I saw an interesting tweet from Alex Kontorovich earlier this week:

Our "Crystallographic Sphere Packings" paper (with Nakamura) appeared in @PNASNews last week https://t.co/qDFN3kAroC Here's a geometrized Cuboctahedron and its dual, the Rhombic Dodecahedron, as well as their stereographically projected clusters. (Basically high school math…) pic.twitter.com/MflpHrseiF

We’ve looked at but the Cuboctahedron and the Rhombic dodecahedron before, but I thought it would be fun to revisit the shapes. I also hoped that we’d be able to recreate the shape in the picture with our Zometool set.

So, first we built a cuboctahedron and the boys talked about what they saw in the shape:

At the end of the last video the boys thought that the dual of the cuboctahedron would possibly also be another cuboctahedron. Off camera we built the dual, and happily were able to recreate the shape from Kontorovich’s shape!

They were a little worried that we didn’t have the “true” dual, but I think they came around to believing that these two shapes were indeed duals:

Definitely a fun project – it is always fun to see what you can make with a Zometool set. Maybe tomorrow we’ll revisit an old project of finding the volume of a rhombic dodecahedron. That’s another project which Zometool really brings a lot to the table.