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!

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.

A while ago I found an interesting paper about rotating rings of tetrahedra (aka kaleidocycles) by Jean Pedersen¹. 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:

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!

 

¹The paper is “Braided Rotating Rings”, Jean J. Pedersen (The Mathematical Gazette, 62, 1978).