English

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}
}
R2 v1 2026-06-22T17:13:18.203Z