One might think that having produced prototypes of the Gengzhi Goblets, our work is just about done to produce sufficient quantity (roughly 300 of each) to serve as G4G13 giveaways. The question comes down to materials and expense. If the Gengzhi Goblets are actually to be used as measuring cups, then they need to be made from a food-safe material.

By exploring the theory, the following shapes arose as a natural G4G13 giveaway: a regular 13-gon prism, a cup with octagonal cross sections whose octagon sides scaled with height as √(1-h³), and a cup with pentagonal cross sections with sides scaling as h^3/2.

In addition to the main, planned build at the Golden Gate STEM Fair, and thanks to donations of materials from Primed Minds, there was also a do-it-yourself/take-home table at the STEM Fair. Participants produced such towers as this one:

A brief post about the importance of prepping and prototyping for a build, and a couple of things that came up in the prep for the Golden Gate STEM Fair event. First, there’s just the sheer volume of supplies for such an event. Here are lots of beads getting outfitted with twist ties, for example.

Here’s a very pleasant first construction to make with your boxtets.

As a result of the last couple of constructions, when Studio Infinity signed up to do a large-scale construction at the Golden Gate STEM Fair, I had the oct-tet lattice on my mind. And for a long time, I had wanted to exploit the connection between cubes and the oct-tet lattice. I just needed a way to connect cubes edge-to-edge.

So when I was doing the math for the styrofoam-dowel tetrahedron, I noticed that locating the holes necessary for making a regular octahedron should be easy too. Naturally, having done the theory, it’s hard to resist actually building the thing.

Recently a friend of mine was giving a (math) talk and wanted as a prop “a large tetrahedron with the vertices emphasized.” This seemed like a natural for Studio Infinity, so the assignment was accepted.