# Gyroelongated Square Bipyramid Kaleidocycle

Here’s my latest kaleidocycle!

The book “A Mathematical Tapestry” by Peter Hilton and Jean Pedersen has a discussion of the various rotating rings (kaleidocycles) of polyhedra that are possible, including a diagram of one made of 14 hexacaidecadeltahedra – better known as gyroelongated square bipyramids. It was such an intriguing shape I decided to try and construct one from bugle beads. The finished ring is fascinating – in one configuration it’s rigid but in others it’s completely flexible with many degrees of freedom.

It also makes a great bracelet as it will flex enough to fit over your hand but can then be rotated into the rigid configuration to stay on your wrist!

I made the original version with 12mm beads (Matsuno size 5 twisted bugle in Silver-Lined Bronze), but it works with other sizes. The one above is made with 9mm beads (Toho size 3 bugle in Silver-Lined Teal, Opaque Turquoise and Opaque Jet). The bugles just need to be large enough for several thread passes! I use 0.25mm monofilament nylon illusion cord as the thread, which is strong enough not to be damaged by the bugles but thin enough to allow enough passes through each bead.

I did briefly try making a peyote version using triangles (in this case the units are Eva Mari Keiser’s “gyro-eggs”), but unfortunatly it didn’t work very well as the shapes lose their defining sharp geometric shape.

So what is a Gyroelongated Square Bipyramid? It’s two square pyramids (the square bipyramid part) connected with a strip of 8 triangles formed into a ring (the gyroelongated part). Here’s a square pyramid and a square bipyramid (aka an octahedron):

Here’s a strip of 8 triangles which can be made into a ring to make a square antiprism:

Put this in the middle of the square bipyramid (octahedron) and you get a gyroelongated square bipyramid:

It’s an interesting shape! The two pyramids are at angles to each other and you can find pentagons made from 5 triangles at almost every corner.

They can put together into a kaleidocycle by using evenly spaced bugle beads from the middle (the gold ones in the photo above) as shared hinges. These hinges will be at an angle to each other if you look at the shape from the side, rather than parallel. Turns out that this is the critical feature for getting a kaleidocycle to work, and it’s why you end up with sets of mirror polyhedra in a complete cycle.

Below is a tutorial on how to make a four-colour version of this kaleidocycle! Please be careful with it though – remember that it’s made from fragile glass beads which may have sharp edges, so should be treated with care!

# Truncated Tetrahedron

When I made the Sunburst dodecahedron I thought that the technique could be easily adapted to make other polyhedra. The flexible nature of the edges make it easy to adapt to shapes with different angles between the faces. I recently tested this idea by making a truncated tetrahedron, the piece below is the result:

A truncated tetrahedron has four hexagonal faces and four triangular faces, so the resulting shape looks quite complicated, and looks very different from different angles!

It’s a bit smaller than the original dodecahedron, but not by much. Here they are side-by-side for comparison:

I really enjoyed making this piece and I was pleased by how easily the components could be used to make both triangular and hexagonal faces. I have a lot more ideas for other shapes now too!

Instructions for both these pieces are in the Sunburst tutorial in my Etsy shop! (And a huge thank you to Sue Harle for permission to use her original diagonal tubular peyote technique in the tutorial!)

Please be aware that a number of phishing websites have come to light over recent days that have copied a large number of beadwork and craft listings from Etsy, apparently in order to scam people out of payment information. Unfortunately some of my tutorial listings appear on some of these sites. These are not genuine listings!

My tutorials are only available from my Etsy shop, Interweave and here on my website.

You can find a full list of those available on the tutorials page.

Finally, please be careful when following links from sites such as Pinterest – always check that the link is genuine before clicking! Be(ad) safe out there!

# Rick Rack Dodecahedron (with Tutorial!)

I was challenged a while ago to see if I could make a dodecahedron out of rick racks. After a bit of experimenting I ended up with this, a Contemporary Geometric Beadwork rick rack dodecahedron!

It’s made from small 5-sided rick racks joined together with warped squares. The rick racks are the light blue beads you can see, zipped together at the top with dark blue beads. The warped squares joining them together are the dark blue diamonds you can see in-between each rick rack.

# New tutorial: Hypernova

Do you remember this piece I posted photos of a while ago? Well, there’s now a tutorial for it available in my Etsy shop!

I’ve named the piece Hypernova as it’s made from hyperbolic hexagons – or warped hexagons as they’re better known! If you want to learn more about the piece my original post about it is here.

# 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.

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!)