Delaunay on surface

hello to everyone! I want to thank you in advance for your help!
I'm in crisis! are only a few days by an examination at university and I can not complete my work because I can not find a solution (I entered the world of grasshopper a few weeks)

I would like to create this ( http://improved.ro/blog/?p=374 ) from a surface such as a sphere or a cylinder, can you help me? the same process but not start from point but start from surface. how can i do?

I would also like to create a file for laser cutting and create a model in paper and then create all the individual faces with the tabs and then paste themwhat you see in the picture ( https://www.youtube.com/watch?v=FhGG3ra2oiI ) in this last video he make a paper model from a file that he make in grasshopper

Thanks to all for your help!