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}
}