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 vertices and the mixed volume of 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.
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}
}