English

Self-Polar Polytopes

Combinatorics 2019-02-05 v1

Abstract

Self-polar polytopes are convex polytopes that are equal to an orthogonal transformation of their polar sets. These polytopes were first studied by Lov\'{a}sz as a means of establishing the chromatic number of distance graphs on spheres, and they can also be used to construct triangle-free graphs with arbitrarily high chromatic number. We investigate the existence, construction, facial structure, and practical applications of self-polar polytopes, as well as the place of these polytopes within the broader set of self-dual polytopes.

Keywords

Cite

@article{arxiv.1902.00784,
  title  = {Self-Polar Polytopes},
  author = {Alathea Jensen},
  journal= {arXiv preprint arXiv:1902.00784},
  year   = {2019}
}
R2 v1 2026-06-23T07:30:28.114Z