3D Printing a Cube Frame

I’ve been having a lot of fun exploring mathematics through 3D printing.

Recently, I had the idea to 3D-print a “cube frame”, that is, the edges of a cube.  My first mathematical task was to figure out an equation whose graph was such a cube frame.

It took a little work, but I ended up with this.I exported the graph into the appropriate file format and successfully printed my cube frame!

Just as fun as the mathematical challenges of producing the graph are the engineering challenges, and mysteries, of the 3D printing process itself.  For example, notice the scaffolding that the software automatically adds in order to print the top square of the cube.

There are some interesting mathematical and structural consequences of the scaffold-building algorithm, but even more amazing was that one “face” of the cube contained no scaffolding at all.  This meant the 3D printer printed one edge of the top square into thin air!  And it succeeded!

I’m excited and inspired by 3D printing, and I’m looking forward to finding more ways to integrate into our math classrooms.