Spherical F-Tilings by Triangles and $r$-Sided Regular Polygons, $r \ge 5

• Published in: The Electronic journal of combinatorics Vol. 15; no. 1
• Main Authors: Avelino, Catarina P., Santos, Altino F.
• Format: Journal Article
• Language: English
• Published: 04.02.2008
• ISSN: 1077-8926; 1077-8926
• DOI: 10.37236/746

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.