The Farthest Point Map on the Regular Octahedron
Metric Geometry
2021-03-03 v4
Abstract
On any compact space one can consider the map which sends a point to the set of points farthest from this point. In nice cases, there is just a single point farthest from a given point and so by restricting the domain slightly one can form a dynamical system on the space based on this map. We give a complete characterization of this map, including explicit formulas, when the metric space is the regular octahedron equipped with its intrinsic flat cone metric.
Cite
@article{arxiv.2004.11852,
title = {The Farthest Point Map on the Regular Octahedron},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:2004.11852},
year = {2021}
}
Comments
This version of the paper is being published, as is, in the Journal of Experimental math. It is very similar to the previous version, except that I corrected some typos and mildly simplied the argument in Chapter 3