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.
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