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.
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!
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.
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!
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.
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!
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.
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!
Here’s a variation on my Sunburst dodecahedron from a while back. Unfortunately it wasn’t very sunny when I tried to photograph it though!
It’s made in the same way with Sue Harle’s diagonal tubular peyote technique, but the construction is a bit different. Here it is side by side with the original version:
The difference is where the outward points are on each side – in the original they are in the middle of the edges of the polyhedron, while in the variation they are at the vertices. I really like the contrast between the two shapes!
This technique is so flexible – which means I have a lot more polyhedra like this planned!
The original five colour version of the bugle bead interlinked tetrahedra is available here as a pdf: Five Colour Interlinked Tetrahedra Tutorial. This version uses a different colour for each individual tetrahedron.
Three Colour Interlinked Tetrahedra
A three colour version of the interlinked tetrahedra tutorial is available here: Three Colour Interlinked Tetrahedra Tutorial. This version uses three different colours of bugles in each tetrahedron.
The animations above were made using Stella4D Pro.
Additional Colourways
Diagrams for other colourways are available here: Interlinked Tetrahedra Additional Colourway Diagrams. These are diagrams for each step for the silver-yellow-green, yellow-orange-red, silver-blue-purple and green-yellow-silver-blue-purple colourways.
Kits
Kits for both versions are available in my etsy shop!
It’s the start of International Beading Week! The week is a world wide celebration of the craft, aiming to bring beaders together and encourage people to try some beading!
There are a lots of events being held this week – you can read about them here. There’s also a wealth of free patterns that have been donated by designers all over the world in celebration – and you can browse through them all here.
This year I’m acting as a Guest Ambassador, and as part of that I’ve written a free tutorial for the bugle bead interlinked tetrahedra design!
You may remember this shape from a previous blog post about it. It’s based on the origami model Five Intersecting Tetrahedra by Thomas Hull. With his permission, and with the help of the brilliant geometric software Stella4D for the diagrams, I put together a step by step guide on how to assemble the beaded version. The pdf of the tutorial is available from the IBW downloads page and is also linked below!
The piece is a fun geometric challenge, and requires very little previous beading experience so is suitable for anyone thinking of trying some beadwork for the first time as well!
A new tutorial is available in my Etsy shop for the Rhombic Mosaic icosahedron! This icosahedron is Not Made From Triangles! Instead it uses peyote diamonds for a new take on this basic geometric shape!
This method of making an icosahedron means than you get distinct triangular faces rather than the diamond shaped faces you get if you use triangles. Here’s a comparison of two – Rhombic Mosiac is on the left and an icosahedron made from peyote triangles on the right:
I really like the effect this construction method gives! I started working on this idea last year with my initial Not Made From Triangles tetrahedron:
Since then I’ve tried a few other shapes as well – here is a Not Made From Triangles octahedron along with the triangle version:
I really enjoy making polyhedra using this method and have a number of other shapes already planned!
The pattern in the tutorial uses five different colours for the faces of the icosahedron and has every possible combination of each five at each vertex exactly once. Both colourways are in the tutorial too!
A little while ago I wrote about the Beaded Johnson Solids Project set up by Diane Fitzgerald, a project to make all 92 Johnson solids out of beads. I volunteered to make number 68, the Augmented Truncated Dodecahedron. After a lot of time spent making decagons here it is!
I’ve named the beadwork version Reflecting Pool. In total it’s made from 11 decagons, 1 pentagon, 5 squares and 25 triangles. To give a better idea of the shape here’s an animation of the polyhedron made using Stella4D Pro:
Here’s the net of the beadwork shape before it the final assembly. I think it looks like a series of connected pools, which is where the name Reflecting Pool came from.
Before I started joining the beadwork net together I did a trial run with a paper model – fortunately my beadwork skills are better than my papercraft skills!
I really like how the shape turned out. The decagons seem quite sensitive to even the small size variations in the beads and so ended up slightly concave rather than as flat as the ones I made initially. However, I really like how they end up looking when joined together.
I’m tempted to make a plain truncated dodecahedron, with just decagons and triangles, however it might have to wait a while until I manage to make 12 more decagons!
Bead Mechanics 