This is the second part of my study of Platonic and Archimedean solids made from polyhedral weave – the Archimedean Solids!

I previously posted the series of the Platonic solids made with 4mm crackle glass beads and 0.25mm nylon monofilament, and have now completed the set with the 13 Archimedean solids. Unlike the first series however, not all of these work well with round beads (specifically, the ones with lots of triangles – those in the third photo above). There’s a closer look at each shape individually below.

The truncated tetrahedron – which is made up of triangles and hexagons. This one works well, and is a good candidate for a beaded bead (or the basis of a beaded bead).

The cuboctahedron – which is made up of triangles and squares. This also works well, despite being quite a small shape, and is another good candidate for a beaded bead.

The truncated cube – which is made up of triangles and octagons. I wasn’t sure how well the shapes with the larger polygon faces would work as sometimes they can be quite unstable when constructed with polygon weave. However, they actually all worked very well!

The truncated octahedron – which is made up of squares and hexagons. This also worked really well, although is a bit too large to be a beaded bead.

The rhombicuboctahedron – which is made up of triangles and squares. This one did not work so well, it has slightly too many triangles close enough together that there isn’t enough space when made with round beads, so it’s distorted.

The truncated cuboctahedron – which is made up of squares, hexagons and octagons. This did work well, and could be the basis of a large beaded bead.

The snub cube – which is made up of triangles and squares, and is also one of the chiral Archimedean solids – that is, there is a mirror image of this one as well (although I only made one!). This is another one with a lot of triangles close together and as you can see did also not work well with round beads.

The icosidodecahedron – which is made up of triangles and pentagons. This just about works, despite having a lot of triangles close together as well. It’s also very spherical, so would be a good companion with the dodecahedron from the Platonic series.

The truncated dodecahedron – which is made of triangles and decagons. This is another one with decagon faces that works surprisingly well!

The truncated icosahedron – which is made from pentagons and hexagons. This is a classic beaded bead that you will have seen many times before!

The rhombicosidodecahedron – which is made from triangles, squares and pentagons. I thought this would work better, but unfortunately has too many triangles too close to each other and as a result just doesn’t work with round beads.

The truncated icosidodecahedron – made from squares, hexagons and decagons. This is the largest one in the series, and was a surprise how well it worked and how stable it is!

The snub dodecahedron – which is made up of triangles and pentagons, and is the other chiral Archimedean solid. This did not work at all! Way too many triangles to work with round beads unfortunately, and there’s no way to get it too look even remotely symmetric.

This brings the study to a close – several of these will be useful in future, and it was interesting to see which of the Archimedean solids worked and which did not. Here’s all of them together!

One of the stitches I use a lot for geometric shapes is polyhedral weave – this is like right angle weave, but used to make the various polygons that make up the faces of a polyhedron. It works well with both bugle beads and round beads, and I’ve made a variety of shapes over the years – including some near-miss Johnson Solids and some more complex shapes. However, I’ve never systematically made each one of the Platonic and Archimedean Solids, so I started a study of each using 4mm crackle glass beads and 0.25mm nylon monofilament.

Here are the results for the Platonic solids!

The first and smallest is the tetrahedron. Because of the round beads it doesn’t first look like a tetrahedron – but if you consider that each bead is one edge of the shape you can see the structure underneath. I was a bit concerned that it wouldn’t be possible to weave in the thread on this one, as there isn’t much space, but it actually turned out fine. Even though it’s a simple shape I really like it, and will definitely be using it as a component in other work in the future!

The next two shapes are duals of each other – the octahedron and the cube. If you connect the central point of each face of an octahedron you end up with a cube – a vice versa. The beaded versions of these two shapes therefore look very similar when made with round beads, as you can see in the photo below. The one on the left is an octahedron and the one on the right is a cube – the only difference is the direction the thread goes – otherwise they look almost identical! Made this way the cube is just a standard cubic right angle weave unit, while the octahedron is different thread path – which opens up some interesting design options for combining shapes in larger designs.

The last two shapes are also duals of each other – the icosahedron (left) and the dodecahedron (right). I’ve made many of these polyhedral RAW dodecahedrons over the years, but I don’t think I’ve ever made an icosahedron. Although they are essentially the same shape overall when made this way, I think the different orientation of the beads in the icosahedron make it a little bit more interesting.

This was a very simple study of the five Platonic solids, but has provided several design ideas. The next task is the Archimedean solids!

The last in the series of polyhedra rings is a ring of 17 Disphenocingulum:

A Disphenocingulum is Johnson Solid J90, as is made up of 4 squares and 20 triangles. It’s sets of triangular pyramids joined together with pairs of squares:

It’s not the easiest shape to make, as it’s easy to lose track of the triangles, but it got easier after 17 of them! It’s made with polyhedral angle weave, 12mm bugle beads and nylon monofilament like the others in the series.

The disphenocingulum are joined together square pyramids on the outside of the ring, with the base of the pyramid linking up with a pair of the squares on the J90s to make a ribbon of squares all around the edge.

Like most of this series, I learnt about this shape on Rafael Millán’s GeoMag website. It’s much larger than the other three in this series, and unfortunately it’s not very stable at all. The disphenocingulum themselves tend to collapse at the slightest touch, and generally look a little bit warped. This means the ring is not very stable as well, as the polyhedra need to be exactly in the right position to keep it in shape.

This was the last in a series of rings of polyhedra – here are all four together:

From left to right it’s a ring of 14 snub disphenoids (J84), a ring of 15 hebesphenomegacoronona (J89), a ring of 16 sphenocoronae (J86) and this ring of 17 disphenocingulum (J90). This was a fun series to make, and I think I’ll try and hang them on a wall somewhere they will catch the light, as I love how the rainbow finish twisted bugle beads sparkle in the sun!

Next in the series of bugle bead rings of polyhedra is a ring of 16 Sphenocoronae!

A Sphenocoronae is another Johnson Solid – this time J86. It’s made up of 12 triangles and 2 squares. It’s essentially two pentagonal pyramids on a base of 2 squares, with 2 more triangles filling in the gaps:

It’s quite a nice shape to weave together, and like the previous two rings this one is made with 12mm bugles, nylon monofilament and polyhedral angle weave. It does use an extra “linking” bugle to join the polyhedra together – forming a tetrahedra in between each sphenocoronae on the outside of the ring.

Like the ring of snub disphenoids, I learnt about this shape on Rafael Millán’s GeoMag website.

This one is quite a bit larger than the other two, so doesn’t work as a bangle with 12mm beads. I’m enjoying making this series though and have one more shape to try!