In here, George Hart gives some exciting examples on how to create polyhedra by cutting playing cards and sliding them inside one another.
I was wondering if such an approach can be generalized to other polyhedra (a quick search found some other polyhedra, but I am more interested in a method).
My idea is as follows: obviously what we want to do is take every edge of the polyhedron and extend it to a rectangle (whose size is the size of the playing card). The first question that comes into mind is how to do that, as there are infinitely many planes that pass through a single line. I thought that for "nice" polyhedra (i.e. one circumscribed in a sphere), a good selection would be a plane orthogonal to the line connecting the center of the polyhedron and the middle of the edge.
Then I would have to calculate the intersection line between any two adjacent planes; is there an easy way to do that? What other questions come to mind?