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.

whirlwind_beadmechanics_1

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!)

whirwind_beadmechanics_2

Happy beading!

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:

beadmechanics_diamond2

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?).

beadmechanics_diamond3

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!

beadmechanics_spiral5

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, Tutorials

Folding cube tutorial

Here it is – a detailed tutorial for the folding cube!

beadmechanics_cube_verrier

This is the first tutorial I’ve ever written so hopefully it makes sense! Any questions just ask.

Materials

I used the following beads for the original cube:

  • Size 11 seed beads – about 22g – Miyuki, gunmetal, colour 451
  • 4mm crystals – 24 – Swarovski bicones, blue zircon

You’ll also need:

  • Size B nylon (nymo or s-lon etc.) thread – black
  • Size 12 beading needle
  • Curved beading needle (size 10, but I think that’s the only size you can get)

Cubic Right Angle Weave (CRAW)

The individual cubes are made using cubic right angle weave (CRAW). I’ve written the tutorial assuming familiarity with this stitch, such as how to go round corners and how to build off existing work. If you’re not familiar with it don’t worry – there are many tutorials online! The pattern shouldn’t be too difficult once you master the basics of the stitch.

Modified Right Angle Weave (MRAW)

The hinges on each cube are done with modified right angle weave (MRAW). If you’ve not come across this stitch before you should check out the instructions on the CGB site. They can be found on page 39 of the freely available ‘Basics’ section of CGB volume 1.

Making a model

I found it very helpful to have a model of an unfolding cube to refer to – it makes it much easier to work out which hinge goes where when you have an example right in front of you!

There are several options for making a model. The first is to find 8 small cubes and join them together (see below for the joining pattern). The second is to print out a paper net and make a complete cube all in one go (although this was not the easiest to do!).

Hinge pattern

I’ve used some 20mm wooden cubes and some stickers and tape to put together a model. (Wooden cubes seem pretty easy to get hold off from craft shops or online – or you could also make individual cubes out of paper.)

beadmechanics_cube_model1

The stickers mark the faces where the crystals are going to go – 3 on each cube. Each cube is identical until the hinges are added – this makes everything much easier! They look like this – 3 adjacent faces have stickers/crystals, and the other 3 are blank:

beadmechanics_cube_model2

Here’s how the 8 cubes go together. I’m going to number them 1 to 8 to make the later instructions clearer.

First join cubes 1 and 2 by making a single hinge by sticking tape along the edge as shown (I stuck a piece of tape on both sides of the hinge to make it stronger):

beadmechanics_cube_model3

Then add cube 3 like this, paying close attention to where the stickers are:

beadmechanics_cube_model4

Then add cube 4 on the other side, and fold cubes 3 and 4 in as shown on the right:

beadmechanics_cube_model5

Then add cube 5:

beadmechanics_cube_model6

And cube 6 (still making sure all the stickers are in the right place – although don’t worry if you make a mistake, you can always peel them off and stick them back on!):

beadmechanics_cube_model7

Then add cube 7 like this:

beadmechanics_cube_model8

And finally add cube 8 as shown:

beadmechanics_cube_model9

There’s one more hinge to go – the one between cube 7 and cube 8, which is along the bottom horizontal edge as shown:

beadmechanics_cube_model10

That’s it! You should now have a working model, which folds into two different cubes – one with stickers on all the faces, and one with blank faces:

beadmechanics_cube_model11

If you’ve made a model as above and rotated it around a few times you may notice you can unfold it into a rectangle so it looks like the photos above but the hinges are all in the wrong places. Don’t panic! This is because there are two different places in the complete folding-unfolding cycle where the cube flattens out to a rectangle, and they have the individual cubes in a different order. Just continue folding and unfolding and you’ll get back to where you started.

Now you have a model, on to the beadwork!

The pattern

The pattern is split into 2 parts:

  1. Making the 8 individual CRAW cubes
  2. Adding the hinges to each cube and joining them together

CRAW cubes

Here are the instructions for making each individual cube. You’ll need to make 8 of these.

The individual cubes are made out of cubic right angle weave (CRAW) units.

Start with a comfortable length of thread and a normal size 12 needle – I use about one and a half armspans length of thread at a time, since CRAW uses up the thread fairly fast. When you need to end a thread, just weave the end into the beadwork following the existing CRAW paths until it’s secure, and cut it off. Join the new thread into the beadwork in a similar way.

I’ve used different coloured beads to the original here to make the photos clearer. The original was made entirely using gunmetal coloured beads throughout.

Step 1

Make a 2 by 2 block of CRAW units, leaving enough of a tail to comfortably stitch back in.

(Right click a photo and select ‘view image’ to see a larger version!)

beadmechanics_cube_step1

Step 2

Add another 2 by 2 block on top of this to make a cube.

This will be the centre of the completed cube.

beadmechanics_cube_step2a

This is also a good point to stitch the thread tail in. (It’s also a good idea not to cut it off completely for the time being, just leave it fairly short so it’s out of the way, otherwise you can end up stitching through it and pulling the end back out.)

beadmechanics_cube_step2b

Step 3

We’re now going to add the first ‘frame’ face – one that will eventually have a crystal in the centre. This is done by adding a frame of CRAW to the top of the 2 by 2 cube, anchoring it to the edge beads of this face.

I’ve made a new cube with different coloured beads to highlight the edges of the top face. Here’s how the first unit is attached:

beadmechanics_cube_step3a

First, make the bottom of the new CRAW unit as so:

beadmechanics_cube_step3bi

Then add the sides and top to complete the unit:

beadmechanics_cube_step3bii

We’re now going to work along the edge by adding a second CRAW unit next to the first in a similar way:

beadmechanics_cube_step3c

Now we’re at the corner. This corner CRAW unit is different, it has no edge bead to start from so is just joined to the previous (blue) unit on one side and is suspended in mid-air!

beadmechanics_cube_step3d

The next edge and corner is completed as before – just keep working around the next two sides:

beadmechanics_cube_step3e

Continue around onto the last edge, adding one corner unit and one edge unit.

The second edge unit on this last edge is going to be slightly different, since it has to include a bead from the very first unit we made:

beadmechanics_cube_step3f

Here I’ve added the bottom of the unit, the next RAW face is at the back and includes a bead from the previous unit, a new bead, a bead from the very first frame unit, and an orange edge bead from the central cube. The rest of the unit is then completed as before.

Finally, make the last corner (easier as you now have 2 units to join it to!):

beadmechanics_cube_step3g

Step 4

We’re now going to work on two of the three blank faces. Now is a good time to switch to a curved beading needle, as it will make stitching through the existing beads much easier. Start by turning the beadwork upside-down, so the completed frame is facing downwards:

beadmechanics_cube_step4a

Now start by adding a row of 4 CRAW units along one side, building off the existing beadwork as necessary:

beadmechanics_cube_step4b

Continue on around the corner, adding 3 more units:

beadmechanics_cube_step4c

Now we’re going to work another row back the way we came. First add 4 units above the previous row:

beadmechanics_cube_step4d

Then continue on round the corner, adding 3 more units to finish that row:

beadmechanics_cube_step4e

Now we have two more faces almost complete!

Step 5

Rotate the beadwork around and add 2 units along the remaining edge, separating these two faces into two frames:

beadmechanics_cube_step5

That’s two more faces almost complete!

Step 6

We just need to add the final blank face on the top to complete the cube. I found it easiest to start in the middle and work out. Start by adding 4 CRAW units in the middle on top, like this:

beadmechanics_cube_step6a

Once all 4 are done it will look like this:

beadmechanics_cube_step6b

Just the outer edge left to do! Work around the edges, adding a single row of units all around the outside:

beadmechanics_cube_step6c

Keep going until the top face is complete:

beadmechanics_cube_step6d

And that’s it for the CRAW! The cube should now have 3 blank faces that meet at a vertex, and 3 frame faces that meet at the opposite vertex:

beadmechanics_cube_step6e

The last thing to do is to add the crystals!

Step 7

We’re going to add a 4mm crystal to the centre of each frame face. With the cube orientated as shown in the left-hand photo below, we’re going to follow the thread path shown in the right-hand photo from ‘a’ to ‘b’ to add a crystal to the top face:

beadmechanics_cube_step7

This is shown in more detail in the photos below. First work through the beadwork to exit the bead shown, then add the crystal and continue:

beadmechanics_cube_step7a

Work around through the beadwork following the threadpath shown above and stitch back through the crystal, like this:

beadmechanics_cube_step7b

Now add a crystal to the other two remaining faces. Note that point ‘b’ in the threadpath of the top face is point ‘a’ for the next frame (as shown in the right-hand photo above). Once you’ve completed this second face, the thread will be in the correct place to start the frame on the left-hand side. You should end up with all three crystals pointing towards the top vertex, like this:

beadmechanics_cube_step7c

Don’t end the thread yet, you’ll need it to complete the hinges.

Up to this point all the cubes are identical, so just repeat the steps above to make all 8 in the same way. Then it’s on to joining them together!

Adding the hinges and joining them together

We’re now going to add some modified right angle weave (MRAW) hinges to each cube and join them together. I’ve followed the same sequence of joining them as I used for the model, so you can refer back to the photos at the start of this post while joining the beaded cubes together.

Cube 1

The hinge pattern for cube 1 looks like this:

beadmechanics_cube_1

The number next to each hinge is the cube it joins to. The first hinge we’re going to add is the one labelled ‘4’ in the photo above. Turn the cube so it’s orientated as shown in the photo below and work through the beadwork to exit from the bead shown:

beadmechanics_cube_cube1_a

Now we’re going to add the hinge beads along the edge using the MRAW thread path (see the beginning of the post for more about this stitch). I’ve used orange for the hinge beads so they show up clearly.

First add one bead and continue on through the top of the next MRAW unit (left photo). Then loop around the top of this unit, through the beads indicated in the right photo:

beadmechanics_cube_cube1_b

This extra loop makes sure the hinge beads are held in place nice and securely. Continue along the edge adding in two more hinge beads, following the thread path as shown:

beadmechanics_cube_cube1_c

You want to keep a fairly medium tension here – too loose and the hinge will be unstable, but too tight and you won’t be able to join it to the next cube.

Turn the beadwork so you’re looking at the hinge from the other side. Work along through the beads following the MRAW thread path as shown on this side:

beadmechanics_cube_cube1_d

The hinge beads should now be held in place with stitches on both sides.

Add in the second hinge (the one labelled ‘2’ in the photo) in the same way, so you have a cube that looks like this:

beadmechanics_cube_cube1_e

Weave the end of the thread into the beadwork so it’s secure, and trim it off.

Cubes 2 – 7

For cubes 2 to 7 you’ll add one new hinge, and join to another on a previous cube. For each cube I’ve marked on the photo which other ones they join to, and indicated which is the shared hinge with a circle around the number.

Cube 2

Here’s the hinge pattern for cube 2:

beadmechanics_cube_2

This cube joins to cubes 1 and 3, as labelled. I’ve put a circle around the shared hinge – you don’t need to add this one, just join to it.

So for cube 2 we’re first going to add the hinge labelled ‘3’ using MRAW, just as for cube 1. We’ll end up with a cube that looks like this:

beadmechanics_cube_cube2_a

I’ve made it a slightly different colour so you can tell which cube is which! Now we’re going to join it to the shared hinge on cube 1. Bring the two cubes together as shown on the left:

beadmechanics_cube_cube2_b

The edges we’re going to join are marked with a dot. On the right I’ve moved the cubes so these edges meet.

Join cube 2 to cube 1 following the exact same MRAW thread path as before – only this time you don’t need to add an extra bead, just use the one from the hinge on cube 1:

beadmechanics_cube_cube2_c

The MRAW thread path is exactly as before:

beadmechanics_cube_cube2_d

Once you’ve done one side, rotate the hinge so you can reinforce the other side:

beadmechanics_cube_cube2_e

That’s it, you’ve joined the first two cubes together!

beadmechanics_cube_cube2_f

Cube 3

The hinge pattern for cube 3 is shown below – this one joins to cube 2 using the existing hinge (marked with a circle).

beadmechanics_cube_3

Cube 4

Cube 4 joins to cube 1 on the hinge labelled below:

beadmechanics_cube_4

Cube 5

This cube joins to cube 3 as shown:

beadmechanics_cube_5

Cube 6

Cube 6 joins to cube 4:

beadmechanics_cube_6

Cube 7

This cube joins to cube 5:

beadmechanics_cube_7

Cube 8

The final cube is a bit different – you don’t need to add a new hinge, just join it to the existing hinges on both cube 6 and cube 7 as shown:

beadmechanics_cube_8

The finished cube

That’s it! You should now have a complete folding cube!

beadmechanics_cube_verrier

If you want to share some photos of your completed cube I’d really like to see them! You can always head over to my facebook page and post them there!

Beaded machines, Beadwork

Folding Cube

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:

cube2_verrier

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!