Dihedral \(f\)-tilings of the sphere by equilateral and scalene triangles. II

A. M. d'Azevedo Breda ; Patrícia S. Ribeiro ; Altino F. Santos

The electronic journal of combinatorics, Tome 15 (2008)

Résumé

The study of dihedral f-tilings of the Euclidean sphere $S^2$ by triangles and $r$-sided regular polygons was initiated in 2004 where the case $r=4$ was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and $r$-sided regular polygons, for any $r\ge 5$, was described. Later on, in [3], the classification of all f-tilings of $S^2$ whose prototiles are an equilateral triangle and an isosceles triangle is obtained. The algebraic and combinatorial description of spherical f-tilings by equilateral triangles and scalene triangles of angles $\beta$, $\gamma$ and $\delta$ $(\beta>\gamma>\delta)$ whose edge adjacency is performed by the side opposite to $\beta$ was done in [4]. In this paper we extend these results considering the edge adjacency performed by the side opposite to $\delta$.

Détail

DOI : 10.37236/815

Classification : 52C20, 52B05, 20B35