<%@ Page Language="C#" MasterPageFile="~/Main.master" AutoEventWireup="true" Title="Volume 13 Issue 3" %>
Spherical f-Tilings by (Equilateral and Isosceles) Triangles and Isosceles Trapezoids
Catarina P. Avelino and Altino F. Santos
Department ofMathematics, University of Trás-os-Montes and Alto Douro, Apartado 1013, Vila Real 5001-801, Portugal
{cavelino, afolgado}@utad.pt
Annals of Combinatorics 15 (4) pp.565-596 December, 2011
AMS Subject Classification: 52C20; 52B05; 20B35
Abstract:
Dihedral f-tilings by spherical parallelograms and spherical triangles were obtained in [3–5]. In this paper we extend these results presenting the study of all dihedral f-tilings of the sphere S2, whose prototiles are a spherical equilateral or isosceles triangle and a spherical isosceles trapezoid. The combinatorial structure, including the symmetry group of each tiling, is given in Table 1.
Keywords: dihedral f-tilings, combinatorial properties, spherical trigonometry

References:

1. Avelino, C.P., Santos, A.F.: Spherical f-tilings by triangles and r-sided regular polygons, r ≥ 5. Electron. J. Combin. 15(1), #R22 (2008)

2. Breda, A.M.: A class of tilings of S2. Geom. Dedicata 44(3), 241–253 (1992)

3. Breda, A.M., Santos, A.F.: Dihedral f-tilings of the sphere by rhombi and triangles. Discrete Math. Theor. Comput. Sci. 7(1), 123–141 (2005)

4. d’Azevedo Breda, A.M., Santos, A.F.: Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles. Beitr¨age Algebra Geom. 45(2), 447–461 (2004)

5. d’Azevedo Breda, A.M., Santos, A.F.: Dihedral f-tilings of the sphere by triangles and well centered quadrangles. Hiroshima Math. J. 36(2), 235–288 (2006)

6. Dawson, R.J.: Tilings of the sphere with isosceles triangles. Discrete Comput. Geom. 30(3), 467–487 (2003)

7. Dawson, R.J., Doyle, B.: Tilings of the sphere with right triangles I: the asymptotically right families. Electron. J. Combin. 13(1), #R48 (2006)

8. Dawson, R.J., Doyle, B.: Tilings of the sphere with right triangles II: the (1,3,2), (0,2,n) subfamily. Electron. J. Combin. 13(1), #R49 (2006)

9. Robertson, S.A.: Isometric folding of Riemannian manifolds. Proc. Roy. Soc. Edinburgh Sect. A 79(3-4), 275–284 (1977/78)