Making a nice ball structure out of 1.2 mm wood: Just cut the Woodball.svg form with a laser cutter out of the wood. Stain the wood if necessary. Puzzle the structure together and fixate it with glue. Sandpaper the edges. Finished!
(The main obstacle was the design. But using a program to calculate the tenon structure and just connecting each vertices with each other with thick lines to form the inner structure made things easier than expected).