Right triangular spherical dihedral f-tilings: the $${\left(\frac{\pi}{2},\frac{\pi}{3},\frac{\pi}{5}\right)}$$ , $${\left(\frac{\pi}{2},\frac{2\pi}{5},\frac{\pi}{5}\right)}$$ family

Abstract

In this paper we classify all the dihedral f-tilings of the sphere whose prototiles are the right triangles of angles \({\left(\frac{\pi}{2},\frac{\pi}{3},\frac{\pi}{5}\right)}\) and \({\left(\frac{\pi}{2},\frac{2\pi}{5},\frac{\pi}{5}\right)}\) . Some combinatorial aspects of the structure of each f-tiling are given.