I don't know if I'm in the right place to ask this question!
I have two 3D modeling and I want verify the Euler-Poincaré Formula on them that include face,holes, vertex, etc. Anyone knows about that?
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It is not entirely clear what you are asking, but the Euler formula is V - E + F = 2 (1-g), where g is the number of holes (the genus). Perhaps you also have cavities? Then look at this San José State exposition.