Landscapes of the Octahedron
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910464679608320 |
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| author | Saso, Emiko Schuerger, Houston Shi, Xin |
| author_facet | Saso, Emiko Schuerger, Houston Shi, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Landscapes of the Octahedron Saso, Emiko Schuerger, Houston Shi, Xin Combinatorics Metric Geometry 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. |
| title | Landscapes of the Octahedron |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2405.20344 |