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{\bf A. M. d'Azevedo Breda, Patr\'{\i}cia S. Ribeiro and Altino F. Santos}
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{\bf Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II}
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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 $\delta$.

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