I am training to be a high school Mathematics teacher. I have been following matthen for a while now, and I recommend any maths teachers (and anyone interested in maths) to do the same. Ideas like this are simple and so illuminating, and his many animations bring geometric concepts to life.
I made this elastic frame of an octahedron to demonstrate two of its properties. Firstly it can be stretched so that its edges can be drawn without crossings, as shown in the animation (it is planar; this is true for all convex polyhedra). Secondly the edges can be drawn without lifting the pen, and without going back on an edge (it is Eulerian or unicursal). This means I was able to create the frame with one single piece of elastic and no cuts. This wouldn’t be possible for e.g. the cube, or any other Platonic solid.