# Cubes in a Dodecahedron

A couple of weeks ago we did a fun project with our Zometool set showing how that you can put a cube inside of a dodecahedron:

A 3D Geometry Project for kids inspired by Kip Thorne

One of the neat bits of geometry associated with this project is that there are actually five different cubes that can be inscribed inside of a dodecahedron. At the time we didn’t have enough Zometool pieces to fill out the five cubes and I sort of forgot about getting to the end of the project. But, last night I was flipping through our Zome Geometry book looking for a new project and found that putting cubes inside of a dodecahedron was actually one of their projects (Chapter 11). I’ve purchased an additional Zometool set recently, too, so revisiting the old project today seemed like a great idea.

The first thing we did was build a giant dodecahedron and used it to talk about some basic counting ideas. How many faces, edges, corners, and then the challenge question – how many zome balls?

Next up was inscribing one cube inside of our giant dodecahedron. It was fun to build this large shape, though it is close to the edge in terms of stability – particularly when a kid wants to sit inside of it! The large size really helps you see the cube:

Next we made a smaller version of the dodecahedron with all five cubes inside of it. We’ll try later today to make this same shape with the larger dodecahedron (and, in fact, the write up is going to be rushed because I’m being pulled into that project right now!!), though this build was going to take a little too long for the time limit I try to keep to for these Family Math projects. This smaller version still allows you to see all five cubes pretty well:

The last thing that we did was an idea from the Zome Geometry book. If you remove the edges of the dodecahedron, the remaining shape is just the five intersecting cubes. It is really neat to hold this shape in your hand, and it is actually easier to see the cubes with the extra edges are gone.

So, a fun morning building on our old dodecahedron project. I really love all of the ideas in the Zome Geometry book and love how the Zometool sets helps us visualize these 3D geometry projects.

[post publication update]

We did finish building the larger dodecahedron with 5 cubes. Here’s a video of that structure spinning around with the corners of one of the cubes highlighted:

We tried to take the dodecahedron edges off and show just the cubes, but the structure wasn’t strong enough to support itself with those outer edges missing. It was fun trying, though!