I would like to thank Rochelle for pointing out that the procedure in the tabular form I posted before is incorrect. I have to admit that I have never used this kind of table for making C60. I think it is easy to make mistakes by just following this table literally and without thinking. If you are a little bit careful, you should be able to see the hidden rules for making the C60 just after about 10 steps.
Below is a few slides I used to teach people how to make a buckyball.
But, it is much easier to follow the simple mnemonic for making a buckyball.
If one wants to make a beaded C60 with two different colors, a single color for pentagons and two different colors alternatively for hexagons, one can use these two colors as a mnemonic for deciding whether one need to make a pentagon or hexagon in the next step. Remember that in a C60 every pentagon is surrounded by 5 hexagons and every hexagon is surrounded by 3 pentagons and 3 hexagons alternatively. Then one can start with a pentagon with a single color, then hexagons with two colors alternatively, eventually, one should get a beaded C60 correctly without using any other information.