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!

Amazing and wonderful; thanks so much for sharing this with the world.

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This series is amazing.

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Oh my word, these are stunning! The creation and assembly is as complicated as the pronounciation of these. Really beautiful objects!

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Thank you! đŸ™‚

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Wow!

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