Classification of tilings of the 2-dimensional sphere by congruent triangles
Ueno, Yukako ; Agaoka, Yoshio
Hiroshima Math. J., Tome 32 (2002) no. 3, p. 463-540 / Harvested from Project Euclid
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.
Publié le : 2002-11-14
Classification:  52C20,  05B45,  51M20
@article{1151007492,
     author = {Ueno, Yukako and Agaoka, Yoshio},
     title = {Classification of tilings of the 2-dimensional sphere by congruent triangles},
     journal = {Hiroshima Math. J.},
     volume = {32},
     number = {3},
     year = {2002},
     pages = { 463-540},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1151007492}
}
Ueno, Yukako; Agaoka, Yoshio. Classification of tilings of the 2-dimensional sphere by congruent triangles. Hiroshima Math. J., Tome 32 (2002) no. 3, pp.  463-540. http://gdmltest.u-ga.fr/item/1151007492/