Calculating the volume of our rhombic dodecahedron

Yesterday we did a fun project involving a rhombic dodecahedron:

A project for kids inspired by Nassim Taleb and Alexander Bogomolny

At the end of that project we were looking carefully at how you would find the volume of a rhombic dodecahedron in general. Today I wanted to move from the general case to the specific and see if we could calculate the volume of our shapes. This tasked proved to be much more difficult for the boys than I imagined it would be. Definitely a learning experience for me.

Here’s how we got going. Even at the end of the 5 min here the boys are struggling to see how to get started.

So, after the struggle in the first video, we tried to back up and ask a more general question -> how do we find the volume of a cube?

Now we grabbed a ruler and measured the side length of the cube. This task also had a few tricky parts -> do we include the zome balls, for example. But now we were making progress!

Finally we turned to finding the volume of one our our 3d printed rhombic dodecahedrons. We did some measuring and found how many of these shapes it would take to fill our zome shape and how many it would take to fill a 1 meter cube.

So, a harder project than I expected, but still fun. We’ve done so much abstract work over the years and that makes the concrete work a little more difficult (or unusual), I suppose. I’m happy for this struggle, though, since it showed me that we need to do a few more projects like this one.