A note concerning frames and geometric inequalities

2025/09/06 by Jeff Ledford, Ledford, Jeff, Kevin Rivera-Ayala +2
Engineering · #41A99 #52B10 #52B11 #52B60 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2509.05611

openalex publication_date 2025/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in ℝ^d and polytopes with d+2 vertices in dimension 2 and 3.

Citations

• Optimal Measures for Multivariate Geometric Potentials
• Optimal Parseval frames: Total coherence and total volume
• Harmonic equiangular tight frames comprised of regular simplices
• Tables of the existence of equiangular tight frames
• Some observations on the simplex

Related

• More Colourful Simplices
• Simplex inequalities of order and chain polytopes of recursively defined posets
• A Lost Counterexample and a Problem on Illuminated Polytopes
• Three-dimensional polyhedra can be described by three polynomial inequalities
• Combinatorially rigid simple polytopes with d+3 facets