Can you believe that a dodecahedron folds into a cube

Last week I saw an incredible post by Simon Gregg:

In Gregg’s post there is an amazing GIF of a dodecahedron unfolding into a cube:

dodecahedron fold

which Gregg found on this other amazing blog post:

The Golden Section, The Golden Triangle, The Regular Pentagon and the Pentagram, The Dodecahedron

After seeing the post I guessed that there would be a way to make the shape from our Zometool set and gave it a shot on Tuesday while the kids were out for the evening:

Playing around with a neat post from Simon Gregg

Today I went through the same exercise with the boys. It took about an hour – because it isn’t obvious, especially for kids, how to make the shapes – but it was so much fun. The project has a great balance between “there’s no way to do this” and “there must be because I just saw it”. Definitely one of the most interesting Zome projects we’ve ever done.

The boys did all of the work on their own. My only suggestion to them was to build the original dodecahedron out of medium blue zome struts. This choice minimizes the number of Zome balls you need later in the project which also minimizes confusing about the shape.

We started by looking at the original gif:

 

After that the boys decided to build a dodecahedron and along the way the thought that putting a cube on the inside would help:

 

The shape in the previous video gave them an idea of how the dodecahedron would unfold into a cube. It took probably 20 minutes for them to build the shape representing the folded up doedcahedron. Their approach was to build the cube first and they try to construct the parts on the inside. Understanding all of the rotations and how the various pieces fit together is fairly challenging.

 

One bit of this shape that the boys found interesting was the shape on the inside, so I had them build that shape next. This part of the build probably took about 15 minutes – even holding the shape in the cube right in front of you, this shape is not super easy to understand:

 

Finally, I had them connect up the Zome balls inside of the shape to form an icosahedron. It was pretty surprising to me to find this icosahedron hiding inside of this “8 pointed star.” They built that shape and we wrapped up the project:

 

So, I think this is a fantastic project for kids. The approach that Simon Gregg took with paper is incredible, and if you have a Zometool set you can create the various shapes pretty quickly. I’m still amazed that an dodecahedron can fold up into a cube! Platonic solids are amazing 🙂

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