Or is it more of a cube? It is based on a rhombicuboctahedron, and uses the same technique as I used for this rhombicosidodecahedron, a variant of the hyperhedra method.

It took me ages to get the colours picked out but I’m really happy with how the yellows turned out. Bit of a change from my usual blues but definitely going to try more yellows in future!

Unfortunately I discovered when I went to photograph it that my camera now has a column of defunct pixels in the middle of the image – so sorry about the odd line down the middle of the photo!

Polyhedra, Tutorials

Interlinked Tetrahedra Diagrams for Additional Colourways

I had a bit of free time this week so have put together some diagrams for some different colourways for the interlinked tetrahedra shape!

There are step-by-step diagrams for the silver-yellow-green, yellow-orange-red, silver-blue-purple and green-yellow-silver-blue-purple colourways. The pdf is available here: Interlinked Tetrahedra Additional Colourway Diagrams.

They match the steps in the original 3- or 5-colour instructions, which you can find here.

Happy beading!


Bugle Bead Airplant Stand

I made this airplant stand last year. It’s based on an icosidodecahedron, and is both partially augmented and partially excavated.

Augmentation means that you add another shape to each face – in this case it’s a tetrahedron on each triangle face. Since an icosidodecahedron has both triangle and pentagon faces, this means only some of the faces have been augmented, so it’s a partial augmentation.

Excavation means sort of the opposite – where you would join five triangles to make a dome or pyramid over a pentagon face to augment it, excavation is the reverse – the dome or pyramid points down into the centre of the polyhedron, making a bowl-like depression. Because this is only done to the pentagon faces again it’s a partial excavation.

The combination of the two gives and interesting combination of peaks and valleys that I really like, and also makes it an excellent air plant stand! The shape itself is just made by using a modified form of right-angle weave to place the bugles over each edge of the polyhedron.

I used 30mm bugles meaning the finished piece is quite large, so it became home to a Tillandsia Xerographica, one of the bigger airplants! Here it is back when I finished it last summer:

And here it is now – the airplant has a beautiful flower spike on it at the moment so is clearly happy with the stand!

The flowers are really interesting – most of the spike is the flower bract, while the flowers themselves are quite small with tightly closed pale pink petals:

This isn’t my first attempt at combining plants and beads either – I’ve made a few smaller airplant stands from bugle beads too, although they don’t currently have any airplants in them.

They’re only suitable for very small plants, and the ones that were in them have outgrown them. They’d probably be better if they were the other way up, although I’d need to take care to find airplants that are happy growing upside down if I did that.

Still a bit of a work in progress, but a fun series of experiments!

The animations of the icosidodecahedron shown in this post were created with Stella4D Pro.

Beadwork, Polyhedra, Tutorials

New Tutorial: Mira Star

A new tutorial is available in my Etsy shop for Mira Star! This is a truncated octahedron made from warped hexagons in a similar way to Hypernova, but with a twist – it uses a mix of 1-drop and 2-drop peyote to create the different length sides and add extra dimension to the piece!

A truncated octahedron is an Archimedean solid, and it has square and hexagon faces:

I think the combination of the two different types of faces with the different types of peyote works really well! The shape looks very different from different angles:

I named it Mira Star as the different lenghs of the sides made me think of variable stars, stars which periodically increase and decrease in brightness. A Mira variable is a particular type of these variable stars.

I love the orange silver lined beads I used in this piece, but I also made a version in green as well:

I really like this version too, not sure which is my favourite!

I decided to add a cord to this one so it can be hung as an ornament – it looks really good like this as you can rotate to see all the different sides.

Both colourways and a guide on how to make the cord to hang it as an ornament are in the tutorial.

Happy beading!

The animation of the truncated octahedron shown in this post was created with Stella4D Pro.

Beaded machines

Cuboctahedron Prismatic Structure by Sieuwke Bijlsma

I recently wrote about reconfigurable materials – materials or surfaces which can be folded into different shapes in a similar way to kaleidocycles or folding cubes. Diane Fitzgerald posted a challenge in the Johnson Solids Project group on facebook to try making beadwork versions of some of these structures and there have been some amazing responses. I’m really excited to be able to show one of these pieces here, a cuboctahedron prismatic structure made by Sieuwke Bijlsma. It’s absolutely stunning!

Beadwork cuboctahedron prismatic structure by Sieuwke Bijlsma

This piece is a reconfigurable material originating from the research of Johannes Overvelde. You can find more details on the structure in the paper Rational design of reconfigurable prismatic architected materials (Overvelde et al., 2017, Nature 541, 347). It’s based on a cuboctahedron:

Prisms are then added to each face. This is done by placing squares along each edge like so:

When you replace all the faces on a cuboctahedron with prisms like this you end up with a structure that looks like this:

This structure will now fold into lots of different shapes! In beadwork the joins between squares are hinges like those used in a peyote triangle kaleidocycle.

This structure alone is pretty amazing, but it turns out you can join several of them together to make something even more spectacular! If you join two together you get this:

You can then join two of these compounds together to end up with a ‘square’ of prismatic cuboctahedra:

And then you can join two of these ‘squares’ together to get a ‘cube’ of prismatic cuboctahedra!

This is the amazing structure that Sieuwke has beaded!

Because the individual prismatic cuboctahedra will fold into different shapes, the combination of eight of them also folds into different shapes! You can see this in this video by Johannes Overvelde:

Here’s a view of Sieuwke’s beaded structure folded into a different shape:

Here’s another configuration:

The structure is made up of 384 beaded squares and was made over several months. It’s one of the most beautiful beadwork sculptures I’ve seen, and I’m really grateful to Sieuwke for allowing me to show her work to you all!

The photos in this post are copywrite Sieuwke Bijlsma and are used with permission. The prismatic cuboctahedron structure was designed by Johannes Overvelde. The animations in this post were created with Stella4D Pro.

Beadwork, Polyhedra

Hyparhedra Update

About two years ago I posted about Archimedean Edge Hyparhedra – Archimedean polyhedra made by placing warped squares over the edges of the polyhedra. At that point I’d completed 3 of the 13 polyhedra, and started 3 more. I thought it was about time for an update on my progress on this series – I now have 7 of them completed!

The original 3 are in the middle – the green truncated octahedron, the black and white cuboctahedron (this one ends up looking more like its dual shape, the rhombic dodecahedron) and the blue and brown truncated tetrahedron. The new shapes are, anticlockwise from the lower right, the white, red and blue snub cube (which also ends up looking more like its dual, the pentagonal icositetrahedron), the white, brown and red rhombicosidodecahedron, the brown and red truncated icosahedron and the blue and black truncated cube.

Here’s a close up of the snub dodecahedron. This one is a really interesting shape, and it’s also a chiral polyhedron – it looks different reflected in a mirror – so I might make a mirror image to match when I eventually finish this series! Because of the angle of the edges of this polyhedron the warped squares end up curving the wrong way to form surface, so it ends up inside out and looking like its dual shape like the cuboctahedron.

The rhombicosidodecahedron however workd really well with the warped squares! It took me a while to finish this one as it was a lot of squares (120!) but I’m really pleased with how it turned out.

I’ve made a similar shape to this before, the rhombicosidodecahedron hyparhedron variation, which uses warped hexagons in place of the white triangular faces.

The truncated icosidodecahedron turned out really well too. It didn’t take quite as long as it’s only 60 squares, but was still a bit of a marathon. I really like this shape though, it was one of the very first ones I started and I’m really glad to have finished it at last.

The last shape, the truncated cube, was more challenging. The problem with this one is that it has octogonal faces, which need 8 warped squares to join together. Unfortunately, 8 warped squares joined together are not flat or concave, but instead start to ruffle and concertina and don’t make a very good interpretation of a flat shape – here’s my initial attempt::

It just wasn’t going to work, but I realised that if I used 2-drop peyote on the parts of the warped square that join into the octagons then they would be more pointy and the shape would be more concave rather than starting to ruffle like above. Fortunately this worked, and made an interesting shape!

The 2-drop octagons really give it a different character to the other shapes:

I was wondering how I would do the 4 Archimedean solids which have octagon and decagon faces, as I didn’t think they would work with the normal warped squares, so I’m glad I’ve found a solution and can now make the other 3 – a truncated cuboctahedron, a truncated dodecahedron and a truncated icosidodecahedron.

That leaves me with the snub dodecahedron and rhombicuboctahedron to do with the normal 1-drop warped squares, both of which are in progress. I think the snub dodecahedron will end up like the snub cube and cuboctahedron, looking more like its dual. I’m not sure about the rhombicuboctahedron yet, it could go either way or not work at all, and might have to be done with the 2-drop method instead. Hopefully it will take me less than 2 years this time to complete the set!


More Interlinked Tetrahedra

I’ve been trying out some new colour combinations for the bugle bead Interlinked Tetrahedra! Here’s a new version of the original five-colour one in silver, yellow, green, blue and purple:

And here’s the three-colour version in silver-blue-purple:

And another version in green, yellow and silver:

I’ve enjoyed playing with the different colour combinations, and I still really love making this piece, it works up quickly and is a really interesting mathematical object. I have a lot of them scattered around my house now!

You can find the tutorials for both the 5- and 3-colour versions here, and I have kits for these new colourways along with the originals in my Etsy store.

Beaded machines, Beadwork, Tutorials

Beaded Reconfigurable Materials

Reconfigurable materials are materials without a fixed shape – surfaces with a shape that can be changed to different configurations. They have some similarities to kaleidocycles and folding cubes, as you can see from this video from the Harvard John A Paulson School of Engineering and Applied Sciences:

Here’s another video from Johannes Overvelde, one of the researchers who studies these surfaces:

Diane Fitzgerald recently posted a challenge in the Johnson Solids Project group on facebook to try making beadwork versions of these structures. Lots of people rose to the challenge and before long there were lots of photos of beaded reconfigurable materials!

Here’s one I made in response to the challenge:

This is based on the hexagonal prism unit from the paper Rational design of reconfigurable prismatic architected materials (Overvelde et al., 2017, Nature 541, 347), which you can see in subfigure k in Supplementary Figure 7.

You can see that it follows the outline of a hexagonal prism, with pairs of squares added to each edge. It reconfigures to a lot of different shapes:

It’s interesting to see just how different it can be made to look! However, it is also however very fragile, as the peyote squares put the corner beads under a lot of pressure, so you need to be very very careful with it (I had a sliver of glass ping off one of the beads while folding it into a different shape!).

If you want to try making one of these fragile but interesting shapes, here’s a brief walkthrough of how I made this hexagonal prism unit. I used the same sized squares as in the Beaded Johnson solid project and used size 15 seed beads for the hinges.

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Beaded machines, Tutorials

Decagonal Kaleidocycle Tutorial

Some while ago I made a decagonal kaleidocycle using irregular tetrahedra based on a paper model of a half-closed decagonal kaleidocycle by Gijs Korthals Altes. Because the tetrahedra have different length sides the different faces you see as it turns are all different shapes.

I drafted a tutorial for this a while ago, and have finally got around to finishing it – and here it is!


This tutorial is also available as a pdf!

This kaleidocycle is made from ten tetrahedrons. Each tetrahedron is made from six peyote ovals. There are two different types of tetrahedra and each of these contains four different types of ovals.

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Beadwork, Polyhedra

Johnson Solid J40

Here is my contribution to the UK Johnson Solid Project – number 40, an elongated pentagonal orthocupolarotunda!

This one is quite a bit smaller than the J68 I made for the US project, but still took me a while to make as it has a lot of components. There are 15 triangles, 15 squares and 7 pentagons in total, and it is made up of a pentagonal cupola (which is Johnson solid number 5) and a pentagonal rotunda (Johnson solid number 6) joined together by a decagonal prism (essentially a ring of ten squares around the middle).

The J68 I made also has a pentagonal cupola as part of the shape (this is a decagonal face made up of a pentagon surrounded by squares and triangles) so I thought it would be nice to use the same colours to highlight the connection between them and the two projects.

The shape is interesting as it looks completely different from different sides. I really like the pentagonal rotunda side (a partial icosidodecahedron made from pentagons and triangles) as well.

I really glad that I got to make a second Johnson Solid for the UK project – it’s been fun making a piece that’s very different to the other shape!