Carol from extremecards sent me a picture of a “Riemann sphere” and suggested to make a woven sphere. Here is the result.
The exact shape of the strips was made by Anna using the Smash function in Rhino, see diagram. Because the size of the pattern is limited by the A4 sized paper an ordinary cutter or printer may manage, I had to figure out how the shape might be patched together by smaller pieces. I ended up with the pattern below.
Print/cut 4 sheets, two of each colour. Before you start weaving you must glue the 12 strips to the small circle forming the pattern on the diagram. Weaving the sphere is just like weaving a cone. Place the two pieces so that the circles line up and the strips go in opposite directions. Make sure that the colour you want on the outside shows the full circle and not the strips and glue. You must take great care to make a firm and tight weaving. Else the strips will not be long enough to form the same pattern on the other side of the sphere’s equator. There must be at least 10 paperclips in the shape at any time. When you have done all weaving glue stick the matching arms together two by two at the pole and finish covering the pole with another of the small paper circles. Weaving tight is a bit difficult. Don’t despair if you need to cover the top of the sphere with a small circle of the other colour.
This is a -.pdf file for cutting. sphere001 cut