04 Apr

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.

Jürgen Richter-Gebert, founder of the ix-quadrat mathematics museum in Munich, Germany, suggested I could adapt the hinges he uses for making variable-angle kaleidoscopes. These hinges work extremely well, but they require a strap that at the joint changes which side of the strap is fastened to the boxes. This could probably be done by arranging the hooks and loops of double-sided velcro straps carefully, but I was afraid that the attachment would be too complex for a large-scale construction.

In another vein, I did a small construction connecting cubes vertex-to-vertex while I was the author of Math Mondays at Make: Magazine online. That connection method, however, required working on the insides of boxes in place in the structure before closing them up, which was much too intricate to scale up.

But then I realized that with a good, tight, vertex-to-vertex attachment, you can simply connect pairs of adjacent vertices to each other to create a strong edge-to-edge connection (and you can even put cubes face to face and attach all four corners to connect them that way as well).

So, here’s the procedure for making a cube with a securely fastened twist tie protruding from each vertex, ready for twisting together however you like to make cube-based sculptures. Given how they can be used to create oct-tet truss structures, I like to call them boxtets.

Materials
(for one boxtet)
cubical cardboard box
8 heavy-duty twist ties