Beaded machines, Beadwork

Decagonal Kaleidocycle

Last week I finished my second beaded kaleidocycle – a half-closed decagonal kaleidocycle!

decagonal_kaleidocycle_beadmechanics_7

It’s made in a similar way to my last kaleidocycle, except that this time the tetrahedra aren’t regular – some of the sides are different lengths. I based the shape of them on a paper model of a half-closed decagonal kaleidocycle from www.korthalsaltes.com – an amazing website with lots of kaleidocycle models!

Here’s a video of it in action:

The “decagonal” part of the name means it’s made of ten tetrahedra, the “half-closed” part means that some the faces meet with no gap in the centre – or at least they’re supposed to! The beaded version ends up with small gaps in the centre of these faces since the beadwork tetrahedra are only an approximation of the exact shapes.

Using tetrahedra with different length sides means that the different faces you see as it turns are all different shapes – which is pretty neat!

decagonal_kaleidocycle_beadmechanics_11

The colours didn’t quite turn out how I expected them to, with one side of the kaleidocycle entirely blue – I designed the pattern on just one tetrahedra and didn’t quite manage to predict how it would all fit together. At least now I have a complete model that will help with the next one!

I’m very happy with with it as it is though – I was quite nervous as I was making it that it wouldn’t turn properly, so I’m very happy it rotates as it should! Definitely going to be making more of these!

decagonal_kaleidocycle_beadmechanics_9

Beadwork, Polyhedra

Rhombicosidodecahedron

Rhombi-what? Like a dodecahedron, but with some extra squares and triangles between the pentagons! My beaded version looks like this:

beadmechanics_diamond7

Technically it’s a small rhombicosidodecahedron, since there’s also a great rhombicosidodecahedron, which has hexgaons instead of triangles and decagons (I think that’s the right word for a ten-sided polygon) instead of pentagons.

It’s actually based on my previous icosahedron model, although it ended up being a slightly different shape in the end. It took me a while to work out which polyhedra it corresponded to, but a rhombicosidodecahedron is an expanded icosahedron so that makes sense! Here’s photo of the two together:

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Another thing it turned out to be is really difficult to photograph! Not helped either by the lack of sunshine today (why is it always cloudy every time I finish a piece?).

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It’s made using 30 individual diamond-shaped pieces. These are made using some CGB techniques – each one is made up of two layers built from an MRAW band, with two side increases on the bottom side and four on the top. It was definitely a bit of a marathon making 30 MRAW bands though!

beadmechanics_diamond4

Hopefully the weather will improve and I’ll be able to get some better photos soon!

Beadwork, Beadwork objects

Spring spirals

It’s been fairly chilly here the last few months and apparently delicas break pretty easily when they’re cold, so I haven’t been able to get much beadwork done. While I wait for spring (maybe further off than I thought as I sit here watching the hail outside!) I’ve been trying to organise my “in-progress” beadwork… a large proportion of which is half-finished test pieces that I don’t want to take apart, but aren’t really anything useful and seem destined to sit in a box forever.

Occasionally however I do manage to make a test piece into an actual object – if only to feel like I’ve achieved something! This one is a small trinket pot I made out of a test piece for an idea about cellini horns a couple of years ago:

beadmechanics_spiral1

The spikes are just Contemporary Geometric Beadwork half-horns – that is, a side incease (wing) that then gets stitched together along its top, instead of decreasing back to the main work like you would for a horn. The spirals all meet at the right place on the join, but don’t quite line up how I’d like where the half-horn meets the rest of the beadwork – if I ever make these again I need to sit down and work out how to get the counts completely correct so there’s a smooth transition to the rest of the work.

beadmechanics_spiral3

It started out like a very small CGB bangle, a plain tubular piece of peyote from a MRAW start. The transition from circular at the base to square at the top is entirely the result of the cellini spirals changing the shape of the beadwork!

I made it into a trinket pot by just adding a few rows of size 11 and 15 seed beads to the MRAW start at the bottom (like the back of a bezel), as well as a row of 15s at the top. I then cut out a piece of card the right size and stuck some grey suede to either side to make the base:

beadmechanics_spiral4

I’m not sure that cellini horns have much of a future as a bangle idea, but a thinner piece could make a pretty interesting pendant!

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It is unfortunately a bit lopsided. I probably wouldn’t use matte beads for the sides again, they seem to result in a fabric which doesn’t have much flexibility – a bit of a problem since the cellini horns cause the beadwork to warp significantly! Still, I think it looks pretty neat:

beadmechanics_spiral2

It’s also a nice spring colour – like green shoots emerging from the winter ground!

Beadwork, Polyhedra

Fractal Tetrahedra

So I was playing around with beaded triangles thinking about making some Sierpiński triangles. These fractals are simple to make – you start with a triangle (the first iteration) and remove an inverted half-size triangle from the centre, leaving three smaller triangles joined together to form the larger one (the second iteration). Then you do the same with each of these three triangles to make the third iteration. Keep doing this and you end up with a series of fractals like this:

beadmechanics_triangle

I was looking at these and thought – can you do something similar, but with tetrahedra? A quick search told me that yes, you can! It’s called a Sierpiński tetrahedron, or a tetrix. I went and found some beads and started beading straight away!

The first iteration of a tetrix is just a plain tetrahedron:

beadmechanics_tetrix_1

The matte black beads I used here are some of the first delicas I ever brought, over a decade ago!

The second iteration is where it starts to get more complicated! This is four tetrahedra, half as large as before, assembled to make one larger tetrahedron like this:

beadmechanics_tetrix_2

Each outer face of the tetrahedron is a Sierpiński triangle!

I was worried that joining the pieces together would be difficult, but I just followed a threadpath as if completing the last row of each missing triangle on the outer faces. This seems to hold the pieces together well, and also means the top piece rests on top of the others at each corner, so it doesn’t collapse.

The third iteration proved to be more of a challenge – at this point my tetrahedra were made up of triangles with only three rows. I split it up into four separate groups of four tiny tetrahedra. Each group is made with one thread, and each face is added by working inwards from an outline connected to the rest, rather than by making each one individually. It was quite tricky to do, and there were a few broken beads – I regret picking a matte finish for the edge beads! – but I managed to stitch it all together in the end. Here’s the completed third iteration:

beadmechanics_tetrix_3

At this point I had to stop since I couldn’t make the tetrahedra any smaller. Should have started with a larger tetrahedron!

Here’s the completed sequence of beaded fractals all together:

beadmechanics_tetrix_5

Definitely going to try this again – what’s the largest tetrahedron I can start with??

Beaded machines, Beadwork

Folding Cube

UPDATE: A tutorial for this cube is available here on the blog!

So I finally managed to finish the new machine I was working on! This time it’s not a kaleidocycle but a folding cube made using cubic right angle weave. Here’s a video:

I can’t find out if these cubes have a technical name, but they seem to generally be known as magic folding cubes. They’re actually quite similar to kaleidocycles, since they’re  a ring of eight linked cubes that can be rotated around back to the original starting point. However, they’re also very different since they alternately form two larger cubes during this rotation. I made the faces on each of these bigger cubes distinct – one is just the plain cubic right angle weave surface:

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and the other has crystals embedded in it:

cube1_verrier

Each individual cube is a 4 by 4 block of cubic right angle weave, with a 2 by 2 gap for the crystals on three sides. Each of these cubes are joined to the two neighbouring cubes using modified right angle weave to make a hinge. I used size B nymo, size 11 seed beads and 4mm crystals (although 3mm or a flatter bead might have been better as the 4mm is just slight too big). I also found a curved beading needle a big help for some of the later rows!

If you want to try making one then I recommend making a paper model first for the hinge pattern – there are a lot of websites with instructions for making paper versions and having a model really helped a lot when I was putting it together.

Eventually I’d like to try making one out of 8 stellar octangula (a polyhedron that looks like two intersecting tetrahedra), since they have the same layout of vertices as a cube so could be fitted together in a similar way. Worked out that I’d need to make 192 triangles to do this though – might take a while!

Beadwork, Polyhedra

Warped polyhedra

So I’ve finally finished the pair of beaded shapes I was working on over the last few months! Here they are – a rhombic hexecontahedron and what is probably best described as a hyperbolic dodecahedron:

hexecontahedron_hyperbolic2_beadmechanics

So around the start of July I was reading about various polyhedra and I came across a rhombic hexecontahedron (the shape on the right) and realised that I could make one out of warped squares. I then realised that I could do a similar shape using warped hexagons and end up with the shape on the left. This isn’t really a polyhedron as the faces aren’t flat, but it’s similar to a hyperbolic dodecahedron shape, which is also known as spikey, the Mathematica logo (while a hexecontahedron is currently the Wolfram Alpha logo). I used Mathematica a lot when I worked in research, and spikey was one of the first ‘mathematical art’ polyhedra I encountered!

hexecontahedron1_beadmechanics

It seems that July was a month for making shapes out of warped squares though! While I was making this I saw Joy Davidson’s 3-star beaded box on facebook, and later saw Kat Oliva’s lovely patchwork rhombic hexecontahedron as well. I also ran across a photo of one on pinterest shortly after I finished it, which turned out to be a pattern by June Huber (Juniper Creek Designs). So it seems that I have just reinvented the wheel on this one!

hyperbolic2_beadmeachanics

I really like the hyperbolic dodecahedron, although it was at times challenging to make. I managed to make the tension a little too tight on some of the points and there were a couple of broken beads that had to be fixed by removing a section and repairing it, but I finially managed to finish it last week. I was also worried that it would be very difficult to stitch the last few pieces together, but it turned out to be much easier than I thought it would be (curved beading needles are an awesome invention!).