## Spherical F-tilings by triangles and $r$-sided regular polygons, $r \ge 5$

### Summary

Summary: The study of dihedral f-tilings of the sphere S2 by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented in [3]. Also, in [6], 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 $\geq 5$. The combinatorial structure, including the symmetry group of each tiling, is given in Table 1.

### Mathematics Subject Classification

52C20, 52B05, 20B35

### Keywords/Phrases

dihedral f-tilings, isometric foldings, spherical trigonometry