2 papers
math.CO2024
Landscapes of the Octahedron
Emiko Saso, Houston Schuerger, Xin Shi
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 ba…
math.MG2022
Landscapes of the Tetrahedron and Cube: An Exploration of Shortest Paths on Polyhedra
Kenzie Fontenot, Erin Raign, August Sangalli +4
We consider the problem of determining the length of the shortest paths between points on the surfaces of tetrahedra and cubes. Our approach parallels the concept of Alexandrov's s…