Nesting Platonic Solids

My friend Matt Gorbet showed me this amazing platonic solid video yesterday:


My initial reaction was to wonder if we could build it out of our Zometool set. Luckily we bought some extra green and half green struts last year and were able to figure out how to build it!


My second reaction was to wonder if the icosahedron at the center was the same icosahedron that we’d seen in our “dodecahedron folding into a cube” project:

dodecahedron fold

A neat post from Simon Gregg showing that a dodecahedron can fold into a cube

Can you believe that a dodecahderon folds into a cube?

Some 3D Geometry for Pamela Rawson

The last video in the 1st project shows that there is an icosahedron hiding inside of the shape you get when you fold the dodecahdedron:

I wondered if that icosahedron was the same as the one we were seeing in the nested platonic solids. The kids weren’t sure (and neither was I!), so we built the folded shape with the same size dodecahedron at took a closer look:


The last thing we did was connect the orange balls to form the new icosahedron, and – incredibly! – it was exactly the same size as the first one!! How amazing is that – the icosahedron inside of the nested Platonic solids is exactly the same one as you get when you fold up the large dodecahedron.


As fun of a project as we’ve ever done 🙂