A tale of two polytopes 2: The harmonic polytope
Laura Escobar
This talk, based on joint work with Federico Ardila, is about the harmonic polytope \(H_{n,n}\), which arose in Ardila, Denham, and Huh’s work on the Lagrangian geometry of matroids. We show that the harmonic polytope is a \((2n-2)\)-dimensional polytope with \((n!)^2(1+1/2+···+1/n)\) vertices and \(3n−3\) facets. Lastly, we use the Bernstein-Khovanskii-Kushnirenko Theorem to give a formula for its volume. The two parts of this tale can be followed independently.