Abstract
We give a new classification of tilings of the 2-dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies’ obscure points, give a complete list, and show that there exist ten sporadic and also ten series of such tilings, including some unfamiliar twisted ones. We also give their figures, development maps in a way easy to understand their mutual relations. In Appendix, we give curious examples of tilings on noncompact spaces of constant positive curvature with boundary possessing a special 5- valent vertex that never appear in the tiling of the usual sphere.
Citation
Yoshio Agaoka. Yukako Ueno. "Classification of tilings of the 2-dimensional sphere by congruent triangles." Hiroshima Math. J. 32 (3) 463 - 540, November 2002. https://doi.org/10.32917/hmj/1151007492
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