A post from Simon Gregg showing a dodecahedron folding up into a cube

Saw this cool. Tweet from Simon Gregg today:

Which has this incredible image:

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

I couldn’t stop thinking about the dodecahedron folding up into a cube. We’ve done several similar projects:

A Rhombic dodecahedron folding up into a cube

Cubes in a dodecahedron

5 tetrahedrons in a dodecahedron

But I never knew that a dodecahedron could fold up into a cube – why did nobody tell me this! I figured it would be possible to do it with our Zometool set, so I gave it a shot while the kids were out tonight. I’m definitely going to have the kids try it out this weekend.

Here’s a dodecahedron that shows one of the inscribed cubes. This shape is made with medium blue Zome struts as the edges of the dodecahedron and long blue struts as the edges of the cube:

Once you see the shape above made out of Zome pieces, you can see how it might fold up, so I made the 6 individual pieces of the dodecahedron that were outside of the faces of the cube:

Next I put them together! Here’s what a dodecahedron folded up into a cube looks like:

And here’s what the inside shape looks like, the “pyritohedral dodecahedron” from Gregg’s blog post:

Looking at the inside shape spinning around, I wondered what it would look like if you connected up the Zome balls on the inside. It turns out that those balls connect up to form an icosahedron made out of short blue struts!!

What an amazing thing to learn on twitter today! Can’t wait to try out this project with the boys this weekend.

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