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.

# 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.

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

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.

# 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!

# Tutorial

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.

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.

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.

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!

# New Tutorial: Rhombic Mosaic

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!

# Oval Kaleidocycle Tutorial

This video of a kaleidocycle made from peyote ovals was the first post on my blog almost four years ago.

The tape on my hands in the video is to cover up scrapes from rowing, not beading the kaleidocycle – and since I can’t go out to row at the moment I took the opportunity instead to finish the tutorial for it that I drafted several years ago to share with you all!

# Tutorial

This tutorial is also available as a pdf!

This kaleidocycle is made from six tetrahedrons. Each tetrahedron is made from six peyote ovals. The ovals are all identical apart from the two accent colours used in the pattern. There are then two different combinations of the ovals to form the tetrahedra – pattern 1 and pattern 2, which is a mirror image of pattern 1.

# PDF Tutorials

I’ve now finished creating pdf versions of all the tutorials here on the blog – added to the two from last week are the Folding Cube and the gyroelongated square bipyramid kaleidocycle, which I’ve renamed Solar Cycle since it’s easier to say and the shape makes me think of a simple drawing of the sun!

Here are all four tutorials – click on the name to download the pdf!

Folding Cube

Solar Cycle

Spherical Harmonics

Trefoil Knot Kaleidocycle

# Rhombicosidodecahedron Hyparhedron Variation

Here’s an interesting variation on a hyparhedra – a rhombicosidodecahedron which uses both warped squares and hexagons.

A rhombicosidodecahedron is an expanded dodecahedron with rings of squares and triangles surrounding the pentagon faces. This means that this beaded version can be thought of as an expanded version of Hypernova! Here they are side-by-side:

As you can see it’s pretty big! It took a lot longer to bead than I thought it would, but I’m very happy with how it turned out.

The idea for this started with a geomag 1.5 scale rhombic hexacontahedron by Rafael Millán, which I came across earlier this year. At about the same time I was working on warped square hyparhedra, and I realised that this polyhedron would be possible as a hyparhedron using a combination of both warped squares and warped hexagons. Essentially it’s a variation on the warped square rhombicosidodecahedron hyparhedron where the three warped squares making up the triangular faces are replaced by a single warped hexagon.

I’ve wandered into this idea before with the truncated tetrahedron hyparhedron – on the left in the photo below is the warped square hyparhedron version and on the right is the variation with the triangular faces replaced with warped hexagons:

It’s interesting to see that it also works with a larger shape. I’m still working on the plain hyparhedra version of the rhombicosidodecahedron, but it will be great to see them side-by-side when finished too!

This one took too long to create a tutorial, but here’s a layout diagram if you want to attempt it! In total it needs 20 warped hexagons and 60 warped squares. The warped squares sit over the edges of the pentagons, with the peaks and the corners and the valleys meeting at the centre. The diagrams below show the top half of the rhombicosidodecahedron. On the left is the position of one warped square outlined in red – the increases are shown as dashed lines and the peaks marked with circles. On the right a whole set of warped squares is shown around the top of the shape.

The warped hexagons join it all together. They sit at the centres of the triangular faces and are “zipped” to the warped squares. The diagram on the left shows how one warped hexagon joins to one warped square. The diagram on the right shows a set of warped hexagons around the top of the shape.

I made the warped hexagons completely, and then joined the warped sqaures to them. The angles in the square faces are quite tight, so I tried to always start the join towards them and end it at the pentagon side, so there was more space to work. As ever with these shapes, a curved beading needle is essential!

It took me a while to get my head around the shape, but it eventually clicked! Just ask if you have any questions about it!