in which I ‘fold’ cubes with others

A while back I posted some dice ‘folding’ I did that was inspired by Eric Aberg. While I was working on it, the thought crossed my brain that it would be extra fun to do this with teachers at PCMI. I figured I could probably get a small group together some evening and have some fun.

picture of the group that showed up to fold cubes.

See? Just a small group for an evening of math art shenanigans. If you look closely you can spot @crstn85, @zaduma, and @matienda.

Thanks to Mary, I looked into wooden cubes instead of casino dice. Aesthetically I still prefer the dice, but since the cubes are significantly cheaper in wooden form I ordered 1000+ blocks from WoodWorks Ltd for the 42 people that signed up after I showed a model of what they would be making. Apparently a math teacher conference is the place to find individuals interested in this type of nerdery.

I spent some time pondering how best to explain creating the 24-cube piece before deciding on making some sketches in penultimate and projecting them. I’m rather pleased with how they turned out. [You can download the visual instructions here: PCMI Ghostcubes Instructions]











The evening was a ton of fun and everyone walked away with a working model. The tape we used that night was thin white duct tape and I recommend using pieces that are almost as wide as the cube in order to cut down on the twisting that happens with the model. Here are some photos I snapped of people working:

a table working on assembling

assembling the ghostcubes


I’ll add some more once I get ahold of some other people’s photos.

And, like any teacher, I am extra proud of the group of participants that went and bought their own materials and turned the toy into something lovely. One participant made this for her daughter, Madi:

ghostcube made from children's letter blocks

It’s great fun to make and takes about an hour. Please feel free to send me a note if you have any questions or need any clarification.

The last thing I want to note is how this happened and how it shows the benefit of sharing what you are working on and thinking about. Erik Aberg sees some neat folding cubes and looks up some stuff on the internet then starts to experiment with his own materials. He’s a circus guy by training, so his uses of the cubes are mostly aesthetic and practical and thinking about how he can manipulate them or use them with juggling equipment. Erik posts on YouTube his own neat video that ends up going across my desk and entrancing me because

venn diagram of math and art with me at the intersection

I order his other videos, including a talk he did in late 2013 showing how he started with dice models and the connections to the German mathematician Heinz Strobl. This inspires me to order some casino dice off Ebay and make my own and think that it might be a fun thing at PCMI to share. Now 40 teachers at PCMI know how to make the models and several have already bought supplies and made more with plans to share with students and kids.

So thanks to everyone out there who shares their practice and their art. Sometimes the reach is further than you think.


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