English

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