English

Tilings of the Sphere by Congruent Quadrilaterals or Triangles

Combinatorics 2024-02-09 v3 Metric Geometry

Abstract

We completely classify edge-to-edge tilings of the sphere by congruent quadrilaterals. As part of the classification, we also present a modern version of the classification of edge-to-edge tilings of the sphere by congruent triangles. Together with our series of papers that classifies edge-to-edge tilings of the sphere by congruent pentagons, we complete the classification of edge-to-edge tilings of the sphere by congruent polygons.

Keywords

Cite

@article{arxiv.2204.02736,
  title  = {Tilings of the Sphere by Congruent Quadrilaterals or Triangles},
  author = {Ho Man Cheung and Hoi Ping Luk and Min Yan},
  journal= {arXiv preprint arXiv:2204.02736},
  year   = {2024}
}

Comments

135 pages, 76 figures. slight update on the notations and constructions for tilings