Next I needed to cut the plastic cases into 1cm strips, to do this I marked the top(s) and the bottom(s) of the cases and scored lines with a hobby knife.
At first I thought it would be quite easy to cut through the plastic cases with a hot knife, but it proved to be quite a lengthy process so I resulted in using a modelling jigsaw which turned out to be much quicker. After this I ended up with 60 1cm strips.
Before I started the welding process I aligned three pieces onto the template to form a triangle. Next I slid the tip of the soldering iron set at 300°C over all of the joints from both sides. To strengthen the joints I melted the filament into the grooves made by the soldering iron.
In order to add some color to the lamp shade I placed the transparent plastic film from the cases over the triangle and ran the hot knife along the edges whilst pressing down with a card. I needed to to this for 18 out of 20 triangles, however I only had enough transparent plastic film for 12 triangles so for the remaining 6 I used a transparent bag.
Next I used sharpies in different colors to stain the triangles.
For the top of the lamp shade I cut out a circle from the back side of a case and cut it furthermore to fit into the triangle, not forgetting about the hole for the lamp fitting. Next I welded the two pieces together adding filament as I went.
In order to achieve the 138.19° angle of the icosahedron I stuck the template to the desk and added a piece of wood positioned so that when two triangles meet they would have the correct angle.