Revisiting the Rhombic Dodecahedron

Yesterday we looked at the 24-Cell, or “hyper-diamond” inspired by Matt Parker’s latest video:

Using Matt Parker’s Platonic Solid video with kids

Today I wanted to take a step back and look more carefully at the rhombic dodecahedron. It is a shape we’d studied a few times before:

A 3D Geometry proof with few words courtesy of Fawn Nguyen

Penrose Tiles and some simple 3D Variations

I’ve been sick for the last couple of days and way overslept this morning, so the project was a bit more rushed than I would have liked, but here’s what we did:

First, we looked at our old 3d printed rhombic dodecahedrons and I asked the kids what they remembered about them. They did remember that you could used them to tile space, but it took them a while to find the right configuration:

Next we looked at some Zometool models that we built last night. These models help us answer the question about the volume of the rhombic dodecahedron (or at least the volume in relation to the cube).

So, despite me being sick, this was a nice little project before the kids headed off to school. I love how both the Zometool set and the 3D printer open up the world of 3D geometry to kids.