The Farthest Point Map on the Regular Octahedron

Abstract

In this paper, we give a complete description of the farthest point map, as defined on the regular octahedron with its intrinsic flat cone metric. As a consequence we show that every well-defined orbit of the map converges to the 1-skeleton of the barycentric subdivision of the triangulation.

Keywords:

• Dynamics
• octahedron
• farthest point map
• geometry

Acknowledgements

 

Additional information

Funding

Supported by N.S.F. Grant DMS-1807320.