Tiling the Sphere with Regular Polygons
Combinatorics
2025-12-08 v1 Metric Geometry
Rings and Algebras
Abstract
We give a complete classification of edge-to-edge tilings of the sphere by regular polygons under a unified framework. Without assuming convexity of the tiles or polyhedrality of the underlying graph, our proof is independent of the Johnson-Zalgaller classification of solids with regular faces (1967), which took over 200 pages. We apply a blend of trigonometric, algebraic and combinatorial tools of independent interest.
Keywords
Cite
@article{arxiv.2512.05577,
title = {Tiling the Sphere with Regular Polygons},
author = {Hoi Ping Luk and Roman Nedela and Christopher Purcell},
journal= {arXiv preprint arXiv:2512.05577},
year = {2025}
}
Comments
44 pages, 21 figures, 5 tables