Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons
Metric Geometry
2023-09-27 v4
Abstract
We develop a systematic method for computing the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method is a useful and necessary step in many tiling problems about pentagonal tilings of the sphere. As an application, we find all edge-to-edge tilings of the sphere by angle congruent pentagons, that allow free and continuous choice of two angle values.
Keywords
Cite
@article{arxiv.1308.4207,
title = {Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons},
author = {Hoi Ping Luk and Min Yan},
journal= {arXiv preprint arXiv:1308.4207},
year = {2023}
}
Comments
47 pages, 4 figures