Euler-Poincaré-Characteristic of Polyhedra
Haskell, 49 46 bytes



u=length
f x|j&lt;-x&gt;&gt;=id=maximum j+u x-u j`div`2


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I get the number of vertices by concating the faces and finding the maximum.  I find the number of faces by taking the length.  I find the number of edges by summing the lengths of the faces and dividing by 2.