𝟫𝟢⬡ icosidodecahedron

My submission for the 2024 Bridges Mathematical Art exhibition is this behemoth. Contains 300 pieces, this thing took a year and a half of intermittent work to build, including months of design work to plan its construction. 

Trefoil Icosahedron

 

This piece is a chiral icosahedron composed of 150 strips. 

Each of the 20 triangular faces contains a pinwheel structure with 3 fins.

The outer surface is a 3-fold icosahedron, and the inner surface is 2-fold.

Despite its solid appearance, the geometry is entirely surface - no enclosed volumes.

This structure is extremely rigid, which makes the origami exceptionally strong. 

It's a very satisfying design, with each face reminiscent of a Celtic knot. 

Dura-Lar is the best origami material in existence

Well, it has been a long time (3 years!) since I updated this blog. I haven't been neglecting my folding - far from it - I've just been updating my instagram (@foldedcrystals), and completely neglecting poor Blogger. IG is fine and all, though I do miss the ability to tell stories in a blog post. For me, the biggest story of the past few years has been the discovery of Dura-Lar polyester film, thanks to a recommendation from Mike Tanis (@miketanis_ on IG).

This material is truly ideal for what I do - it's extremely durable (hence the name), holds a sharp crease, is easy to work with, and will never crack or show stress marks, even after folding, unfolding and refolding the same lines repeatedly. Since I bought my first pack I've made countless pieces, but I thought I'd resurrect the blog with my latest piece, this ball based around the icosidodecahedron, which forms the outer surface.

 The inner surface is a simple icosahedron, and 30 fins bridge the outer and inner surfaces, each part of a plane that passes through the centre of the sphere. As you can see here, these fins are distorted along their inner edge. That's not due to sloppiness - because I'm forcing equilateral triangles into a geometry they're not quite suited for (about 10% too large along the inner edge), the triangles have to buckle a bit in order to fit. However, this pre-stressing of the units makes the completed design extremely strong. Seriously, I could kick this thing around like a soccer ball and it would be unharmed.

Here's an in-progress shot that shows the inner icosahedron surface more clearly. The overall scheme of this design is a negative-space icosahedron in the centre, surrounded by 20 octahedronal tubes that span the inner surface and outer icosidodecahedron surface. It's very similar to many designs I've produced in the past, but more elegant and strong than any previous works.

I really love this design, and plan next to make another one 2X the size, which I will be adding LED lights to. The compactness and durability of this design, which I'm calling Armored Icosahedron, will translate ideally into a desk lamp.

Pictured is another design which has the identical outer surface, but looks dramatically different as it's missing the inner half of the structure. My next post will detail this piece - coming soon!

West Austin Studio Tour 2016

This year I'll be exhibiting some of my work at the Little Walnut Creek branch of the Austin public library as part of the West Austin Studio Tour. The official tour is over two weekends: May 14 - 15 & 21 - 22. However, my origami will remain on display at the Little Walnut Creek branch until the 30th of June.

Many thanks to Big Medium for including me in West 2016! I'd also like to thank Carlos Rodriguez-Brondo at Austin public library for hosting my exhibit and coordinating everything.

For some reason, they put me first in the entire catalogue! I certainly wasn't first when we were shown the proofs before the catalogue was sent to the printers.. if I recall correctly I was somewhere in the 300's. I hate writing artist bios, but if you're curious this is what the text reads: "Inspired by nature and mathematics, I created a novel form of modular origami composed of interlocking woven strips. This approach allows for absolute symmetry and high durability; the method of construction ensures that the structures will never sag or unravel, and will even support weight. My ambition is to scale up my designs to create architectural spaces, giving mathematical forms permanence."

Here is the the display case where my origami will reside for the next month. When I arrived to set up the installation, the purple peacock blanket was already in place for the previous exhibit, which was honouring Prince. I had to leave it in place, as it complimented my origami nicely.

I hope you can make it out to the Little Walnut Creek library by 30 Jun to see my display! The library is located at 835 W. Rundberg Ln., Austin TX, 78758.

Icosahedron cage

 My latest piece was begun & finished in one weekend - a scaled-up icosahedron lattice with a small dodecahedron imprisoned inside.

I been using the back side of the paper more in my recent pieces - the all-silver inner surface is a nice effect.

The little dodecahedron inside rattles loudly whenever the piece is moved. The outer icosahedron is very tightly wound, and the tension in the "beams" makes them very strong.

This is the first icosahedron lattice I've made at 1:8 scale (8 strips per square). I like the result - it has a nice heft to it. I've been thinking about designing pieces specifically to be hung outdoors; this one might work, though I'd replace the origami in the centre with something heavy, like a crystal or polished rock. I know the holographic paper is weatherproof - a small dual tetrahedron has been hanging outside my front door for over a year without any fading, cracking or unravelling.

Two more icosidodecahedron lattices: six rings & twelve stars

I've had a week off for Spring Break and have been busy folding - these two new pieces are the result!

I first made this smaller piece using a new colour scheme:  bands of solid colour around each equator. It can be thought of as six interlocking rings.

I next made a double-size version using another new scheme:  each pentagon is one solid colour.

Of course, the holograpic paper only comes in five colours; the silver comes from the back side of the sheets.

I put this larger piece together in only two days. Yesterday afternoon this was just a pile of 120 strips.

I finished the assembly while sitting in the park near my house, then biked home just as the sun was setting.

The light was perfect - I love how this shot turned out.

With these two completed, I've now made (and sold) 4 icosidodecahedron lattices. Many more to come!

Cuboctahedron cage with prism

My latest piece is another cuboctahedron lattice, executed in a different colour scheme & containing a tiny red dual tetrahedron. This thing is truly small - only 1 cm high. I don't think I can make one any smaller. It's also attached to an octagonal prism.

Unlike the last cuboctahedron lattice, which had 3 colours, this one is made with 4 colours that form interlocking hexagons, such as the purple hexagon currently facing the camera.

The line attached to the prism is routed through the origami's structure, so it's not visible in the centre of the cage.

The red dual tetrahedron can be pushed right through one of the square holes, if you can manage to line it up just right.

Light refracted through the prism is tinted pink, while reflected light is green - visible on the right half of the photo.