Landscapes of the Octahedron
Combinatorics
2024-06-03 v1 Metric Geometry
Abstract
The landscapes of a polyhedron are subsets of its nets one must consider to identify all shortest paths. Landscapes of cubes and tetrahedra have been used to identify coordinate based formulas for the lengths of the shortest paths between points on these surfaces. We extend these results to develop formulas for the lengths of the shortest paths between points on the surface of octahedra.
Keywords
Cite
@article{arxiv.2405.20344,
title = {Landscapes of the Octahedron},
author = {Emiko Saso and Houston Schuerger and Xin Shi},
journal= {arXiv preprint arXiv:2405.20344},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2201.04253