Beaded machines

Trefoil Knot Kaleidocycle

A while ago I found an interesting paper about rotating rings of tetrahedra (aka kaleidocycles) by Jean Pedersen┬╣. Apart from some great instructions on how to make them by braiding two strips of paper together it also mentions that with enough tetrahedra, a kaleidocycle can be tied into a knot and still rotate.

So of course I had to try this! The paper says that the minimum number of tetrahedra required is 22, which is quite a lot. I decided to make them out of bugle beads to test the idea. I made a long strip of them using right angle weave (although in this case the angles aren’t right-angles) and illusion cord . When I had enough tetrahedra I tied the strip into a trefoil knot – this is just an overhand knot with the ends joined together. The completed kaleidocycle looks like a bit like 3 normal kaleidocycle merged together:

TrefoilKnotKaleidocycle_BeadMechanics_1

Now for the moment of truth – does it rotate properly?

The answer: yes! It took a few tries to work out how to get it to turn properly, but it’s great fun to play with. Here’s a video:

I think this is my favourite kaleidocycle so far! I want to make a peyote tetrahedra version, but the 88 triangles needed might be going to take me a while!

 

┬╣The paper is “Braided Rotating Rings”, Jean J. Pedersen (The Mathematical Gazette, 62, 1978).

Beadwork, Polyhedra, Tutorials

New tutorial!

I’ve finished the tutorial for my first beaded icosahedron – now named Whirlwind! You can find the tutorial in my brand new etsy shop: www.etsy.com/shop/beadmechanics.

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I’ve been working on this for a while – it’s been quite a learning experience! The tutorial is 21 pages with more than 60 photos and diagrams – there’s also a net for a paper version of the model you can cut out and make to help with putting the beadwork together!

I’d always intended to make this icosahedron again so I took the opportunity to take photos as I went along so I could write a tutorial. The new version is actually the mirror image of the original – so now I have a matching pair! (Some brief instructions on how to make a second one so you have a matching pair are also included in the tutorial!)

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Happy beading!

Beaded machines, Beadwork

Decagonal Kaleidocycle

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

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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!

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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!

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Beadwork, Polyhedra

Rhombicosidodecahedron

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

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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!

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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:

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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.

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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:

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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:

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