Beadwork objects, Polyhedra, Tutorials

The Saturn Box Tutorial

There is now a standalone tutorial available for the Saturn Box!

The Saturn Box is a beaded geometric box I designed in 2020 for the Beadworkers Guild Journal. The tutorial originally appeared in issues 87 to 90 of the journal between 2020 and 2021.

At the time the Saturn Box was the most complicated piece I’d ever designed (or written instructions for!). It was during lockdown and I was really focussing on beadwork as a distraction. I’d never made a beaded box before, so wanted to try something new for the journal.

It combined a few different ideas I had been playing around with and thinking of how to incorporate into a bigger design – the ring of half-stars and the half-diamond finish to the edges of the bowl in particular. It’s also one of the few of my pieces that includes crystals as well. I tend to keep geometric pieces to purely peyote stitch and Delicas, but the inside of the bowl was just missing something, and that something was crystal bicones!

Of course, as soon as I included them Swarovski announced they were going to stop selling crystals to beaders – typical! Fortunately I found Preciosa made a bicone in a similar (and possibly slightly better!) colour to accent the Delicas.

The original idea for the box started off with a near-miss Johnson solid. These are polyhedra that don’t quite have regular polygon faces, so aren’t one of the 92 Johnson solids, but are so close to being so you can make them pretty well with regular polygons. Some of the known near-miss Johnson solids have unusual patterns of polygons on their surfaces which offer lots of design possibilities! The particular shape I decided to base the box on is a near-miss discovered by Robert Webb:

Image of a near-miss Johnson solid consisting of hexagons, triangles and pentagons.

This polyhedron has hexagons at the top and bottom, and a ring of triangles in the middle of upper and lower rings of pentagons. This shaped seemed ideal to base a box on, as it has a clear top and bottom and could be split along the central ring of triangles to make the lid and base.

The ring of triangles would also allow me to incorporate the half-star idea I’d been playing around with into the design to form a ring around the box. I used to be an astrophysicist, and studied planets in particular, so that led me immediately to thinking about Saturn! That in turn led me to my colour inspiration – the false colour images of the aurora on Saturn:

Image credit: ESA/Hubble, NASA, A. Simon (GSFC) & OPAL Team, J. DePasquale (STScI) & L. Lamy (Obs. Paris).

These images were taken with the Hubble Space Telescope in 2017, and show the aurora at the North Pole of Saturn. These aurora mostly emit ultraviolet light, rather than visible light like the aurora on Earth. The image above is actually a composite image – a visible light photograph of Saturn from Hubble combined with a false colour representation of observations of the ultraviolet light captured using one of Hubble’s spectrographs. The false colour representation shows the ultraviolet light emitted by the aurora in blue, and I just love this representation of the physics and had to include it in the box design, with silver-lined beads doing their best to bring to mind this image!

After a lot of engineering and even inventing a new component I ended up with the final design! The lid of the box sits on the ring of half-stars, standing on six “spikes” formed by the points of the blue stars on the lid. I was really happy with the final design!

I’ve been meaning to write a standalone tutorial for this piece for a while – the size and complexity of the project was a bit daunting though! I finally convinced myself to sit down and start it before Christmas, and I’m really glad to now have it available in my Etsy shop.

I’m also really grateful to the small army of pattern testers who stuck with me while I tried to get this all written down in a reasonable size document the last few months!

If you decide to try making the box I hope you will enjoy it – although it is a lot of work, it’s also a varied piece with lots of different types of peyote shapes combined together. There are triangles, squares, pentagons, hexagons and some others you may not be familiar and some new ones invented just for this piece!

Although it was challenge to design and document this piece it’s a challenge I’d gladly undertake again – in fact I’m thinking of doing a few more planetary-inspired boxes!

Bangles, Polyhedra, Polyhedral Angle Weave

Ring of Snub Disphenoids

I’ve been working on a tutorial recently so haven’t done that much beading, but have found some time to try out a new bugle bead shape. It’s a ring of 14 Snub Disphenoids:

A Snub Disphenoid is one of the Johnson Solids, and is otherwise known as J84, and is made up of 12 triangles. These polyhedra are joined together with square pyramids (which are also one of the Johnson Solids!) to create the ring.

I learnt about this shape on Rafael Mill├ín’s GeoMag website. It’s actually about a degree short of being a perfect ring, but you can’t tell when it’s made with beads!

I used 12 mm bugle beads, nylon monofilament and what I call polyhedral angle weave – which is just regular angle weave used to make the various polygons that make up a polyhedron. It can just about be worn as a bracelet, although I think I will hang it up in a window as a geometric sun catcher instead!

Polyhedra

Rhombicuboctahedron

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!

Polyhedra

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.

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!

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!

Beadwork, Polyhedra

Sunburst Variation

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!

Beadwork, International Beading Week, Polyhedra, Tutorials

Interlinked Tetrahedra Tutorials

Five Colour Interlinked Tetrahedra

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.

newcols

Kits

Kits for both versions are available in my etsy shop!

BeadMechanics_InterlinkedTetra_Kit3

Happy Beading!

BeadMechanics_InterlinkedTetrahedra