I decided for Mothers' Day I would make a paper truncated icosahedron out of the Moroccan tile design I'd recreated. Or, to put it another way, wrap a zig-zag of 90-degree bends around a soccer ball.
I fired up Inkscape and put together a unit based on four stars, thinking that I could rotate them 90 degrees and then stick them together; but this resulted in extra (I think) overlaps, and then I made a gluing mistake and wound up with a pile of junk.
What I didn't realize at the time was that I was catching something which not only was fatiguing, but which made me kind of stupid. I probably could have made a four-fold unit work, but not without being very careful. I wasn't too far gone, though, and I figured out that what I really wanted was three-fold symmetry.
A few days of mostly sleeping later... I set out the star units. From my earlier mistakes, I knew that I wanted to have a design where six-pointed stars (flat) would surround five-pointed stars (curved), that no five-pointed star could touch another five-pointed one, that a six-pointed star would be surrounded by a ring of alternating five- and six-pointed stars. This was more difficult to keep straight than I anticipated, and I was glad that I had a left over unit to help me see the symmetry more easily.
Luckily, over the last year I've glued together enough hexagonal and triangular designs to know that it's easy to make most Platonic and Archimedian solids out of them. So I knew what I wanted was possible.
The first thing I did was lay out four units and then look at them very carefully to make sure I wasn't doing something stupid. The trick here is to only glue wholly overlapping stars, and not to glue the slightly overlapping bits, which would force the design to stay flat. Gluing whole stars flat this way allows for cleaner gluing.
Next I glued parts so that they would over-lap and made five-pointed stars (you can see the white glue dots). I put just a dot on the cells I wanted to glue; if I put too much glue on, the paper got a little mushy.
When gluing a six-pointed star over another one, I would grasp opposite crossing spokes (where they made an X) to align the star, then work around the star to get a good coverage. I think if I went more slowly, the stars would stay in alignment more than they did; in this case, there was a tendency for the stars to slide around a little. (I wanted to finish while I still had the design in my muddled head.)
From this point, I worked along the edge of the halves. Near the end, I used the eraser end of a pencil to poke through the design and pressed the eraser against the paper for a flat join.
The next time I do this, I think I'll work a little more slowly and work up from one half instead of gluing two halves together. Which requires completely recovering from this stupid cold thing.