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.

Icosahedron lattice

This piece is based around the icosahedron, with 20 triangular faces. There are 60 strips, half as many as my previous entry, the icosidodecahedron lattice.

The open structure certainly casts some interesting shadows.

I love how well these photos turned out - the sun was just minutes from setting behind my neighbour's house so I ran outside with the camera.

This design has a lot in common with a previous entry, the cuboctahedron lattice. The icosahedron has 5 edges meeting at each point, while the cuboctahedron has 4 edges at each point.

Both designs are about the same size, and actually have the same number of points - 12.

It's completely dwarfed by my previous entry, the large icosidodecahedron lattice, which used 8 times as much paper.

It fits right into one of the "cups" of the icosidodecahedron, as they have the same geometry.

This is a satisfying design to make; I will definitely be making more of these!

Icosidodecahedron lattice - double size

 This piece is identical to the previous entry, but each strip is twice as wide. It required 4 times the paper (15 sheets) and occupies 8 times the volume.

 This piece was much easier to assemble than its small predecessor. Once the sheets were folded, the strips came together over a weekend.

 The larger holes allow you to easily see the interior structure. The inner surface has 12 pentagons and 20 triangles.

This piece is about 13 cm at its widest point. The half-sized piece is about the same width as a soda can.

Icosidodecahedron lattice

This is the first execution of a new design based around the icosidodecahedron, a polyhedron composed of 12 pentagons and 20 triangles. The inner surface of the hollow origami is an icosidodecahedron, while the outer surface is a bit more complex.

Each block of solid colour can be described as 1/2 of an icosahedron, with one open triangular face facing inward. Neighbouring icosahedrons are joined along one edge.

From this angle, the triangular & pentagonal windows line up allowing you to see right through.

Each of the star surfaces lies flat, giving the spiky ball a very compact profile.

I wanted to include something to show scale; the piece is almost exactly as wide as a soda can. After completing this work, I have exactly enough holographic paper left to make another icosidodecahedron lattice twice the size. I began work on it today - check back soon to see it finished!

Cuboctahedron lattice

My most recent piece is very similar to my last piece, the Cubical lattice. In fact, each can be disassembled and rebuilt into the other using the same pieces.

Just like the Cubical lattice, this piece has 6 square faces - 2 each of green, blue & violet. The difference between them is that the square faces meet at the corners here, while they meet at the edges in the cube.

When looked at corner-on, you can see that the piece has no profile - you can see right through it. You can think of it as being made from 6 interlocking hexagonal rings.

From this perspective you can see that the shape is essentially a cube with the corners cut off.

I love to photograph these pieces at sunset! The holographic paper really needs to be seen in this light.

Cubical lattice

My latest piece is a small cube with open sides. After the complexity of the hexecontahedron I wanted to use the same techniques on a much smaller scale.

As you can see from the orthogonal view, the edges are very thin.

The corners are open triplets, and each edge is a narrow 'valley'.

This thing is very strong - when deformed like this it doesn't want to flatten, and will spring right back to a cube when released.

The strips are in the same scale as the hexecontahedron (1:16) which makes the final product quite small.

Pentagonal Hexecontahedron

An old friend contacted me months ago and asked me to design him something based on his favourite polyhedron, the Pentagonal Hexecontahedron. I'd never even heard of this shape, but I love a challenge & agreed to come up with something.

After weeks of drawing and thinking very hard, this is what I came up with. The squiggly line in the upper-right is the path that one strip takes through the shape. Below that I've drawn a single face - the numbers correspond to the path drawing and show how the strip passes through each face in order. The column in the middle shows how I've divided the full strip into its components:  the full length of 76 triangles is far too long so I divided it into 4 subunits. A = red, B = blue, C = yellow, D = green. E strips are purple, and aren't a component of the long strips.

Once the design was finished, it was time to get folding! It took me weeks to fold 20 sheets, each having 16 strips. I needed 300 strips in all (I wound up with 20 extra strips - never hurts to have backups).

Here's the first unit (of 60), front & back view. The tape was needed to hold it together during construction, but isn't present in the final model.

Three units finished.

Six units, front & back.

Nine units.

Here are 14 units - I decided to switch to a pentagonal face, rather than a triangular face as I had been doing.

20 units, and 2 pentagonal faces done.

Halfway done, with 30 units! I really like the inside view.

40 & 50 units. Getting close..

55 units - no tape is left, as it's not needed; the strips can't fly apart anymore.

Just one piece left to add!

4 months later, it's finished. By far the most complex & difficult thing I've made, but it was worth it!