A Short Proof of Euler--Poincar\'e Formula
Metric Geometry
2021-09-10 v3 Combinatorics
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-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.
Keywords
Cite
@article{arxiv.1612.01271,
title = {A Short Proof of Euler--Poincar\'e Formula},
author = {Petr Hliněný},
journal= {arXiv preprint arXiv:1612.01271},
year = {2021}
}