For the first three polyhedrons I used a fastening technique were demonstrated by the following images:
I used large sheets of chipboard to cut out identical sides of each polygon and then measure the same space to be hollowed out. I used gold short fastners and chipboard as the hinges. Scoring was used to make the hinges from the very sturdy chipboard in order for it to bend easily.
The straw truncated icosahedron was made by using this template. The straws are all equal lengths, cut just below the bend of the straw for the most consistent length. It took about 200(+) straws to create the entire ball and 150 round head fasteners. I will keep the truncated icosehedron in my room~