Revisiting folding a dodecahedron into a cube

Saw this great twitter thread from Vincent Pantaloni a few weeks ago:

It made me want to revisit an old project exploring how a dodecahedron can fold into a cube:

Can you believe that a dodecahedron folds into a cube?

I started by asking the boys to each make a dodecahedron with a cube inside using our Zometool set:

Next I asked them to turn one of their shapes inside out. They did that off camera and we compared the two structures:

Finally, they connected the zome balls that were inside of the “inside out” dodecahedron and found that those balls did indeed form an icosahedron. That’s one of the great surprises in this neat shape!

For me, this project illustrates the fun you can have exploring 3d geometry with a Zometool set. Even though I’ve seen the folding dodecahedron many times now, it never gets old!