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arXiv · 1902.00784

Self-Polar Polytopes

Alathea Jensen
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Abstract

Self-polar polytopes are convex polytopes that are equal to an orthogonal transformation of their polar sets. These polytopes were first studied by Lovász 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.

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Alathea Jensen. 2019-02-02. Self-Polar Polytopes. https://arxiv.org/abs/1902.00784

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