A Short Proof of Euler--Poincar\'e Formula
  "V - E + F = 2", the famous Euler's polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as the Euler-Poincar\'e Formula. We provide another short inductive proof of the general formula. Our proof is self-contained and it does not use shellability of polytopes. 
Petr Hlin\v{e}n\'y
math.MG math.CO