Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals
Combinatorics
2022-08-05 v3 Metric Geometry
Number Theory
Abstract
We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete classification by Cheung, Luk and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for the tilings.
Keywords
Cite
@article{arxiv.2204.02748,
title = {Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals},
author = {Ho Man Cheung and Hoi Ping Luk},
journal= {arXiv preprint arXiv:2204.02748},
year = {2022}
}
Comments
79 pages, 41 figures, 16 tables, 2 algorithms. Spherical Geometry