English

Volume of convex polytopes equals mixed volume of simplices

Metric Geometry 2021-08-31 v1 Algebraic Geometry Combinatorics

Abstract

This note provides a simple proof for the equality between the normalized volume of a convex polytope with mm vertices and the mixed volume of mm simplices and thus shows the seemingly restrictive problem of computing mixed volume of simplices is still at least as hard as computing volumes of convex polytopes.

Keywords

Cite

@article{arxiv.2108.12875,
  title  = {Volume of convex polytopes equals mixed volume of simplices},
  author = {Tianran Chen},
  journal= {arXiv preprint arXiv:2108.12875},
  year   = {2021}
}