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.

Kits

Kits for both versions are available in my etsy shop!

BeadMechanics_InterlinkedTetra_Kit3

Happy Beading!

BeadMechanics_InterlinkedTetrahedra

Beadwork, International Beading Week, Tutorials

Happy International Beading Week!

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!

IBW Logo

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!

InterlinkedTetrahedra_BeadMechanics

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!

Happy beading everyone!

People Chain x 12

Click to access BeadMechanics_InterlinkedTetrahedra.pdf

People Chain x 12

Beadwork, Polyhedra, Tutorials

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!

BeadMechanics_RhombicMosaic2

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:

BeadMechanics_RhombicMosaic3

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:

BeadMechanics_NotMadeWithTriangles2  BeadMechanics_NotMadeWithTriangles1

Since then I’ve tried a few other shapes as well – here is a Not Made From Triangles octahedron along with the triangle version:

BeadMechanics_RhombicMosaic4

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!

Happy Beading!

BeadMechanics_RhombicMosaic1

Beadwork, Polyhedra

Augmented Truncated Dodecahedron J68

A little while ago I wrote about the Beaded Johnson Solids Project set up by Diane Fitzgerald, a project to make all 92 Johnson solids out of beads. I volunteered to make number 68, the Augmented Truncated Dodecahedron. After a lot of time spent making decagons here it is!

BeadMechanics_J68_1

I’ve named the beadwork version Reflecting Pool. In total it’s made from 11 decagons, 1 pentagon, 5 squares and 25 triangles. To give a better idea of the shape here’s an animation of the polyhedron made using Stella4D Pro:

J68

Here’s the net of the beadwork shape before it the final assembly. I think it looks like a series of connected pools, which is where the name Reflecting Pool came from.

BeadMechanics_J68_Net

Before I started joining the beadwork net together I did a trial run with a paper model – fortunately my beadwork skills are better than my papercraft skills!

BeadMechanics_J68_PaperModel

I really like how the shape turned out. The decagons seem quite sensitive to even the small size variations in the beads and so ended up slightly concave rather than as flat as the ones I made initially. However, I really like how they end up looking when joined together.

BeadMechanics_J68_2

I’m tempted to make a plain truncated dodecahedron, with just decagons and triangles, however it might have to wait a while until I manage to make 12 more decagons!

BeadMechanics_J68_3

 

Beadwork, Polyhedra

Augmented Dodecahedron

Making polyhedra using round beads and polyhedral angle weave is my current favourite bead technique! Here’s an augmented dodecahedron made using 4mm beads:

BeadMechanics_Dodecahedron1

This is a dodecahedron with extra dodecahedra added to each face (augmentation). In theory there should be a slight gap between each neighbouring dodecahedron, but with the beadwork you can merge them together to end up with this shape.

It did require quite a lot of concentration to weave but it was still an enjoyable experiment. I’m definitely going to be trying more shapes like this!

BeadMechanics_Dodecahedron2

 

Beadwork, Polyhedra

Near-Miss Johnson Solids

The Johnson solids are strictly convex polyhedra with regular polyhedra as faces – that is polygons with sides and angles that are all the same. Near-miss Johnson solids however are strictly convex polyhedra that almost have regular polyhedra as faces, but not quite. There are actually a lot of interesting polyhedra that meet this definition. And since they are almost regular you can try making them using same sized beads and let the beadwork distort slightly to make up for the slight differences needed.

Here are a few of them made with illusion cord and 4 mm beads using “polyhedral angle weave” (which is just regular angle weave used to make the various polygons that make up a polyhedron).

BeadMechanics_JSNearMiss11

The first one is a truncated triakis tetrahedron, which has 12 pentagon and 4 hexagon faces:

BeadMechanics_JSNearMiss2

This was easy to make and only needs 42 beads. It’s fairly small and makes a nice little beaded bead!

The next is a chamfered dodecahedron. This is similar to a truncated icosahedron but with ten more hexagons:

BeadMechanics_JSNearMiss4

This one has 120 beads and works really well. It’s a bit bigger than a truncated icosahedron and looks very round, definitely one of my favourites!

The third is a rectified truncated icosahedron. This is basically a truncated icosahedron with triangles added between all the faces:

BeadMechanics_JSNearMiss6

This one has 180 beads and is less round but is still an interesting shape!

The next is an expanded truncated icosahedron, which is sort of like a truncated icosahedron version of a rhombicosidodecahedron. It has triangle, square, pentagon and hexagon faces:

BeadMechanics_JSNearMiss7

This has a lot more beads – 360 in total – and is much bigger than the others. It was a struggle to keep it looking reasonably symmetric, but the patterns made up by the combination of pentagons or hexagons surrounded by triangles and squares are really quite pretty.

The last one is a snub rectified truncated icosahedron and is like a truncated icosahedron version of a snub dodecahedron. It’s made up from triangles, pentagons and hexagons:

BeadMechanics_JSNearMiss10

This is larger still at 450 beads and does not work well at all! The faces are just too far away from regular to work with identical beads and it just wasn’t possible to get it to be symmetric. Well, not all experiments work! I’ll definitely be making some of the smaller ones again though!

 

Beaded machines, Beadwork, Tutorials

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.

Continue reading

Beadwork, Tutorials

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

BeadMechanics_FoldingCubePDF

Solar Cycle

BeadMechanics_SolarCycle

Spherical Harmonics

BeadMechanics_SphericalHarmonics

Trefoil Knot Kaleidocycle

BeadMechanics_TrefoilKnot

Happy Beading!