Side-to-side Tiling of the Sphere by Congruent Curvilinear Triangles
Combinatorics
2026-01-14 v1 Metric Geometry
Abstract
The edge-to-edge tilings of the sphere by congruent polygons, where all edges are straight, have been completely classified. We classify the curvilinear version of the similar triangular tilings, where the edges may not be straight, and find that these are the modifications of the straight triangular tilings.
Cite
@article{arxiv.2601.08250,
title = {Side-to-side Tiling of the Sphere by Congruent Curvilinear Triangles},
author = {Keyi Jin and Linming Lu and Erxiao Wang and Lijuan Wu and Min Yan},
journal= {arXiv preprint arXiv:2601.08250},
year = {2026}
}
Comments
33 pages, 39 figures