Geodesic complexity of a tetrahedron

Geodesic complexity of a tetrahedron

Donald M. Davis – GJM, Volume 8, Issue 2 (2023), 15-22.

The topological (resp.~geodesic) complexity of a topological (resp.~metric) space is roughly the smallest number of continuous rules required to choose paths (resp.~shortest paths) between any points of the space. We prove that the geodesic complexity of a regular tetrahedron exceeds its topological complexity by 1 or 2. The proof involves a careful analysis of shortest paths on the tetrahedron.

Categories: Issue2


Received: July 25, 2023
Accepted: October 30, 2023
Revised: November 03, 2023


Donald M. Davis
Department of Mathematics, Lehigh University,
Bethlehem, PA 18015, USA