A Short Proof of Euler–Poincaré Formula

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Authors

HLINĚNÝ Petr

Year of publication 2021
Type Article in Proceedings
Conference Extended Abstracts EuroComb 2021. Trends in Mathematics
MU Faculty or unit

Faculty of Informatics

Citation
web http://arxiv.org/abs/1612.01271
Doi http://dx.doi.org/10.1007/978-3-030-83823-2_15
Keywords Euler–Poincaré formula; Polytopes; Discharging
Description "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 combinatorial proof of the general formula. Our proof is self-contained and it does not use shellability of polytopes.
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