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Volume of convex polytopes equals mixed volume of simplices

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Abstract

qaaa We provide a simple proof for the equality between the normalized volume of a convex polytope with m vertices and the mixed volume of m simplices and thus show the seemingly restrictive problem of computing the mixed volume of simplices is still at least as hard as computing volumes of convex polytopes in general.

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Acknowledgements

The author thanks Frank Sottile, Ivan Soprunov, and the anonymous referees for their insightful comments.

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  1. Department of Mathematics, Auburn University at Montgomery, Montgomery, AL, USA

    Tianran Chen

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  1. Tianran Chen
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Correspondence to Tianran Chen.

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The author’s research is supported, in part, by National Science Foundation under grant DMS-1923099 and Auburn University at Montgomery Grant-In-Aid program.

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Chen, T. Volume of convex polytopes equals mixed volume of simplices. Arch. Math. 120, 431–436 (2023). https://doi.org/10.1007/s00013-023-01836-3

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  • DOI: https://doi.org/10.1007/s00013-023-01836-3

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