Spherical Tiling by 12 Congruent Pentagons
Combinatorics
2013-01-07 v5 Differential Geometry
Abstract
The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is known about the tilings by other congruent polygons. In this paper, we classify the simplest case, which is the edge-to-edge tilings of the 2-dimensional sphere by 12 congruent pentagons. We find one major class allowing two independent continuous parameters and four classes of isolated examples. The classification is done by first separately classifying the combinatorial, edge length, and angle aspects, and then combining the respective classifications together.
Cite
@article{arxiv.1009.2361,
title = {Spherical Tiling by 12 Congruent Pentagons},
author = {Honghao Gao and Nan Shi and Min Yan},
journal= {arXiv preprint arXiv:1009.2361},
year = {2013}
}
Comments
53 pages, 40 figures, spherical geometry