Geodesic
Spherical F-tilings by triangles and \(r\)-sided regular polygons, \(r \geq 5\)
The electronic journal of combinatorics, Tome 15 (2008)
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The study of dihedral f-tilings of the sphere $S^2$ by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented by Breda and Santos [Beiträge zur Algebra und Geometrie, 45 (2004), 447–461]. Also, in a subsequent paper, the study of dihedral f-tilings of $S^2$ whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scalene triangles as the prototiles will lead to a wide family of f-tilings). In this paper we extend these results, presenting the study of dihedral f-tilings by spherical triangles and $r$-sided regular polygons, for any $r \ge 5$. The combinatorial structure, including the symmetry group of each tiling, is given.
DOI : 10.37236/746
Classification : 52C20, 05B45, 53C20
Mots-clés : dihedral folding tiling, f-tiling, spherical tiling, isometric foldings, Riemannian manifolds 
@article{10_37236_746,
     author = {Catarina P. Avelino and Altino F. Santos},
     title = {Spherical {F-tilings} by triangles and \(r\)-sided regular polygons, \(r \geq 5\)},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/746},
     zbl = {1177.52010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/746/}
}
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Catarina P. Avelino; Altino F. Santos. Spherical F-tilings by triangles and \(r\)-sided regular polygons, \(r \geq 5\). The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/746

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