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{\bf Catarina P. Avelino and Altino F. Santos }
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{\bf Spherical F-Tilings by Triangles and $r$-Sided Regular Polygons, $r \ge 5$}
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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
[{\it Beitr\"{a}ge zur Algebra und Geometrie}, {\bf 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, presen\-ting 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.

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