notice the difference till I took a picture.  When I looked at the picture, there was just too much empty space.  So I took out the 3 middle cages and redid them, with much closer spacing.  That'e the bottom picture.    I think it was an improvement (although until now I didn't notice that the necklace in the bottom picture isn't centered properly in the picture).

Cage pieces

     I love the idea of a bead or beaded shape caged within another shape, loose enough that it can move around but not get out.  I did it once with seed beads.  It was a bright colored dodecahedron caged inside a clear buckeyball.  I liked it but have never done another.  These oxidized copper tube bead shapes are ideal for that kind of treatment, and it's been on my to-do list for a while. an individual large bead caged in a structure would be nice, but you'd want it to be undrilled, so not really a bead at all.  I've thought of a marble.  Problem is I only have access to 3 sizes of tubes (and one is quite short, to it's effectively 2 sizes), so you need to be able to size the inside piece to the cage, so that it's small enough to move, but not so small it can fall out.

    Patricia Madeja does a really nice pendant with an undrilled pearl captured in a gold cube.  But I can't use a cube because a 4-sided shape isn't rigid when done in tube beads.  Also the sizing between the sphere and the square has a pretty small tolerance.  I found the same to be true if I used a tetrahedron cage, i.e. if it was big enough to not fall out it couldn't move much.  An octahedron, though, worked really well, as you can see.  There's lots of  room for the inner balls to move.  In the bracelet and the back of the necklace I used RAW cubes inside octahedrons made of 12 mm tubes.  In the front of the necklace I used dodecahedrons inside 22 mm shapes.  All the inside shapes are made from 4 mm stone beads. 

   There was just one minor problem with the necklace.  The point of the oct is toward your neck as you wear it, so it feels just a bit prickly.  It's not bad; I wore it all day, but I noticed it just  bit.  After this picture was taken I added a small bead at the inner and outer points of the octs, but it didn't really change anything.  It's not any sharpness in the tubes themselves that creates the slight prickliness, but just the shape of the oct itself.  It wasn't noticeable at all on the bracelet, where the weight is evenly distributed. Both pieces are quite lightweight, it's just that in the necklace whatever weight there is is concentrated in 4 points on your neck.  2 possible answers: reposition the octs so that there's a triangular face toward you instead of a vertex; or leave out the octs at the back of the necklace altogether.  I'm experimenting with both.

Oxidized copper earrings

Just a quick post.  I've been getting ready for a show in Atlanta (the Atlanta Dogwood Festival in Piedmont Park, if you're in the area).  The oxidized copper tube beads I've been working with lend themselves well to making structures for earrings, so I've just finished several new earring designs.They're all just combinations of tetrahedrons and octahedrons, but by using different length tubes you get interesting structures.  The ear wires are oxidized sterling silver.  I like to do the kind of post that needs an earring back to hold it on.  That's because the earrings are so open that I don't want an extra wire hanging down behind the ear, the way you'd have with something like a French wire.  So far they all have mirror image pieces for the other ear, but I'd like to do some where the 2 earrings are close, but not identical.