A Short Proof of Euler--Poincaré Formula
arXiv:1612.01271
Abstract
"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-Poincaré Formula. We provide another short inductive proof of the general formula. Our proof is self-contained and it does not use shellability of polytopes.