05 Apr

Boxtahedral Trusses

Ok, all of the ingredients were in place to plan a large-scale construction for the Golden Gate STEM Fair: cubical units that can attach at edges and the theory linking them to the oct-tet lattice. I just needed to put it all together into a plan for something interesting and substantial that could be built… [Read more]

05 Apr

An Oct-Tet of Cubes

In the last MathStream post, we concluded that if you took spheres with holes at the points indicated by black dots in the diagram below, you could connect them with struts to form a lattice composed of alternating octahedra and tetrahedra. But for building large-scale constructions, we’d like something comprised of components that are a… [Read more]

05 Apr

Cuboxtahedron

Here’s a very pleasant first construction to make with your boxtets. To link two boxtets together at a vertex, first make sure that the two vertices are snug up against each other — don’t leave any space. Then twist the two (long ends) of the twist ties together …

04 Apr

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… [Read more]

04 Apr

More Spherical Construction

The ease with which we could draw an equilateral triangle on the sphere naturally leads to wondering whether other constructions work out so nicely. For example, can we construct the square of points that would be needed to locate the holes for building a regular octahedron from styrofoam balls and sticks? Since the central angle… [Read more]

04 Apr

Ruler and Compass on a Sphere

For this project, I needed to figure out (a) where should the holes be in spheres to connect them by straight lines to form a regular tetrahedron, and (b) how to locate those points on a physical sphere. The diagram makes part (a) fairly straightforward. We can see that the angle between any two holes… [Read more]

03 Apr

Marshmallow Shapes Grown Up

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. And my immediate first thought was of the classic marshmallow shapes that you may have made in school or Girl… [Read more]