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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... (Update)
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BibTeX entry: (Update)
@misc{ ueno-classification,
author = "Yukako Ueno and Yoshio Agaoka",
title = "Classification of Tilings of the 2-Dimensional Sphere By Congruent Triangles",
url = "citeseer.ist.psu.edu/590051.html" }
Citations (may not include all citations):72 Unsolved Problems in Geometry (context) - Croft, Falconer et al. - 1991
17 Regular Complex Polytopes (context) - Coxeter - 1991
4 The Geometrical Foundation of Natural Structure: A Source Bo.. (context) - Williams - 1979
4 Packings of spherical triangles and tetrahedra (context) - Davies - 1967
4 Spherical tilings with transitivity properties (context) - Grunbaum, Shephard - 1981
4 Division of space by congruent triangles and tetrahedra (context) - Sommerville - 1922
3 Spherical Models (context) - Wenninger - 1979
2 New York (context) - Patterns - 1987
2 Spaces of Constant Curvature (context) - Vinberg, Geometry - 1993
2 Tilings of the 2-dimensional sphere by congruent right trian.. (context) - Ueno, Agaoka - 1996
1 A class of tilings (context) - Breda - 1992
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