# Warped polyhedra

So I’ve finally finished the pair of beaded shapes I was working on over the last few months! Here they are – a rhombic hexecontahedron and what is probably best described as a hyperbolic dodecahedron:

So around the start of July I was reading about various polyhedra and I came across a rhombic hexecontahedron (the shape on the right) and realised that I could make one out of warped squares. I then realised that I could do a similar shape using warped hexagons and end up with the shape on the left. This isn’t really a polyhedron as the faces aren’t flat, but it’s similar to a hyperbolic dodecahedron shape, which is also known as spikey, the Mathematica logo (while a hexecontahedron is currently the Wolfram Alpha logo). I used Mathematica a lot when I worked in research, and spikey was one of the first ‘mathematical art’ polyhedra I encountered!

It seems that July was a month for making shapes out of warped squares though! While I was making this I saw Joy Davidson’s 3-star beaded box on facebook, and later saw Kat Oliva’s lovely patchwork rhombic hexecontahedron as well. I also ran across a photo of one on pinterest shortly after I finished it, which turned out to be a pattern by June Huber (Juniper Creek Designs). So it seems that I have just reinvented the wheel on this one!

I really like the hyperbolic dodecahedron, although it was at times challenging to make. I managed to make the tension a little too tight on some of the points and there were a couple of broken beads that had to be fixed by removing a section and repairing it, but I finially managed to finish it last week. I was also worried that it would be very difficult to stitch the last few pieces together, but it turned out to be much easier than I thought it would be (curved beading needles are an awesome invention!).

## 23 thoughts on “Warped polyhedra”

1. Judie marshall says:

Wow! Love it

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2. Roheng Chen says:

I tried to make a spikey. Would you please share with me how many warped hexagons I need to make.
And how to connect them together. I tried as least six times with different ways but still could not make one like yours. I love your design. Looking forward to your reply.

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1. Sheila Churchill says:

Iwould love a copy of your tutorial

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3. Roheng Chen says:

Can’T wait to view it.
My next project will be your Kaleidocycle in oval shape.
Thanks a lot.

Take care

Zoe

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1. I finally finished the tutorial – it’s up on Etsy, there’s a link in my comment below!

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4. suzanne golden says:

I also tried making one of these shapes but not quite sure if I’m doing it correctly…..Would love to be notified if you do a tutorial. I am fascinated with these shapes…d

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1. I’m halfway through writing the tutorial at the moment – hoping to have it done by next month!

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1. Well it took a little bit longer than I thought but it’s now finished and up on Etsy!

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5. I just purchased your tutorial and will give it a shot. My only comment is actually photography could have been a little brighter…or lighter colored beads used.. It’s a little hard to see the beads clearly because of the dark colors used. But thanks for the instructions…Hoping I can follow…

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1. Oh no – I’m so sorry about the photography! Is it on screen or printed that it’s hard to see? (Or both?) Let me know how you get on – if anything is unclear just ask and I will try and help! If the photos are really impossible I will try and reshoot them with different coloured beads (I think I may have just learnt here why people rarely use dark blue beads in tutorials… sorry I am still new to all this!)

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1. There’s always a first time and learning curve…..I’m must happy that you took the time to make a tutorial. I’m in the middle of a bead project making a geometric shape that is different from your….I’m making 4 sided pyramids, 12 pyramids in all…Octahedron??

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2. I can’t immediately think what shape that will be – intriguing! I don’t think an octahedron – aren’t they 8 triangular sides? Some kind of truncated cube maybe? Can’t wait to see! Just saw your most recent tetrahedra on facebook – wonderful!

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3. Suzanne Golden says:

I am not good with Geometric names and Dianne Fitzgerald pointed out that the pieces I posted in Facebook aren’t really Tetrahedrons?? She’s researching the shape..I personally don’t care what they’re called!! Thank you for the compliments.. if you are familiar with geometric shapes (and you are), might you be interested in responding to her post about what is the correct name of the shapes?

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4. I’ll have a look – I am hopeless at remembering the names but I think they are stellar octangular? Which is a shape that is just two tetrahedrons merged together – so still tetrahedrons! 🙂

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5. Could I quote you??? I barely got thru Geometry in school and totally lost at all the names…

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6. Sure – although I’ve just realised it’s spelled ‘stella octangula’ without the extra r’s (and also I think sometimes called a stellated octahedron?) – I replied to the post but someone else beat me to it! I have a cheat sheet – a page with pictures of all the more common polyhedra and their names on it!

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