Maybe this will help you: Regular Polyhedra
I have proved Euler's Characteristic in my discrete lecture last semester in my discrete class simply by induction on F, but this was only for planar graphs, how do you extend this to 3D shapes? Do we have that each 3D shape can be flattened into a planar graph? sorry if this is a stupid question but I'm kind of lost,
Thanks for any help
Maybe this will help you: Regular Polyhedra