2019/02/02 by Jensen, Alathea
#05C69 #06D50 #52B05 #52B12 #52B15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.00784
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.