Cages

I've been working on pieces, mostly earrings, where there's a "cage" made from oxidized sterling silver tubes. Then another structure, usually a sphere of sorts floats freely inside that cage.  I've done spheres of 4 mm gemstone beads, but my favorite, and my best selling one is a dodecahedron (sometimes called a Plato bead because it's a Platonic solid) made from 3 mm gold filled beads.  Lately, though, I've wanted to make a shape that wouldn't stay so much inside the cage, but would hang out more.  I thought what I wanted would be a stellated structure with different points hanging out of different triangles in the cage.  But I found I didn't like those.  The problem was using my gold filled tubes to make a stellated structure.  The gold filled tubes are a bit bigger in diameter, around 1.8 mm, and when you make a stellated structure that's small enough for an earring using tubes that fat, it just looks kind of clunky.  I had thought of using just a cube, which doesn't require

so many short tubes and doesn't have such acute angles.  But a cube, since it isn't made from triangles, isn't rigid the way something like a stellated tetrahedron would be.  However, I found that if I made a cube using my stiffest 10 lb test monofilament, and went around each of the square faces an extra time, the cube came out almost as stiff as something made from squares.  And since it's just floating, and so has no strain on it, it turned out to work just fine.  I love the asymmetry it gives to each earring.

New structures

I entered this piece (and 1 other) in the latest Bridges math art gallery (http://gallery.bridgesmathart.org/exhibitions/2021-joint-mathematics-meetings). The exhibit included explanations by the artists of each piece, and it's amazing how explaining your ideas makes you think about them more clearly.  As I said in the explanation this bowl is basically half of an icosidodecahedron, which is made up of pentagons separated by triangles.  I can't make a simple pentagon with my tubes, as 5 tubes joined together with thread will be shapeless.  So I made 5 tets that share a central tube as a hub.  I'll call them pods.  These pods are relatively flat, but if they were thicker, I wouldn't actually need the central tube.  That got me thinking about the fact that without that central tube it would be easy to stellate the structure.  Also that you could do that with 6 sided pods, or, for that matter, any-sided ones. With that idea, I could recreate those interesting structures that I learned from thebeadedmolecules.blogspot.com and that I made using round beads. What fun!

These 3 pieces are what I did first.  The top one is a truncated tet.  The second is a dodecahedron. And the 3rd is a truncated oct.  In each case the actual structure is done in gold filled tubes, and the rest is done in oxidized sterling ones.  I didn't truncate the triangular faces because they're rigid without it.  I wasn't sure if I'd have to stellate the square faces in the 3rd piece (they would stellate into octahedrons). I didn't, and the piece seemed pretty firm as is, so I guess it was OK, although technically I probably should have.  I was pretty careful
 not to stellate them too sharply, as you can have a real probem getting

your needle down into the valleys of a piece with tall stellations.  I did

some stellated pieces back when I was working with seed beads and nearly drove myself crazy that way.

   Once I had made the 3 pieces, the question was what to do with them.  I had decided on some sort of wall piece, as they're too big for jewelry. My plan was to make a straight truss out of octs and hang them from it side by side.  But the top piece, the trucdated tet, is smaller than the rest, so I couldn't seem to make an arrangement I liked.  Eventually I decided to  hang them in a single row, and the smaller shape looks fine that way. 

One last thing I wanted to do:  the icosidodecahedron I had started out

to do in the first place.  It was going to take a lot of tube length, so I didn't want to do it in silver and gold fill.  I found a source for really inexpensive brass tubes in Istanbul (via etsy) so I made it in brass. I stellated more that the others because I knew the triangles separating the pentagons would allow me to get my needle in without a problem.  What I found was that in that case the limit on how steep you want your stellations to be is that if they're too steep that outside point becomes subject to not holding its shape tightly.

Redoing

   I mentioned in the last post that I redid my arrow-ish piece without the colored zigzags because the anodized aluminum colored tubes were 25mm long and without adding a seed bead at each end, these were too short to be diagonals in a right angled octahedron that used 20mm tubes for the sides.  Obvious because the hypotenuse for a 20x20 right triangle is roughly 28mm.  So I did a right angle weave version with no angled pieces, just squares.  I really liked the piece, but I still missed the color, and I had all these 25mm colored tubes, wanting to be used.  So after many failed attempts, I finally realized that if I just switched from a 20x20 square to a 17x20 rectangle, the colored tubes would be long enough. Duh.

   So I made the piece out of octahedrons with triangles on the sides of 20/20/10 and cross sections of 17/17/10.  The ones at the junctions of a horizontal row and a vertical one had to be 17x17 squares, and so there I had to cut down the colored tubes, but that was no problem.  And I kept the extra curved arrow that I had put into the plain silver piece, which I liked a lot.  I lost the wide arrow heads, which were cool, but with a triangular cross section I couldn't do them the way I had been able to do with a rectangular cross section.  And the piece is much firmer. I got rid of the seed beads at each end of the colored tubes, which had made the diagonal wobbly, because in recent years I've come up with a much better way to deal with the larger diameter tubes.  I make the piece using just the tubes, no seed beads.  Then after it's made I go back and take a thread just through the colored tubes, zigzagging back and forth, and I add a bead between each tube.  The thread going on a much more direct path through the piece actually does quite a bit to tighten up the piece, instead of making it looser.

All sounds pretty straightforward, doesn't it.  But it wasn't.  Because when I had initially moved from an octagon structure on my first necklace to the RAW structure in my 2nd one, I had dropped one unit of width to make the piece a bit narrower.  I liked that so when I went back to an oct structure I kept it narrower, at 7 units of width instead of 8.  Big mistake.  I long ago realized that with an oct structure you want an even number of octs so that the center of the piece is not an oct but the face between 2 octs.  This will keep the zigzagging symmetrical.  Since I had the 2 arrows going on opposite directions I hadn't thought I had to stick to that rule.  So I had made the whole piece up to the point where the yellow arrow started to taper and curve around the neck.  And I found that on the left and right sides the zigzags were parallel to one another, instead of mirror images. Doesn't sound like a problem, but when you start to taper and curve each shape, it's just about impossible to get the left and right sides to taper and curve symmetrically unless they're mirror images.  So I ended up tearing out the whole yellow arrow and part of the dark green curved one so that I could add in an extra oct to get the zigzags moving in the right direction.  This is why I never answer when a customer asks how long it took to make a piece--because for every one that goes smoothly there's one like this.  Still, all's well that ends well.

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.

What I'm doing now

     Like the rest of you, I'm still home, still experimenting with jewelry structures. I'm still playing with the tetrahedron structure I talked about earlier.  The piece on the right in the picture above is one I showed in my original group of these structures a few months ago.  I liked it, but felt that the central tet, which is built from an octahedron and 4 tets, didn't show up as well as it might have. So I redid it, using gold filled tubes for that center tet, and making it a bit curvier.  Actually I like them both.  I tend to think of pieces with the gold filled tubes as being a bit dressier, so there's a place for both.

     There have been a few happenings in my jewelry making life that I wanted to mention:

            My work is now available online through Contemporary Craft, in Pittsburgh.  The gallery is closed, but there's a good selection online at contemporarycraftstore.com.

            I'm really excited to have been accepted to the Philadelphia Museum of Art Craft Show.  The show is the first week in November, and it too will be online, and you will be able to see and buy work there. 

          

Another new gallery is Wearever Jewelry in Alexandria, VA.  My work is not yet on their  website, but they're open if you're in the area, and I'm sure if you contacted them you  could also buy it online.

            I'll have work in an online show Uncommon Threads on October 18.  It's run by the Fine Line Art Center in St Charles IL. You can find out more at fineline.com

Finally I thought I'd just let you know that these tet structures aren't the only thing I've been doing, jewelry-wise.  Since they're mostly pretty planned and controlled, I had great fun with a necklace that's the opposite of that.  Here's that one. I'm really proud of it.

New work

Well, I'm still hanging around the house and making jewelry (no surprise).  It's all going onto a shelf, since galleries are mostly closed or only partially open.  I found out recently that I've been accepted into the Philadelphia Museum of Art Craft Show this coming November, and I'm pretty excited about that, but, of course, it may not happen, or it may become a virtual show.  We'll see.The first picture shows 2 more pieces in the series I talked about in April, with a series of triangles in the center that form the base of tetrahedrons.  For these 2 I wanted to make that base have an inward slant to it by making the top tubes shorter than the bottom ones.  These will be brooches. I also wanted to try 2 different ways of creating asymmetry. The one on the left has asymmetry in the shape of the star.  The one on the right has a symmetrical shape, but asymmetry in the placing of the gold tubes.  Myself, I prefer the one on the left, but we'll see what customers think.

The second picture is something I did with some of the shapes I initially made in trying this structure.  In my April post I showed a picture of several of them.  My intent was to hang each one on a chain as a pendant.  But till I got around to it I just had them all in a pile.  I saw these 3 piled together, and decided I liked them that way, and wanted to join them into a single pendant.  I wasn't sure how to do it so I've been staring at the group of 3 arranged like this for several weeks.  Yesterday I decided it was time to wade in and join them together.  I like the way it worked out, and it means that instead of 3 nice pendants, I have one that I think is way more interesting. 

More sculptural work

Here's one more in my sculptural series using the tetrahedron series I've been playing with.  I wanted a bigger piece.  This one is about 9" across and 2.5" high. I made the zigzagging tubes on what is usually the outside quite short.  This creates a negative curve and so the zigzag edge is the inside instead of the outside. I have to confess I did this so as not to use so much gold, as I buy it in much smaller quantities.  On most jewelry, bracelets for instance, it's the outside where you want to put the emphasis, but with a bowl form, it's the inside.

Taking it in a new direction

 I'm still working on my tet structures, but over the last week or so I've expanded my explorations.  It started out with the idea that I could stack my torus (donut) shapes on top of one another. For example I could make a wider bracelet that way.  But as I stacked a couple of rounds, I started thinking about a bowl form.  That required a torus at the bottom that would angle inward, which was no problem. Then all I had to do was join the octagon I had on the bottom with 8 spokes and add feet to make this little bowl.  It's about 3.5" in diameter, and has gold triangles on the inside. On the outside I had gold zigzags.  I joined the toruses with verticals and so the zigzags became hexagons (which are hard to see in the picture).  For a bracelet the outside is more important but for a bowl it's the inside that shows best.  I'm thinking about more, and bigger, vessel forms.  Also I'm

thinking about putting the triangle bases on the outside and the zigzags on the inside. We'll see where this takes me.

explorations during the lockdown

Like everyone else (except healthcare workers and the like) I've got time on my hands just now, as I'm home all day except for a walk.  And because my shows were cancelled and my galleries are all closed, I don't need to be just producing "inventory".  Mostly my pieces are one-offs, but by now in several categories (pendants, bracelets and, especially, earrings) there are some styles that I repeat, sometimes with variations, because they sell well.  But I have enough of those now.
Since I didn't want to do repeats, I decided to do a series based on a single idea and see where it took me. I often do 3 or 4 pieces based on an idea before I get hijacked by another idea/structure, but this time I decided to stick with one for a while.  It's a tetrahedron structure that I've used a lot and written about before. The earlier posts were in January, 2015 and March, 2016.  But I decided to really beat the idea to death.  One inspiration, for those of you who, like me, keep old copies of American Craft magazine, is a picture in the Feb/Mar 2011 issue.  It shows a series of well over 100 glass vases by Dante Marioni.  All are similar in overall size and made of clear glass with black accents.  Within those tight limits he goes crazy.  To me it's like a theme and variations in music.  Even better, it's like a Chopin etude, where you take something that is basically an exercise and make it beautiful.  Anyway, I really love it.  I'll never do a series that big, but this is what I've done so far.  Most have gold accents that don't show up well in this picture. The first 5 will be focals hanging from chains.  #5 (top on right) has 1 fat tube at the back that I'll insert a handmade safety pin-type structure to make a brooch.  #6 will be a pendant focal, or I'll add a fat tube (although it would cross the circular open space in the center, and I'm not sure I want to do that). The last 3 could be used separately or together, not sure which. I really like them together, but it makes a pretty big group.  Time will tell.

Brancusi necklaces

 I'm stuck at home like everyone else so, of course, I'm playing with jewelry, and thought I'd post something. A few months ago I made some bracelets based on the 4-sided columns that Constantin Brancusi created.  The first 2 pics here were my first necklaces.  I liked them a lot, for their simplicity.  Of the 2, though, I preferred the longer, narrower one that's on top.  And I started thinking about breaking up the symmetry just a bit.  I ended up taking apart the bottom on #2 and redoing it as #3.  I know that asymmetry in the structure is not what the Brancusi columns were about, but I find I like it.

developing an idea

 I haven't posted in an age, but I felt like doing a post that shows how my ideas sometimes grow and develop.  A while ago, I decided to step back from making a new piece, and just focus on finding 2 types of workable units for my work.  What I wanted to find was octahedrons that would have adjacent faces at right angles to one another, i.e.where the overall shape of the oct would be a rectangle.  That way I could have a chain of octs that would be a straight line.  The 2nd shape I wanted was octs that would make symmetrical

trapezoids.  That way you could make an oval shaped necklace by using the rectangular octs for the long straight sides and trapezoidal ones for the curves at front and back.  I came up with several of each that I could make with the lengths of tubes that I cut, and I am amazed at how many times I've gone back and used the units I came up with.  But also in the course of doing this, I happened on an oct I could make where 3 of the sides  formed the angles I've pictured--a right angle with an adjacent 45 degree angle.  This meant that eight of them joined at the 45 degree angle would make a square, one with a sort of star shaped center.  You can see it at the center of the 1st necklace shown.  Also one of my symmetrical trapezoids had an angle of (roughly) 60 degrees between the 2

angled sides, so 6 of them made a circle (actually more of a torus, as the center is open).  I really liked having these 2 regular shapes.  But I thought I could accent the geometry by using some gold tubes in the middle layer of each shape.   That way there's a silver square and circle (hexagon actually, but it reads as a circle) and a gold triangle and diamond.That's necklace 2 and I thought it was an improvement. 
  I wanted to make a pendant of the square shape, but I wanted it to be bigger than what I had.  The square I had so far was a bit over 2" on a side.  But I found that if I turned it 45 degrees so it was a diamond and then added 2 right angle tetrahedrons on each edge I'd get a square that was almost 3" on a side, which was more like what I wanted. I also changed the arrangement of gold tubes, putting them on the inside star shape and on what used to be the outside edge, but was now an intermediate diamond. 
  Finally, I wanted to make a whole necklace using the square as the focal point, but I wanted to go still bigger.  As I've worked out the tube lengths that I want as stock units, I've

found that lengths that approximate multiples of the square root of 2 are useful.  So since my smallest length is 10mm, I'd ideally want one of 14.15xxx...mm, then 20mm then 28.3xxx...mm then 40 mm.

Obviously my tube cutting jig and ruler will only approximate that so I use 10, 14, 20, 28 and 40mm.  In between those I have another series that's 12, 17, 24 and 34mm. Again in an ideal world the 2 series would fit together so that the relationship between each length and its neighbor would be the same, i.e. 12/10 would be the same as 14/12, 17/14 etc.  If that were the case you could come up with a shape, and then you could scale it up or down and it would work at any place on the series, just the way that in music a melody stays the same as you move it up or down an octave ( or a fifth or whatever). 

As I've said, my ratios are close, but not exact, particularly between the 2 series.  So it took a fair amount of trial and error, but I finally found that if I scaled everything up 1size on my tubes except for one on the outside that I left the same, I could make a square that was the size I wanted, almost 3.5" across. Then there was a fair amount of trial and error to get a good curve that got gradually smaller so as to not be too bulky in the back, but I'm really happy with the result, and with all the steps along the way as well.

another mathematical rabbit hole

     I've been having fun playing with a new area of mathematics.  Up to now my explorations have had to do with building polyhedra.  But I do look occasionally at Kate McKinnon's peyote stitch based work done in seed beads. Under the heading Contemporary Geometric Beadwork, she's produced several books, as well as lectures and lots of other stuff.  I admit I don't have the books.  Since I don't do peyote stitch and I no longer do seed bead based work, I thought lots of it wouldn't apply to my work.  But I do look at the pictures of what she and her group do, and find it quite interesting (as an aside--since the people who read this blog are mostly beaders with a mathematical bent, if anyone knows which of the books in the Contemporary Geometric Beadwork series would have a good coverage of the theories for someone who doesn't actually do peyote stitch with seed beads, I'd love a recommendation). I've often thought I should play around with the hyperbolic plane that she uses. She calls it a warped square, and it's made of 4 triangles.  If they were right triangles it would be a flat square but since the "hypotenuse" is longer than it would be in a right triangle there's more perimeter and the structure isn't flat.  It has always seemed to me that my way of making triangles has much more flexibility than the peyote stitch way.  It seems to me the shape of her triangles is determined by the shape of the seed beads--the relationship between the height and the diameter of the bead used sets the shape of the triangle.  In that way I have much more flexibility. I can  cut any length tubes and get whatever triangle I want.  Of course it's also much faster, but on the other hand I can't do the great stuff with colors and patterns that she can.
   Above is a single warped square made into an earring, and another earring with 2 of them.  I said my way of working  gives me more flexibility, but on the other hand my "stock" lengths are sort of set to be able to build right triangles. For example, I cut lengths of 10, 14, 20, 28 and 40 mm. Each one is more or less the one before it times the sq root of 2. So 10/10/14 makes a  right triangle ( or would except that the sq root of 2 isn't 1.4 but 1.4xxxx to infinity), as does 14/14/20 or 20/20/28 etc.  I also do 17, 24 and 34mm lengths, which fill in the gap and work the same way.  But to jump to 14/14/24 makes a very warped square,
(similar to what's in the earrings, which use triangles of 10/10/17) and more than I wanted.  So I decided to try making squares where just one of the outer edges was 24 and the rest were 20s.Here's a double row of these squares.

I liked it, and thought it could make a good bracelet ( you can see on the left end an additional structure I added where I could put a clasp). But there was 1 problem.  There are 2 versions of the square.  If you arrange the "plane" so that the tube on the bottom is horizontal, the tube on top can either go from high on the left and low on the right or vice versa.  Since the triangles are theoretically rigid you can't change it once it's made. In this way it's different from the peyote triangles which are inherently flexible. In the top pic I arranged the squares so that each is the mirror image of the ones beside it, which is the way it would have to be for a bracelet.  But since the hyperbolic-ness ( hyperbolicity? no idea what the proper word is) is fairly minimal, if you push on one of the high points in the center of the structure you can flip it, and then it turns into pic 2.  You can just as easily flip it back, but a potential customer wouldn't know that and I didn't want to get bogged down in long explanations. So I changed it, making essentially warped rectangles, where the outside edges were 2 20s and 2 24s.  That made the bumpiness more extreme and hence more stable. 
   I also tried a structure where the warped squares didn't go back and forth between the 2 versions, but were all the same version.  That made the warping spiral.  That's the last picture, but you can't see what's happening very well. In order to make it work, I'd need to replace 1 tube in each square with a gold or colored one so that you could see it spiral around.
  There's another way to make a hyperbolic plane. Instead of adding length to the tubes that make the perimeter of the structure you can add an extra triangle, i.e, where 4 right triangles would make a flat square, 5 of them would make a hyperbolic pentagon.  That's the sort of structure that will get progressively more wavy in the way of a lettuce leaf.  But doing it with 5 right triangles was too extreme.  Each pentagon was very non-flat. And if the first row had n structures the next would have 2n, and then 4n etc.  Again too  extreme and fast a progression.  I did it several years ago (you can see it in a post on hyperbolic planes from that time) using equilateral triangles, and where 6 would make a flat hexagon, 7 makes a hyperbolic heptagon. And each row will have 4 units for every 3 units in the one before, so the progression is still fast, but not so very fast. I really liked the one I did in colored glass beads back then, but had some trouble with the glass cutting the thread. I'd like to try one in silver tubes, possibly bright silver, but haven't gotten it done yet.