English

Tilings of the Sphere by Congruent Pentagons IV: Edge Combination $a^4b$

Combinatorics 2024-02-09 v3 Metric Geometry

Abstract

We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edge-to-edge tilings of the sphere by congruent equilateral pentagons of other types, and our classification of edge-to-edge tilings of the sphere by congruent quadrilaterals or triangles, we complete the classification of edge-to-edge tilings of the sphere by congruent polygons.

Keywords

Cite

@article{arxiv.2307.11453,
  title  = {Tilings of the Sphere by Congruent Pentagons IV: Edge Combination $a^4b$},
  author = {Hoi Ping Luk and Min Yan},
  journal= {arXiv preprint arXiv:2307.11453},
  year   = {2024}
}

Comments

174 pages, 74 figures. update on the notations and constructions for tilings