Abstract
In this paper we define and investigate a class of polytopes which we call “vertex generated” consisting of polytopes which are the average of their 0 and n dimensional faces. We show many results regarding this class, among them: that the class contains all zonotopes, that it is dense in dimension n = 2, that any polytope can be summed with a zonotope so that the sum is in this class, and that a strong form of the celebrated “Maurey Lemma” holds for polytopes in this class. We introduce for every polytope a parameter which measures how far it is from being vertex-generated, and show that when this parameter is small, strong covering properties hold.
| Original language | English |
|---|---|
| Pages (from-to) | 1171-1192 |
| Number of pages | 22 |
| Journal | Pure and Applied Functional Analysis |
| Volume | 10 |
| Issue number | 5 |
| State | Published - 2025 |
Bibliographical note
Publisher Copyright:© Copyright 2025.
Keywords
- Brunn-Minkowski inequality
- convex bodies
- covering
- polytopes
- zonotopes